```r
## AIC: 98.271
##
## Number of Fisher Scoring iterations: 5
```

```r
tidy(mdl.glm) %>%
  select(term, estimate) %>%
  mutate(estimate = round(estimate, 3))
```

```r
## # A tibble: 2 x 2
```

<table><thead><tr><th>term</th><th>estimate</th></tr></thead><tbody><tr><td>&lt;chr&gt;</td><td>&lt;dbl&gt;</td></tr><tr><td>1 (Intercept)</td><td>-1.61</td></tr><tr><td>2 grammaticalitygrammatical</td><td>4.61</td></tr></tbody></table>

```r
# to only get the coefficients
```

```r
mycoef2 <- tidy(mdl.glm) %>% pull(estimate)
```

### 2.6.2.2 Model's fit

```r
print tab_model (mdl.glm, file = paste0("outputs/mdl.glm.html")))
htmltools::includeHTML("outputs/mdl.glm.html")
```

The results show that for one unit increase in the response (i.e., from no to yes), the logodds of being “grammatical” is increased by 4.6051702 (the intercept shows that when the response is “no”, the logodds are -1.6094379). The actual logodds for the response “yes” to grammatical is 2.9957323

### 2.6.2.3 Logodds to Odd ratios

Logodds can be modified to talk about the odds of an event. For our model above, the odds of “grammatical” receiving a “no” response is a mere 0.2; the odds of “grammatical” to receive a “yes” is a 20; i.e., 20 times more likely

```r
exp(mycoef2[1])
```

```r
## [1] 0.2
```

```r
exp(mycoef2[1] + mycoef2[2])
```

```r
## [1] 20
```

### 2.6.2.4 LogOdds to proportions

If you want to talk about the percentage “accuracy” of our model, then we can transform our logodds into proportions. This shows that the proportion of “grammatical” receiving a “yes” response increases by 99% (or 95% based on our “true” coefficients)
```r
plogis(mycoef2[1])

## [1] 0.1666667

plogis(mycoef2[1] + mycoef2[2])

## [1] 0.952381
```

### 2.6.2.5 Plotting

```r
grammatical <- grammatical %>%
  mutate(prob = predict(mdl.glm, type = "response"))

grammatical %>%
  ggplot(aes(x = as.numeric(grammaticality), y = prob)) +
  geom_point() +
  geom.smooth(method = "glm",
    method.args = list(family = "binomial"),
    se = T) + themeBW(base_size = 20) +
  labs(y = "Probability", x = "") +
  coordCartesian(ylim = c(0,1)) +
  scale_x_discrete(limits = c("Ungrammatical", "Grammatical"))
```

<figure><img src="image_54.png" /></figure>

## 2.6.3 GLM - Numeric predictors

In this example, we will run a GLM model using a similar technique to that used in Al-Tamimi (2017) and Baumann & Winter (2018). We use the package LanguageR and the dataset English.
In the model above, we used the equation as lm(RTlexdec ~ AgeSubject). We were interested in examining the impact of age of subject on reaction time in a lexical decision task. In this section, we are interested in understanding how reaction time allows to differentiate the participants based on their age. We use AgeSubject as our outcome and RTlexdec as our predictor using the equation glm(AgeSubject ~ RTlexdec). We usually can use RTlexdec as is, but due to a possible quasi separation and the fact that we may want to compare coefficients using multiple acoustic metrics, we will z-score our predictor. We run below two models, with and without z-scoring

For the glm model, we need to specify family = "binomial".

### 2.6.3.1 Without z-scoring of predictor

```r
dml.glm2 <- english2 %>
  glm(AgeSubject ~ RTlexdec, data = ., family = "binomial")

tidy(dml.glm2) %>
  select(term, estimate) %>
  mutate(estimate = round(estimate, 3))
```

#### 2.6.3.1.1 Model estimation

```r
## # A tibble: 2 x 2
##   term          estimate
## <chr>         <dbl>
## 1 (Intercept)  -129.
## 2 RTlexdec     19.6

# to only get the coefficients
mycoef2 <- tidy(dml.glm2) %>% pull(estimate)
```

```r
print.tab_model(dml.glm2, file = paste0("outputs/dml.glm2.html")))
htmltools::includeHTML("outputs/dml.glm2.html")
```

#### 2.6.3.1.2 Model's fit

#### 2.6.3.1.3 LogOdds to proportions

If you want to talk about the percentage "accuracy" of our model, then we can transform our logodds into proportions.

```r
plogis(mycoef2[1])

## [1] 1.368844e-56
plogis(mycoef2[1] + mycoef2[2])
```
## [1] 4.678715e-48

english2 <- english2 %>%
  mutate(prob = predict(mdl.glm2, type = "response"))
english2 %>%
  ggplot(aes(x = as.numeric(AgeSubject), y = prob)) +
  geom_point() +
  geom.smooth(method = "glm",
    method.args = list(family = "binomial"),
    se = T) + themeBW(base_size = 20) +
  labs(y = "Probability", x = "") +
  coordCartesian(ylim = c(0,1)) +
  scale_x_discrete(limits = c("Young", "Old"))

<figure><img src="image_55.png" /></figure>

### 2.6.3.1.4 Plotting

The plot above shows how the two groups differ using a `glm`. The results point to an overall increase in the proportion of reaction time when moving from the "Young" to the "Old" group. Let's use z-scoring next

#### 2.6.3.2 With z-scoring of predictor

english2 <- english2 %>%
  mutate(`RTlexdec_z` = scale(RTlexdec, center = TRUE, scale = TRUE))
english2['RTlexdec_z'] <- as.data.frame(scale(english2$RTlexdec))
```r
mdl.glm3 <- english2 %>%
  glm(AgeSubject ~ RTlexdec_z, data = ., family = "binomial")

tidy(mdl.glm3) %>%
  select(term, estimate) %>%
  mutate(estimate = round(estimate, 3))
```

### 2.6.3.2.1 Model estimation

```r
## # A tibble: 2 x 2
## term          estimate
## <chr>         <dbl>
## 1 (Intercept)  0.077
## 2 RTlexdec_z   3.08

# to only get the coefficients
mycoef2 <- tidy(mdl.glm3) %>% pull(estimate)
```

```r
print.tab_model(mdl.glm3, file = paste0("outputs/mdl.glm3.html")))
htmltools::includeHTML("outputs/mdl.glm3.html")
```

### 2.6.3.2.2 Model's fit

#### 2.6.3.2.3 LogOdds to proportions

If you want to talk about the percentage "accuracy" of our model, then we can transform our logodds into proportions.

```r
plogis(mycoef2[1])

## [1] 0.5192147
plogis(mycoef2[1] + mycoef2[2])

## [1] 0.959313
```

#### 2.6.3.2.4 Plotting

```r
english2 <- english2 %>%
  mutate(prob = predict(mdl.glm3, type = "response"))

english2 %>%
  ggplot(aes(x = as.numeric(AgeSubject), y = prob)) +
  geom_point() +
  geom.smooth(method = "glm",
              method.args = list(family = "binomial"),
              scale_y = scale_x)
```
```r
se = T) + themeBW(base_size = 20) +
labs(y = "Probability", x = "") +
coordCartesian(ylim = c(0,1)) +
scale_x_discrete(limits = c("Young", "Old"))
```

<figure><img src="image_56.png" /></figure>

#### 2.6.3.2.4.1 Normal

We obtain the exact same plots, but the model estimations are different. Let's use another type of predictions

```r
z vals <- seq(-3, 3, 0.01)

dfPredNew <- data.frame(RTlexdec_z = z vals)

## store the predicted probabilities for each value of RTlexdec_z
pp <- cbind(dfPredNew, prob = predict(mdl.glm3, newdata = dfPredNew, type = "response")

pp %>%
  ggplot(aes(x = RTlexdec_z, y = prob)) +
  geom_point() +
  themeBW(base_size = 20) +
  labs(y = "Probability", x = "") +
  coordCartesian(ylim = c(-0.1, 1.1), expand = FALSE) +
  scale_y continuous(breaks = c(0,1), labels = c("Young", "Old")) +
  scale_x continuous(breaks = c(-3, -2, -1, 0, 1, 2, 3))
```
<figure><img src="image_57.png" /><figcaption>2.6.3.2.4.2 z-scores</figcaption></figure>

We obtain the exact same plots, but the model estimations are different.

### 2.6.4 Signal Detection Theory

#### 2.6.4.1 Rationale

We are generally interested in performance, i.e., whether we have “accurately” categorised the outcome or not and at the same time want to evaluate our biases in responses. When deciding on categories, we are usually biased in our selection.

Let's ask the question: How many of you have a Mac laptop and how many a Windows laptop? For those with a Mac, what was the main reason for choosing it? Are you biased in anyway by your decision?

To correct for these biases, we use some variants from Signal Detection Theory to obtain the true estimates without being influenced by the biases.

#### 2.6.4.2 Running stats

Let's do some stats on this

<table><thead><tr><th></th><th>Yes</th><th>No</th><th>Total</th></tr></thead><tbody><tr><th>Grammatical (Yes Actual)</th><td>TP = 100</td><td>FN = 5</td><td>(Yes Actual) 105</td></tr><tr><th>Ungrammatical (No Actual)</th><td>FP = 10</td><td>TN = 50</td><td>(No Actual) 60</td></tr><tr><th>Total</th><td>(Yes Response) 110</td><td>(No Response) 55</td><td>165</td></tr></tbody></table>
grammatical <- grammatical %>
mutate(response = factor(response, levels = c("yes", "no")),
        grammaticality = factor(grammaticality, levels = c("grammatical", "ungrammatical")))

### 2.6.4.3 Below we obtain multiple measures

#### 2.6.4.3.1 TP, FP, FN, TN TP = True Positive (Hit); FP = False Positive;

FN = False Negative; TN = True Negative

TP <- nrow(grammatical %>
           filter(grammaticality == "grammatical" &
                   response == "yes"))
FN <- nrow(grammatical %>
           filter(grammaticality == "grammatical" &
                   response == "no"))
FP <- nrow(grammatical %>
           filter(grammaticality == "ungrammatical" &
                   response == "yes"))
TN <- nrow(grammatical %>
           filter(grammaticality == "ungrammatical" &
                   response == "no"))

TP

## [1] 100

FN

## [1] 5

FP

## [1] 10

TN

## [1] 50

#### 2.6.4.3.2 Accuracy, Error, Sensitivity, Specificity, Precision, etc.

(TP+TN)/nrow(grammatical) # accuracy

##### 2.6.4.3.2.1 Accuracy and Error

## [1] 0.9090909

(FP+FN)/nrow(grammatical) # error, also 1-accuracy

## [1] 0.09090909
```r
# When stimulus = yes, how many times response = yes?
TP/(TP+FN) # also True Positive Rate or Specificity
```

### 2.6.4.3.2.2 Sensitivity, Specificity, Precision, etc.

```r
## [1] 0.952381
```

```r
# When stimulus = no, how many times response = yes?
FP/(FP+TN) # False Positive Rate,
```

```r
## [1] 0.1666667
```

```r
# When stimulus = no, how many times response = no?
TN/(FP+TN) # True Negative Rate or Sensitivity
```

```r
## [1] 0.8333333
```

```r
# When subject responds "yes" how many times is (s)he correct?
TP/(TP+FP) # precision
```

```r
## [1] 0.9090909
```

### 2.6.4.3.2.3 STD measures We can get various measures from Signal Detection Theory. using the package psycho.

* dprime (or the sensitivity index)

* beta (bias criterion, 0-1, lower = increase in "yes")

* Aprime (estimate of discriminability, 0-1, 1 = good discrimination; 0 at chance)

* bppd (b prime prime d, -1 to 1; 0 = no bias, negative = tendency to respond "yes", positive = tendency to respond "no")

* c (index of bias, equals to SD)

See here for more details

```r
psycho::dprime(TP, FP, FN, TN,
               n_targets = TP+FN,
               n_distractors = FP+TN,
               adjust=F)
```

```r
## $dprime
```

```r
## [1] 2.635813
```

```r
##
```

```r
## $beta
```

```r
## [1] 0.3970026
```

```r
##
```

```r
## $aprime
```
## [1] 0.9419643
##
## $bppd
## [1] -0.5076923
##
## $c
## [1] -0.3504848

The most important from above, is d-prime. This is modelling the difference between the rate of “True Positive” responses and “False Positive” responses in standard unit (or z-scores). The formula can be written as:

$$d' (\text{d prime}) = Z(\text{True Positive Rate}) - Z(\text{False Positive Rate})$$

### 2.6.4.4 GLM and d prime

The values obtained here match those obtained from SDT. For d prime, the difference stems from the use of the logit variant of the Binomial family. By using a probit variant, one obtains the same values (see here for more details). A probit variant models the z-score differences in the outcome and is evaluated in change in 1-standard unit. This is modelling the change from “ungrammatical” “no” responses into “grammatical” “yes” responses in z-scores. The same conceptual underpinnings of d-prime from Signal Detection Theory.

## d prime
psycho::dprime(TP, FP, FN, TN,
  n_targets = TP+FN,
  n_distractors = FP+TN,
  adjust=F)$dprime

## [1] 2.635813
## GLM with probit
coef(glm(response ~ grammaticality, data = grammatical, family = binomial(probit)))[2]

## grammaticalityungrammatical
## 2.635813

### 2.6.4.5 GLM as a classification tool

The code below demonstrates the links between our GLM model and what we had obtained above from SDT. The predictions' table shows that our GLM was successful at obtaining prediction that are identical to our initial data setup. Look at the table here and the table above. Once we have created our table of outcome, we can compute percent correct, the specificity, the sensitivity, the Kappa score, etc.. this yields the actual value with the SD that is related to variations in responses.
```r
## predict(mdl.glm)>0.5 is identical to
## predict(glm(response~grammaticality, data=grammatical, family = binomial), type="response")
grammatical <- grammatical %>%
  mutate(response = factor(response, levels = c("yes", "no")),
         grammaticality = factor(grammaticality, levels = c("grammatical", "ungrammatical")))
```

```r
mdl.glm.C <- grammatical %>%
  glm(response ~ grammaticality, data = ., family = binomial)
```

```r
tbl.glm <- table(grammatical$response, predict(mdl.glm.C, type = "response")>0.5)
colnames(tbl.glm) <- c("grammatical", "ungrammatical")
tbl.glm
```

```
##
##      grammatical ungrammatical
## yes      100          10
## no        5           50
```

```
PresenceAbsence::pcc(tbl.glm)
```

```
##      PCC          PCC.sd
## 1 0.9090909  0.0224484
```

```
PresenceAbsence::specificity(tbl.glm)
```

```
##      specificity specificity.sd
## 1  0.8333333  0.04851854
```

```
PresenceAbsence::sensitivity(tbl.glm)
```

```
##      sensitivity sensitivity.sd
## 1  0.952381  0.02088233
```

```
###etc..
```

If you look at the results from SDT above, these results are the same as the following

Accuracy: (TP+TN)/Total (0.9090909)

True Positive Rate (or Specificity) TP/(TP+FN) (0.952381)

True Negative Rate (or Sensitivity) TN/(FP+TN) (0.8333333)

### 2.6.4.6 GLM: Other distributions

If your data does not fit a binomial distribution, and is a multinomial (i.e., three or more response categories) or poisson (count data), then you need to use the
glm function with a specific family function.

## 2.7 Cumulative Logit Link Models

These models work perfectly with rating data. Ratings are inherently ordered, 1, 2, ... n, and expect to observe an increase (or decrease) in overall ratings from 1 to n. To demonstrate this, we will use an example using the package "ordinal".

We use two datasets. We previously ran these two models, however, in this subset of the full dataset, we did not take into account the fact that there were multiple producing speakers and items.

### 2.7.1 Ratings of percept of nasality

The first comes from a likert-scale a rating experiment where six participants rated the percept of nasality in the production of particular consonants in Arabic. The data came from nine producing subjects. The ratings were from 1 to 5, with 1 reflecting an **oral** percept; 5 a **nasal** percept.

#### 2.7.1.1 Importing and pre-processing

We start by importing the data and process it. We change the reference level in the predictor

```
rating <- read_csv("data/rating.csv")[-1]
```

```
rating
```

```
## # A tibble: 405 x 5
```

<table><thead><tr><th>##</th><th>Response</th><th>Context</th><th>Subject</th><th>Item</th><th>Rater</th></tr><tr><th>##</th><th>&lt;dbl&gt;</th><th>&lt;chr&gt;</th><th>&lt;chr&gt;</th><th>&lt;chr&gt;</th><th>&lt;chr&gt;</th></tr></thead><tbody><tr><td>## 1</td><td>2</td><td>n-3</td><td>p04</td><td>noo3-w</td><td>R01</td></tr><tr><td>## 2</td><td>4</td><td>isolation</td><td>p04</td><td>noo3-v</td><td>R01</td></tr><tr><td>## 3</td><td>2</td><td>o-3</td><td>p04</td><td>djuu3-w</td><td>R01</td></tr><tr><td>## 4</td><td>4</td><td>isolation</td><td>p04</td><td>djuu3-v</td><td>R01</td></tr><tr><td>## 5</td><td>3</td><td>n-7</td><td>p04</td><td>nuu7-w</td><td>R01</td></tr><tr><td>## 6</td><td>3</td><td>isolation</td><td>p04</td><td>nuu7-v</td><td>R01</td></tr><tr><td>## 7</td><td>1</td><td>3--3</td><td>p04</td><td>3oo3-w</td><td>R01</td></tr><tr><td>## 8</td><td>2</td><td>isolation</td><td>p04</td><td>3oo3-v</td><td>R01</td></tr><tr><td>## 9</td><td>2</td><td>o-7</td><td>p04</td><td>loo7-w</td><td>R01</td></tr><tr><td>## 10</td><td>1</td><td>o-3</td><td>p04</td><td>bii3-w</td><td>R01</td></tr></tbody></table>

```
rating <- rating %>%
```

```
mutate(Response = factor(Response),
```

```
Context = factor(Context)) %>%
```

```
mutate(Context = relevel(Context, "isolation"))
```

```
rating
```
```
## # A tibble: 405 x 5
##   Response Context   Subject Item   Rater
## <fct>  <fct>  <chr>  <chr>  <chr>
## 1  2      n-3      p04      noo3-w  R01
## 2  4      isolation p04      noo3-v  R01
## 3  2      o-3      p04      djuu3-w R01
## 4  4      isolation p04      djuu3-v R01
## 5  3      n-7      p04      nuu7-w  R01
## 6  3      isolation p04      nuu7-v  R01
## 7  1      3--3     p04      3oo3-w  R01
## 8  2      isolation p04      3oo3-v  R01
## 9  2      o-7      p04      loo7-w  R01
## 10 1     o-3      p04      bii3-w  R01
## # i 395 more rows
```

### 2.7.1.2 Our first model

We run our first clm model as a simple, i.e., with no random effects

```
mdl.clm <- rating %>%
  clm(Response ~ Context, data = .)
summary(mdl.clm)
```

```
## formula: Response ~ Context
## data: .
##
## link threshold nobs logLik AIC niter max.grad cond.H
## logit flexible 405 -526.16 1086.31 5(0) 3.61e-09 1.3e+02
##
## Coefficients:
```

<table><thead><tr><th></th><th>Estimate</th><th>Std. Error</th><th>z value</th><th>Pr(&gt;|z|)</th></tr></thead><tbody><tr><td>Context3--3</td><td>-0.1384</td><td>0.5848</td><td>-0.237</td><td>0.8130</td></tr><tr><td>Context3-n</td><td>3.5876</td><td>0.4721</td><td>7.600</td><td>2.96e-14 ***</td></tr><tr><td>Context3-o</td><td>-0.4977</td><td>0.3859</td><td>-1.290</td><td>0.1971</td></tr><tr><td>Context7-n</td><td>2.3271</td><td>0.5079</td><td>4.582</td><td>4.60e-06 ***</td></tr><tr><td>Context7-o</td><td>0.2904</td><td>0.4002</td><td>0.726</td><td>0.4680</td></tr><tr><td>Contextn-3</td><td>2.8957</td><td>0.6685</td><td>4.331</td><td>1.48e-05 ***</td></tr><tr><td>Contextn-7</td><td>2.2678</td><td>0.4978</td><td>4.556</td><td>5.22e-06 ***</td></tr><tr><td>Contextn-n</td><td>2.8697</td><td>0.4317</td><td>6.647</td><td>2.99e-11 ***</td></tr><tr><td>Contextn-o</td><td>3.5152</td><td>0.4397</td><td>7.994</td><td>1.30e-15 ***</td></tr><tr><td>Contexto-3</td><td>-0.2540</td><td>0.4017</td><td>-0.632</td><td>0.5272</td></tr><tr><td>Contexto-7</td><td>-0.6978</td><td>0.3769</td><td>-1.851</td><td>0.0641 .</td></tr><tr><td>Contexto-n</td><td>2.9640</td><td>0.4159</td><td>7.126</td><td>1.03e-12 ***</td></tr><tr><td>Contexto-o</td><td>-0.6147</td><td>0.3934</td><td>-1.562</td><td>0.1182</td></tr></tbody></table>

```
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
```
## Threshold coefficients:

<table><thead><tr><th></th><th></th><th>Estimate</th><th>Std. Error</th><th>z value</th></tr></thead><tbody><tr><td>##</td><td>1|2</td><td>-1.4615</td><td>0.2065</td><td>-7.077</td></tr><tr><td>##</td><td>2|3</td><td>0.4843</td><td>0.1824</td><td>2.655</td></tr><tr><td>##</td><td>3|4</td><td>1.5492</td><td>0.2044</td><td>7.578</td></tr><tr><td>##</td><td>4|5</td><td>3.1817</td><td>0.2632</td><td>12.089</td></tr></tbody></table>

### 2.7.1.3 Testing significance

We can evaluate whether “Context” improves the model fit, by comparing a null model with our model. Of course “Context” is improving the model fit.

```
mdl.clm.Null <- rating %>
clm(Response ~ 1, data = .)
anova(mdl.clm, mdl.clm.Null)
```

## Likelihood ratio tests of cumulative link models:

```
##
## formula:              link: threshold:
## mdl.clm.Null Response ~ 1      logit flexible
## mdl.clm Response ~ Context logit flexible
##
## no.par      AIC  logLik LR.stat df Pr(>Chisq)
## mdl.clm.Null      4  1281.1 -636.56
## mdl.clm          17 1086.3 -526.16   220.8 13 < 2.2e-16 ***
## ---
## Signif. codes: 0 '**' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
```

### 2.7.1.4 Model's fit

```
print.tab_model(mdl.clm, file = paste0("outputs/mdl.clm.html")))
htmltools::includeHTML("outputs/mdl.clm.html")
```

### 2.7.1.5 Interpreting a cumulative model

As a way to interpret the model, we can look at the coefficients and make sense of the results. A CLM model is a Logistic model with a cumulative effect. The “Coefficients” are the estimates for each level of the fixed effect; the “Threshold coefficients” are those of the response. For the former, a negative coefficient indicates a negative association with the response; and a positive is positively associated with the response. The p values are indicating the significance of each level. For the “Threshold coefficients”, we can see the cumulative effects of ratings 1|2, 2|3, 3|4 and 4|5 which indicate an overall increase in the ratings from 1 to 5.

#### 2.7.1.5.1 Plotting
### 2.7.1.5.2 No confidence intervals
We use a modified version of a plotting function that allows us to visualise the effects. For this, we use the base R plotting functions. The version below is without confidence intervals.

```r
par(oma=c(1, 0, 0, 3), mgp=c(2, 1, 0))
xlimNas = c(min(mdl.clm$beta), max(mdl.clm$beta))
ylimNas = c(0,1)
plot(0,0,xlim=xlimNas, ylim=ylimNas, type="n", ylab=expression(Probability), xlab="", xaxt="n",
axis(side = 1, at = c(0,mdl.clm$beta), labels = levels(rating$Context), las=2,cex=2,cex.lab=1.5,cex=1.5)
xsNas = seq(xlimNas[1], ylimNas[2], length.out=100)
lines(xsNas, plogis(mdl.clm$Theta[1] - xsNas), col='black')
lines(xsNas, plogis(mdl.clm$Theta[2] - xsNas)-plogis(mdl.clm$Theta[1] - xsNas), col='red')
lines(xsNas, plogis(mdl.clm$Theta[3] - xsNas)-plogis(mdl.clm$Theta[2] - xsNas), col='green')
lines(xsNas, plogis(mdl.clm$Theta[4] - xsNas)-plogis(mdl.clm$Theta[3] - xsNas), col='orange')
lines(xsNas, 1-(plogis(mdl.clm$Theta[4] - xsNas)), col='blue')
abline(v=c(0,mdl.clm$beta), lty=3)
abline(h=0, lty="dashed")
abline(h=0.2, lty="dashed")
abline(h=0.4, lty="dashed")
abline(h=0.6, lty="dashed")
abline(h=0.8, lty="dashed")
abline(h=1, lty="dashed")

legend(par('usr')[2], par('usr')[4], bty='n', xpd=NA, lty=1, col=c("black", "red", "green", "orange"),
legend=c("Oral", "2", "3", "4", "Nasal"), cex=0.75)
```

## Predicted curves – Nasalisation

<figure><img src="image_58.png" /></figure>
lines(xsNas, plogis(mdl.clm$Theta[3] - xsNas)-plogis(mdl.clm$Theta[2] - xsNas), col='green')
lines(xsNas, plogis(mdl.clm$Theta[4] - xsNas)-plogis(mdl.clm$Theta[3] - xsNas), col='orange')
lines(xsNas, 1-(plogis(mdl.clm$Theta[4] - xsNas)), col='blue')
abline(v=c(0,mdl.clm$beta),lty=3)

abline(h=0, lty="dashed")
abline(h=0.2, lty="dashed")
abline(h=0.4, lty="dashed")
abline(h=0.6, lty="dashed")
abline(h=0.8, lty="dashed")
abline(h=1, lty="dashed")

legend(par('usr')[2], par('usr')[4], bty='n', xpd=NA, lty=1, col=c("black", "red", "green", "orange"), legend=c("Oral", "2", "3", "4", "Nasal"), cex=0.75)

## Predicted curves – Nasalisation

<figure><img src="image_59.png" /></figure>

### 2.7.2 Subjective estimates of the weight of the referents of 81 English nouns.

This dataset comes from the LanguageR package. It contains the subjective estimates of the weight of the referents of 81 English nouns. This dataset is a little complex. Data comes from multiple subjects who rated 81 nouns. The nouns are from a class of animals and plants. The subjects are either males or females.
We can model it in various ways. Here we decided to explore whether the ratings
given to a particular word are different, when the class is either animal or a plant
and if males rated the nouns differently from males.

2.7.2.1 Importing and pre-processing

```
weightRatings <- weightRatings %>%
  mutate(Rating = factor(Rating),
        Sex = factor(Sex),
        Class = factor(Class))
weightRatings %>%
  head(10)
```

<table><thead><tr><th>##</th><th>Subject</th><th>Rating</th><th>Trial</th><th>Sex</th><th>Word</th><th>Frequency</th><th>Class</th></tr></thead><tbody><tr><td>## 1</td><td>A1</td><td>5</td><td>1</td><td>F</td><td>horse</td><td>7.771910</td><td>animal</td></tr><tr><td>## 2</td><td>A1</td><td>1</td><td>2</td><td>F</td><td>gherkin</td><td>2.079442</td><td>plant</td></tr><tr><td>## 3</td><td>A1</td><td>3</td><td>3</td><td>F</td><td>hedgehog</td><td>3.637586</td><td>animal</td></tr><tr><td>## 4</td><td>A1</td><td>1</td><td>4</td><td>F</td><td>bee</td><td>5.700444</td><td>animal</td></tr><tr><td>## 5</td><td>A1</td><td>1</td><td>5</td><td>F</td><td>peanut</td><td>4.595120</td><td>plant</td></tr><tr><td>## 6</td><td>A1</td><td>2</td><td>6</td><td>F</td><td>pear</td><td>4.727388</td><td>plant</td></tr><tr><td>## 7</td><td>A1</td><td>3</td><td>7</td><td>F</td><td>pineapple</td><td>3.988984</td><td>plant</td></tr><tr><td>## 8</td><td>A1</td><td>2</td><td>8</td><td>F</td><td>frog</td><td>5.129899</td><td>animal</td></tr><tr><td>## 9</td><td>A1</td><td>1</td><td>9</td><td>F</td><td>blackberry</td><td>4.060443</td><td>plant</td></tr><tr><td>## 10</td><td>A1</td><td>3</td><td>10</td><td>F</td><td>pigeon</td><td>5.262690</td><td>animal</td></tr></tbody></table>

2.7.2.2 Model specifications

2.7.2.2.1 No random effects We run our first clm model as a simple, i.e., with no random effects

```
system.time(mdl.clm2 <- weightRatings %>%
  clm(Rating ~ Class * Sex * Frequency, data = .))
```

```
## user system elapsed
## 0.05 0.02 0.04
```

```
summary(mdl.clm2)
```

```
## formula: Rating ~ Class * Sex * Frequency
## data: .
##
## link threshold nobs logLik AIC niter max.grad cond.H
## logit flexible 1620 -2387.08 4800.16 6(0) 1.71e-13 1.7e+04
##
## Coefficients:
##                 Estimate Std. Error z value Pr(>\|z\|)
## Classplant      -1.16225   0.44191  -2.630   0.00854 **
## SexM           -0.68152   0.55688   -1.224   0.22102
```
## Frequency 0.23871 0.05694 4.192 2.77e-05 ***
## Classplant:SexM 0.38258 0.82629 0.463 0.64336
## Classplant:Frequency -0.26492 0.09231 -2.870 0.00410 **
## SexM:Frequency 0.07563 0.10527 0.718 0.47251
## Classplant:SexM:Frequency -0.08114 0.17315 -0.469 0.63934
## ---
## Signif. codes: 0 '**' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Threshold coefficients:
## Estimate Std. Error z value
## 1|2 -0.8614 0.3025 -2.848
## 2|3 0.5553 0.2985 1.861
## 3|4 1.5121 0.3021 5.005
## 4|5 2.2185 0.3081 7.200
## 5|6 3.0602 0.3169 9.657
## 6|7 3.8655 0.3304 11.698

### 2.7.2.3 Testing significance

We can evaluate whether “Context” improves the model fit, by comparing a null model with our model. Of course “Context” is improving the model fit.

```
mdl.clm.Null2 <- weightRatings %>
clm(Rating ~ 1, data = .)
```

```
anova(mdl.clm2, mdl.clm.Null2)
```

#### 2.7.2.3.1 Null vs no random

## Likelihood ratio tests of cumulative link models:
##
## formula:                      link: threshold:
## mdl.clm.Null2 Rating ~ 1          logit flexible
## mdl.clm2      Rating ~ Class * Sex * Frequency logit flexible
##
## no.par      AIC  logLik LR.stat df Pr(>Chisq)
## mdl.clm.Null2      6 5430.2 -2709.1
## mdl.clm2          13 4800.2 -2387.1  644.05  7 < 2.2e-16 ***
## ---
## Signif. codes: 0 '**' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

The model comparison above shows that our full model is enough.

#### 2.7.2.4 Model's fit
```r
print tab_model (mdl .clm2, file = paste0("outputs/mdl .clm2.html")))
htmltools::includeHTML("outputs/mdl .clm2.html")
```

### 2.7.2.5 Interpreting a cumulative model

As a way to interpret the model, we can look at the coefficients and make sense of the results. A CLM model is a Logistic model with a cumulative effect. The “Coefficients” are the estimates for each level of the fixed effect; the “Threshold coefficients” are those of the response. For the former, a negative coefficient indicates a negative association with the response; and a positive is positively associated with the response. The p values are indicating the significance of each level. For the “Threshold coefficients”, we can see the cumulative effects of ratings 1|2, 2|3, 3|4 and 4|5 which indicate an overall increase in the ratings from 1 to 5.

### 2.7.2.6 Plotting

#### 2.7.2.6.1 No confidence intervals
We use a modified version of a plotting function that allows us to visualise the effects. For this, we use the base R plotting functions. The version below is without confidence intervals.

```r
par(oma = c(4, 0, 0, 3), mgp = c(2, 1, 0))
xlim = c(min(mdl.clm2$beta), max(mdl.clm2$beta))
ylim = c(0, 1)
plot(0, 0, xlim =lim, ylim = ylim, type = "n", ylab = expression(Probability), xlab = "x")
axis(side = 1, at = mdl.clm2$beta, labels = names(mdl.clm2$beta), las = 2, cex = 0.75,
       xs = seq(xlim[1], xlim[2], length.out = 100)
lines(xs, plogis(mdl.clm2$Theta[1] - xs), col = 'black')
lines(xs, plogis(mdl.clm2$Theta[2] - xs) - plogis(mdl.clm2$Theta[1] - xs), col = 'red')
lines(xs, plogis(mdl.clm2$Theta[3] - xs) - plogis(mdl.clm2$Theta[2] - xs), col = 'green')
lines(xs, plogis(mdl.clm2$Theta[4] - xs) - plogis(mdl.clm2$Theta[3] - xs), col = 'orange')
lines(xs, plogis(mdl.clm2$Theta[5] - xs) - plogis(mdl.clm2$Theta[4] - xs), col = 'yellow')
lines(xs, plogis(mdl.clm2$Theta[6] - xs) - plogis(mdl.clm2$Theta[5] - xs), col = 'grey')
lines(xs, 1 - (plogis(mdl.clm2$Theta[6] - xs)), col = 'blue')
abline(v = c(0,mdl.clm2$beta),lty = 3)
abline(h = 0, lty = "dashed")
abline(h = 0.2, lty = "dashed")
abline(h = 0.4, lty = "dashed")
abline(h = 0.6, lty = "dashed")
abline(h = 0.8, lty = "dashed")
abline(h = 1, lty = "dashed")

legend(par('usr')[2], par('usr')[4], bty = 'n', xpd = NA, lty = 1,
        col = c("black", "red", "green", "orange", "yellow", "grey", "blue"),
        legend = c("1", "2", "3", "4", "5", "6", "7"), cex = 0.75)
```
Predicted curves

<figure><img src="image_60.png" /></figure>

2.7.2.6.2 With confidence intervals Here is an attempt to add the 97.5%
confidence intervals to these plots. This is an experimental attempt and any
feedback is welcome!

```r
par(oma = c(4, 0, 0, 3), mgp = c(2, 1, 0))
xlim = c(min(mdl.clm2$beta), max(mdl.clm2$beta))
ylim = c(0, 1)
plot(0, 0, xlim =lim, ylim = ylim, type = "n", ylab = expression(Probability), xlab = "", xaxt = false, yaxt = false)
axis(side = 1, at = mdl.clm2$beta, labels = names(mdl.clm2$beta), las = 2, cex = 0.75, cex.lab = false, axislab = false)
xs = seq(xlim[1], xlim[2], length.out = 100)
```

\#+CI

```r
lines(xs, plogis(mdl.clm2$Theta[1]+(summary(mdl.clm2)$coefficient[,2][1]/1.96) - xs), col='black')
lines(xs, plogis(mdl.clm2$Theta[2]+(summary(mdl.clm2)$coefficient[,2][2]/1.96) - xs)-plogis(mdl.clm2$Theta[3]+(summary(mdl.clm2)$coefficient[,2][3]/1.96) - xs)-plogis(mdl.clm2$Theta[4]+(summary(mdl.clm2)$coefficient[,2][4]/1.96) - xs)-plogis(mdl.clm2$Theta[5]-(summary(mdl.clm2)$coefficient[,2][5]/1.96) - xs)-plogis(mdl.clm2$Theta[6]-(summary(mdl.clm2)$coefficient[,2][6]/1.96) - xs)-plogis(mdl.clm2$Theta[6]-(summary(mdl.clm2)$coefficient[,2][6]/1.96) - xs)), col='black')
```

\#-CI

```r
lines(xs, plogis(mdl.clm2$Theta[1]-(summary(mdl.clm2)$coefficient[,2][1]/1.96) - xs), col='black')
lines(xs, plogis(mdl.clm2$Theta[2]-(summary(mdl.clm2)$coefficient[,2][2]/1.96) - xs)-plogis(mdl.clm2$Theta[2]-(summary(mdl.clm2)$coefficient[,2][2]/1.96) - xs)-plogis(mdl.clm2$Theta[2]-(summary(mdl.clm2)$coefficient[,2][2]/1.96) - xs)-plogis(mdl.clm2$Theta[2]-(summary(mdl.clm2)$coefficient[,2][2]/1.96) - xs)), col='black')
```
lines(xs, plogis(mdl.clm2$Theta[3] - (summary(mdl.clm2)$coefficient[,2][[3]]/1.96) - xs)
lines(xs, plogis(mdl.clm2$Theta[4] - (summary(mdl.clm2)$coefficient[,2][[4]]/1.96) - xs)
lines(xs, plogis(mdl.clm2$Theta[5] - (summary(mdl.clm2)$coefficient[,2][[5]]/1.96) - xs)
lines(xs, plogis(mdl.clm2$Theta[6] - (summary(mdl.clm2)$coefficient[,2][[6]]/1.96) - xs)
lines(xs, 1-(plogis(mdl.clm2$Theta[6] - (summary(mdl.clm2)$coefficient[,2][[6]]/1.96) -

## fill area around CI using c(x, rev(x)), c(y2, rev(y1))
polygon(c(xs, rev(xs)),
  c(plogis(mdl.clm2$Theta[1]+(summary(mdl.clm2)$coefficient[,2][[1]]/1.96) - xs)
polygon(c(xs, rev(xs)),
  c(plogis(mdl.clm2$Theta[2]+(summary(mdl.clm2)$coefficient[,2][[2]]/1.96) - xs)
polygon(c(xs, rev(xs)),
  c(plogis(mdl.clm2$Theta[3]+(summary(mdl.clm2)$coefficient[,2][[3]]/1.96) - xs)
polygon(c(xs, rev(xs)),
  c(plogis(mdl.clm2$Theta[4]+(summary(mdl.clm2)$coefficient[,2][[4]]/1.96) - xs)
polygon(c(xs, rev(xs)),
  c(plogis(mdl.clm2$Theta[5]+(summary(mdl.clm2)$coefficient[,2][[5]]/1.96) - xs)
polygon(c(xs, rev(xs)),
  c(plogis(mdl.clm2$Theta[6]+(summary(mdl.clm2)$coefficient[,2][[6]]/1.96) - xs)
polygon(c(xs, rev(xs)),
  c(1-(plogis(mdl.clm2$Theta[6]-(summary(mdl.clm2)$coefficient[,2][[6]]/1.96) -

lines(xs, plogis(mdl.clm2$Theta[1] - xs), col = 'black')
lines(xs, plogis(mdl.clm2$Theta[2] - xs) - plogis(mdl.clm2$Theta[1] - xs), col = 'red')
lines(xs, plogis(mdl.clm2$Theta[3] - xs) - plogis(mdl.clm2$Theta[2] - xs), col = 'green')
lines(xs, plogis(mdl.clm2$Theta[4] - xs) - plogis(mdl.clm2$Theta[3] - xs), col = 'orange')
lines(xs, plogis(mdl.clm2$Theta[5] - xs) - plogis(mdl.clm2$Theta[4] - xs), col = 'yellow')
lines(xs, plogis(mdl.clm2$Theta[6] - xs) - plogis(mdl.clm2$Theta[5] - xs), col = 'grey')
lines(xs, 1 - (plogis(mdl.clm2$Theta[6] - xs)), col = 'blue')
abline(v = c(0,mdl.clm2$beta), lty = 3)
abline(h = 0, lty = "dashed")
abline(h = 0.2, lty = "dashed")
abline(h = 0.4, lty = "dashed")
abline(h = 0.6, lty = "dashed")
abline(h = 0.8, lty = "dashed")
abline(h = 1, lty = "dashed")

legend(par('usr')[2], par('usr')[4], bty = 'n', xpd = NA, lty = 1,
        col = c("black", "red", "green", "orange", "yellow", "grey", "blue"),
        legend = c("1", "2", "3", "4", "5", "6", "7"), cex = 0.75)

Predicted curves

<figure><img src="image_61.png" /></figure>

2.8 session info

sessionInfo()

## R version 4.5.2 (2025-10-31 ucrt)

## Platform: x86_64-w64-mingw32/x64

## Running under: Windows 11 x64 (build 26200)

##

## Matrix products: default

## LAPACK version 3.12.1

##

## locale:

## [1] LC_COLLATE=English_United Kingdom.utf8

## [2] LC_CTYPE=English_United Kingdom.utf8

## [3] LC_MONETARY=English_United Kingdom.utf8

## [4] LC_NUMERIC=C

## [5] LC_TIME=English_United Kingdom.utf8
<table>
  <tr>
    <td>## [73] pryr_0.1.6</td>
    <td>lattice_0.22-7</td>
    <td>bit_4.6.0</td>
  </tr>
  <tr>
    <td>## [76] survival_3.8-3</td>
    <td>tidyselect_1.2.1</td>
    <td>reformulas_0.4.2</td>
  </tr>
  <tr>
    <td>## [79] gridExtra_2.3</td>
    <td>bookdown_0.45</td>
    <td>litedown_0.8</td>
  </tr>
  <tr>
    <td>## [82] xfun_0.54</td>
    <td>rapportools_1.2</td>
    <td>matrixStats_1.5.0</td>
  </tr>
  <tr>
    <td>## [85] stringi_1.8.7</td>
    <td>yaml_2.3.10</td>
    <td>boot_1.3-32</td>
  </tr>
  <tr>
    <td>## [88] evaluate_1.0.5</td>
    <td>codetools_0.2-20</td>
    <td>tktk_4.5.2</td>
  </tr>
  <tr>
    <td>## [91] cli_3.6.5</td>
    <td>rpart_4.1.24</td>
    <td>xtable_1.8-4</td>
  </tr>
  <tr>
    <td>## [94] Rdpack_2.6.4</td>
    <td>Rcpp_1.1.0</td>
    <td>coda_0.19-4.1</td>
  </tr>
  <tr>
    <td>## [97] parallel_4.5.2</td>
    <td>bayestestR_0.17.0</td>
    <td>gap datasets_0.0.6</td>
  </tr>
  <tr>
    <td>## [100] lme4_1.1-37</td>
    <td>mvtnorm_1.3-3</td>
    <td>scales_1.4.0</td>
  </tr>
  <tr>
    <td>## [103] insight_1.4.3</td>
    <td>crayon_1.5.3</td>
    <td>rlang_1.1.6</td>
  </tr>
  <tr>
    <td>## [106] multcomp_1.4-29</td>
    <td>cards_0.7.0</td>
    <td></td>
  </tr>
</table>
Chapter 3

Random effects - LMM,
GLMM, CLMM, GAMMs

This chapter introduces the reader to the basics of mixed-effects regressions. We explore what random effects are and how they contribute to our models. It demonstrates how what additional information we gain from a mixed effects model beyond the fixed effects. We heavily explore random effects using a Linear Mixed-Effects Regression model (LMM) using the package lme4. We also explore how to use the ggstats and ggstatsplot packages to visualise the results of our models. We also use the sjPlot package to visualise the results of our models. We explore other family distributions using Generalised Linear Mixed-effects Models (GLMMs) using the lme4 package. Here we use various types of predictors: categorical predictors and numeric predictors. For the latter case, we look at how to use z-scored numeric predictors. We also explore how to use the emmeans package to visualise the results of our models. We then move to a cumulative link mixed-effects models (CLMMs). Towards the end, we introduce the user to Generalised Additive Mixed-effects Regressions (GAMMs). We use the package mgcv to explore how to use GAMMs. We also explore how to use the itsadug package to visualise the results of our models.

3.1 Loading packages

```r
### Use the code below to check if you have all required packages installed. If some are not installed,
requiredPackages = c('faux', 'tidyverse', 'broom', 'knitr', 'Hmisc', 'corrplot', 'lme4', 'lmerTest',
  for(p in requiredPackages){
    if(!require(p, character_only = TRUE)) install.packages(p, dependencies = TRUE)
    library(p, character_only = TRUE)
  }
```
detach("package:lmerTest", unload = TRUE)

## 3.2 Random effects?

Random effects are used to account for the inter-dependencies in a dataset. In various domains, including linguistics, we often collect data from multiple Subjects, items, and utterances.

1. Multiple Subjects

2. Multiple Items (words)

3. Multiple utterances where words are embedded

4. Multiple listeners in perception experiments

In the last case, when designing our perception experiment, we can sometimes use multiple items, coming from multiple utterances and from multiple subjects!

When the data comes from multiple subjects, items, etc., there is a clear inter-dependency in the data. Without appropriately accounting for these, inter-dependencies, we are at a greater risk of increasing **Type I** Error and in some cases **Type 2** error (see chapter 3 on the various types of errors).

This is the equation that represents the error term associated with random effects:

$$y = x\beta + \varepsilon + Zu$$

where:

* $y \to$ outcome (DV) $\Rightarrow$ known

* $x \to$ fixed effect (IV) $\Rightarrow$ known

* $\beta \to$ coefficient of fixed effect $\Rightarrow$ unknown

* $\varepsilon \to$ random error term $\Rightarrow$ unknown

* $Z \to$ random effects term $\Rightarrow$ known

* $u \to$ random effects coefficients $\Rightarrow$ unknown

In a linear regression model (see chapter 3), the error term $\varepsilon$ is a general error term related to the unexplained variance in the data. We see that this error term increases when we have inter-dependencies in the data unaccounted for (i.e., an increase in the $\varepsilon$ leads to an increase in **Type I** error). In a random effects structure, some of this error is related to the $Z$ and $u$. These two will lead to a decrease in the error term $\varepsilon$ meaning that we allowed the model to account for the inter-dependencies in the data. However, in some instances, the unexplained variance in the data can decrease drastically with the error term associated with random effects increasing drastically. In these cases, there is a clear increase in **Type II** error.
### 3.2.1 How to choose fixed and random effects

#### 3.2.1.1 Fixed effects

Fixed effects are those that are part of the experimental conditions. If you have exhausted all levels of an experimental condition, then this goes into fixed effects.

Covariates are a special case. Covariates are independent variables that co-vary with the population. For instance, a speaker can either be a male or a female (from a physiological sex perspective not accounting for sociolinguistic gender). This physiological gender then covaries with our subjects, and in some instances, can be used to allow for the coefficients to be adjusted to account for this type of codependency (or covariation).

#### 3.2.1.2 Random effects

Random effects are random selections of the population you have and you want to generalise over them.

E.g., Speakers, listeners, items, utterances, corpora.... are all random effects because you are not using all the population of speakers, listeners, items, utterances or corpora in your data!

BUT.. Can Speakers, listeners, items, or utterances be included as fixed effects? Yes!! When you do this, it means you are interested in this specific population and want to evaluate differences specific to the population!!

### 3.2.2 What about Random Intercepts and Random Slopes

We often find references in the literature to specific notions of random intercepts and random slopes. To demonstrate what these mean (beyond the definitions), we look at an example. For example, using a simulated dataset (for more details see below under Linear Mixed-effects Models), figure A shows the predicted average Looking time. In the incongruent condition, there is a clear increase in the Looking time.

#### 3.2.2.1 Random Intercepts

Random Intercepts are used to obtain averages of your population and these are used in your statistical model to estimate group-specific variations. These are represented in figure B. As can be seen here, the overall increase in looking time in the incongruent condition is confirmed and all subjects show this type of increase. However, what is important to note is that the intercepts (starting and ending times) per subject are different, but all subjects have the same slope. This is normal given that we did not allow subjects to covary with respect to the congruence-incongruence condition.
### 3.2.2.2 Random Intercepts and Random Slopes

When using Random Intercepts and Random Slopes, we mean that we allowed for averages per subject to be computed, in addition to allowing each subject's variability with regards to the fixed effect to covary. The figure C shows this clearly. Not only that subjects have different intercepts (starting and ending times); they also have different slopes with some showing steeper slopes and others shallower slopes.

Random slopes are adjustments to the subjects' observations as a function of the variable(s) of interest. Usually, any within-subject (or within-item) variable(s) is(are) to be included as a random slope(s), but you need to use model comparison to evaluate the need to use it.

```r
plot_model(xmdl.Optimal, type = "pred", terms = "Cond", ci.lvl = 0.95, dodge = 0,
  show.legend = FALSE, title = "A. Predicted average LookingTime") + themeBW
  geom_line() + coordCartesian(ylim = c(-275, 2000)) +
plot_model(xmdlrand.Interc, type = "pred", terms = c("Cond", "Subj"), pred.type = "re",
  ci.lvl = NA, dodge = 0, colors = paletteer_c("grDevices::rainbow",
  length unique(dataCong$Subj)))
  show.legend = FALSE, title = "B. Subject Intercepts of LookingTime") + themeBW
  geom_line() + coordCartesian(ylim = c(-275, 2000)) +
plot_model(xmdl.Optimal, type = "pred", terms = c("Cond", "Subj"), pred.type = "re",
  ci.lvl = NA, dodge = 0, colors = paletteer_c("grDevices::rainbow",
  length unique(dataCong$Subj)))
  show.legend = FALSE, title = "C. Subject Slopes of LookingTime") + themeBW
  geom_line() + coordCartesian(ylim = c(-275, 2000))
```

<figure><img src="image_62.png" /></figure>

In the next section, we start by demonstrating the use of Linear Mixed-effects Models.
## 3.3 Linear Mixed-effects Models. Why random effects matter

Let's generate a new dataframe that we will use later on for our mixed models

We will use the `faux` package. It is available on CRAN, but it is possible that it is not available for your version of R (I used version 4.5). In this case, you need to install it via github. The package `faux` is a package that allows you to simulate data for your experiments. It is a very useful package to test your ideas and to assess the impact of particular predictors on your dependent variable.

To install it, you will first need to install the package `devtools`, and then install the package `faux` using the function `devtools::install_github`. Uncomment the code chunk below

```r
# install.packages("devtools")
# devtools::install_github("debruine/faux")
# library(faux)
```

### 3.3.1 Dataframe (simulated)

Our experiment has the following structure: we asked 40 subjects to respond to 40 items in a fully crossed design. There were two IVs: Condition with congruent and incongruent and Age with young and old. The Condition is a within subject variable; age is a between subject. However, Condition and Age were both within item variables. The dependent variable was LookingTime.

This meant that we used items within each of the young and the old subjects in addition to items within each of the congruent and incongruent conditions.

Our research question is as follows: Age of subject will impact the Looking Time in the two conditions. Our hypothesis is: The older a subject is, the more the looking time it is to the incongruent condition.

We will use the package `faux` to simulate a dataframe. This step is crucial in assessing contributions of particular predictors and for testing ideas as we already know the distribution of the data and what to expect as an outcome when it comes to the fixed effect in question.

The simulated data has the following parameters

```r
set.seed(42)
# define parameters
Subj_n = 40 # number of subjects
Item_n = 40 # number of items
b0 = 100 # intercept
b1 = 2.5 * b0 # fixed effect of condition
u0s_sd = 300 # random intercept SD for subjects
u0i_sd = 200 # random intercept SD for items
```
u1s_sd = 100 # random b1 slope SD for subjects
u1i_sd = 50 # random b1 slope SD for items
r01s = -0.3 # correlation between random effects 0 and 1 for subjects
r01i = 0.2 # correlation between random effects 0 and 1 for items
sigma_sd = 150 # error SD

# set up data structure
dataCong <- add_random(Subj = Subj_n, Item = Item_n) %>%
  # add within categorical variable for subject
  add_within("Subj", Cond = c("Congruent", "Incongruent")) %>%
  add_recode("Cond", "Cond.Incongruent", Congruent = 0, Incongruent = 1) %>%
  # add between categorical variable for subject
  add-between("Subj", Age = c("Young", "Old")) %>%
  add_recode("Age", "Age.Old", Young = 0, Old = 1) %>%
  # add random effects
  add_ranef("Subj", u0s = u0s_sd, u1s = u1s_sd, . cors = r01s) %>%
  add_ranef("Item", u0i = u0i_sd, u1i = u1i_sd, . cors = r01i) %>%
  ##add_ranef(c("Subj", "Item"), u0si = u0s_sd + u0i_sd) %>%
  ##add_ranef(c("Subj", "Item"), u1si = u1s_sd + u1i_sd) %>%
  add_ranef sigma = sigma_sd) %>%
  # calculate DV
mutate(LookingTime = b0 + b1 + u0s + u0i + #u0si + u1si +
  (((b1 + u1s) + 0.5) * Cond.Incongruent) + (((b1 + u1s) + 0.9) * Age.Old) +
  (((b1 + u1i) - 0.3) * Cond.Incongruent) + (((b1 + u1i) - 0.25) * Age.Old) +
  sigma)
write.csv(dataCong, "data/dataCong.csv")

If you were not able to install the faux package, simply uncomment the following line of code below to import the dataset

#dataCong <- read.csv("dataCong.csv")[-1]

### 3.3.1.1 Counts

dataCong <- dataCong %>%
  mutate( Subj = factor( Subj ),
        Item = factor( Item ))

dataCong

## # A tibble: 3,200 x 12
##   Subj Item Cond   Cond.Incongruent Age Age.Old u0s u1s u0i u1i
## <fct> <fct> <fct> <db1> <fct> <db1> <db1> <db1> <db1> <db1>
## 1 Subj01 Item01 Congru~      0 Young      0 -413.  26.2 -306.  56.9
## 2 Subj01 Item01 Incongr~      1 Young      0 -413.  26.2 -306.  56.9
## 3 Subj01 Item02 Congru~      0 Young      0 -413.  26.2 -55.4  69.1
## 4 Subj01 Item02 Incongr~      1 Young      0 -413.  26.2 -55.4  69.1
## 3.3. LINEAR MIXED-EFFECTS MODELS. WHY RANDOM EFFECTS MATTER183

```
## 5 Subj01 Item03 Congru~      0 Young          0 -413. 26.2 -17.4 -7.03
## 6 Subj01 Item03 Incong~      1 Young          0 -413. 26.2 -17.4 -7.03
## 7 Subj01 Item04 Congru~      0 Young          0 -413. 26.2   21.6 50.0
## 8 Subj01 Item04 Incong~      1 Young          0 -413. 26.2   21.6 50.0
## 9 Subj01 Item05 Congru~      0 Young          0 -413. 26.2  239. 12.8
## 10 Subj01 Item05 Incong~     1 Young          0 -413. 26.2  239. 12.8
## # i 3,190 more rows
## # i 2 more variables: sigma <db1>, LookingTime <db1>
```

```
dataCong %>%
  group_by(Cond, Age, Subj) %>%
  summarise(count = n())
```

### 3.3.1.1.1 Subjects

```
## # A tibble: 80 x 4
## # Groups: Cond, Age [4]
##   Cond      Age      Subj  count
## <fct>     <fct>   <fct>  <int>
## 1 Congruent  Young  Subj01   40
## 2 Congruent  Young  Subj03   40
## 3 Congruent  Young  Subj05   40
## 4 Congruent  Young  Subj07   40
## 5 Congruent  Young  Subj09   40
## 6 Congruent  Young  Subj11   40
## 7 Congruent  Young  Subj13   40
## 8 Congruent  Young  Subj15   40
## 9 Congruent  Young  Subj17   40
## 10 Congruent  Young  Subj19   40
## # i 70 more rows
```

### 3.3.1.1.2 Items

```
dataCong %>%
  group_by(Age, Item) %>%
  summarise(count = n())
```

### 3.3.1.1.3 Age

```
## # A tibble: 80 x 3
## # Groups: Age [2]
##   Age      Item     count
## <fct>     <fct>   <int>
## 1 Young    Item01   40
## 2 Young    Item02   40
```
## 3 Young Item03 40
## 4 Young Item04 40
## 5 Young Item05 40
## 6 Young Item06 40
## 7 Young Item07 40
## 8 Young Item08 40
## 9 Young Item09 40
## 10 Young Item10 40
## # i 70 more rows

dataCong %>%
  group_by(Cond, Item) %>%
  summarise(count = n())

### 3.3.1.1.4 Cond

## # A tibble: 80 x 3
## # Groups: Cond [2]
##   Cond    Item    count
## <fct> <fct> <int>
## 1 Congruent Item01    40
## 2 Congruent Item02    40
## 3 Congruent Item03    40
## 4 Congruent Item04    40
## 5 Congruent Item05    40
## 6 Congruent Item06    40
## 7 Congruent Item07    40
## 8 Congruent Item08    40
## 9 Congruent Item09    40
## 10 Congruent Item10   40
## # i 70 more rows

### 3.3.1.2 Visualisations

#### 3.3.1.2.1 Condition by Age
The figure below confirms this, where we see an increase in LookingTime in the incongruent condition and oevrall, older participants show an increase in LookingTime

dataCong %>%
  ggplot(aes(x = Cond,
            y = LookingTime,
            colour = Age)) +
  themeBW() +
  geom_boxplot() +
  geom.smooth(aes(as.numeric(Cond)), method = "lm")
3.3. LINEAR MIXED-EFFECTS MODELS. WHY RANDOM EFFECTS MATTER185

<figure><img src="image_63.png" /></figure>

3.3.1.2.2 Subject by Condition This figure shows that subjects are vari-
able in how they responded to this task

dataCong %>

 ggplot(aes(x = Cond,
           y = LookingTime,
           colour = Subj)) +
   theme() +
   geom_point() +
   geom.smooth(aes(as.numeric(Cond)), method = "lm", se = FALSE) +
   scaleColour_manual(values = paletteer_c("grDevices::rainbow", length unique(dataCong$Subj))))
<figure><img src="image_64.png" /></figure>

3.3.1.2.3 Subject by Age This figure shows that subjects had an impact on the LookingTime in both age groups, simply due to their variable responses to the different items

dataCong %>

 ggplot(aes(x = Age,
             y = LookingTime,
             colour = Subj)) +
   theme() +
   geom_point() +
   geom.smooth(aes(as.numeric(Cond)), method = "lm", se = FALSE) +
   scale.colour_manual(values = paletteer_c("grDevices::rainbow", length unique(dataCong)))
3.3. LINEAR MIXED-EFFECTS MODELS. WHY RANDOM EFFECTS MATTER187

<figure><img src="image_65.png" /></figure>

3.3.1.2.4 Item by Condition This figure shows that items had an impact
on the LookingTime in both conditions

```r
dataCong %>
  ggplot(aes(x = Cond,
            y = LookingTime,
            colour = Item)) +
  themeBW() +
  geom_point() +
  geom.smooth(aes(as.numeric(Cond)), method = "lm", se = FALSE) +
  scale.colour_manual(values = paletteer_c("grDevices::rainbow", length unique(dataCong$Item)))))
```
<figure><img src="image_66.png" /></figure>

3.3.1.2.5 Subject by Age This figure shows that items had an impact on
the LookingTime in both age groups

dataCong %>

 ggplot(aes(x = Age,
           y = LookingTime,
           colour = Item)) +
   themeBW() +
   geom_point() +
   geom.smooth(aes(as.numeric(Cond)), method = "lm", se = FALSE) +
   scale.colour_manual(values = paletteer_c("grDevices::rainbow", length unique(dataCong)))
3.3. LINEAR MIXED-EFFECTS MODELS. WHY RANDOM EFFECTS MATTER189

<figure><img src="image_67.png" /></figure>

3.3.2 Modelling strategy

We use an LMER model with a crossed random effect. To choose our optimal
model, we start first by a simple model with only random intercepts, increasing
complexity by accounting for random slopes for both subjects and items. It is
clear from our visualisation above, that there is no interaction between the two
predictors. However, for demonstration purposes, we do test for this

3.3.2.1 Simple Linear Model

mdl.lm <- dataCong %>

lm(LookingTime ~ Cond + Age, data = .)

summary(mdl.lm)

##

## Call:

## lm(formula = LookingTime ~ Cond + Age, data = .)

##

## Residuals:

##       Min    1Q   Median    3Q     Max
## -1215.59 -290.17 -21.78  264.89  1661.41

##

## Coefficients:

##              Estimate Std. Error t value Pr(>|t|)
## (Intercept) 304.95 12.91 23.61 <2e-16 ***
## CondIncongruent 504.35 14.91 33.82 <2e-16 ***
## AgeOld 566.44 14.91 37.98 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 421.8 on 3197 degrees of freedom
## Multiple R-squared: 0.4472, Adjusted R-squared: 0.4469
## F-statistic: 1293 on 2 and 3197 DF, p-value: < 2.2e-16
hist(residuals(mdl.lm))

<figure><img src="image_68.png" /><figcaption>Histogram of residuals(mdl.lm)</figcaption></figure>

qqnorm(residuals(mdl.lm)); qqline(residuals(mdl.lm))
3.3. LINEAR MIXED-EFFECTS MODELS. WHY RANDOM EFFECTS MATTER191

Normal Q-Q Plot

<figure><img src="image_69.png" /></figure>

Theoretical Quantiles

plot(fitted(mdl.lm), residuals(mdl.lm), cex = 4)

<figure><img src="image_70.png" /></figure>

3.3.2.2 No interaction

xmdlRand.Interc <- dataCong %>
lmer(LookingTime ~ Cond + Age +
       (1 | Subj) +
       (1 | Item), data = ., REML = FALSE,
control = lmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 1e5)))

### 3.3.2.2.1 Crossed random intercepts

xmdlrand.Slope1 <- dataCong %>%
lmer(LookingTime ~ Cond + Age +
(1 + Cond | Subj) +
(1 | Item), data = ., REML = FALSE,
control = lmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 1e5)))

### 3.3.2.2.2 Crossed random intercepts + By-speaker random slopes

xmdlrand.Slope2 <- dataCong %>%
lmer(LookingTime ~ Cond + Age +
(1 + Cond | Subj) +
(1 + Cond | Item), data = ., REML = FALSE,
control = lmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 1e5)))

### 3.3.2.2.3 Crossed random intercepts + By-speaker and by-item random slopes

xmdlrand.Slope3 <- dataCong %>%
lmer(LookingTime ~ Cond + Age +
(1 + Cond | Subj) +
(1 + Cond + Age | Item), data = ., REML = FALSE,
control = lmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 1e5)))

### 3.3.2.2.4 Crossed random intercepts + By-speaker and by-item random slopes

### 3.3.2.3 With interaction

xmdlrand.Interc.Int <- dataCong %>%
lmer(LookingTime ~ Cond * Age +
(1 | Subj) +
(1 | Item), data = ., REML = FALSE,
control = lmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 1e5)))

### 3.3.2.3.1 Crossed random intercepts + Interaction
### 3.3. LINEAR MIXED-EFFECTS MODELS. WHY RANDOM EFFECTS MATTER¹⁹³

```r
xmdlrand.Slope1.Int <- dataCong %>%
  lmer(LookingTime ~ Cond * Age +
       (1 + Cond | Subj) +
       (1 | Item), data = ., REML = FALSE,
       control = lmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 1e5)))
```

#### 3.3.2.3.2 Crossed random intercepts + By-speaker random slopes + Interaction

```r
xmdlrand.Slope2.Int <- dataCong %>%
  lmer(LookingTime ~ Cond * Age +
       (1 + Cond | Subj) +
       (1 + Cond | Item), data = ., REML = FALSE,
       control = lmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 1e5)))
```

#### 3.3.2.3.3 Crossed random intercepts + By-speaker and by-item random slopes + Interaction

```r
xmdlrand.Slope3.Int <- dataCong %>%
  lmer(LookingTime ~ Cond * Age +
       (1 + Cond | Subj) +
       (1 + Cond * Age | Item), data = ., REML = FALSE,
       control = lmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 1e5)))
```

#### 3.3.2.3.4 Crossed random intercepts + By-speaker and by-item random slopes

#### 3.3.2.4 Model comparison

```r
anova(xmdlrand.Interc, xmdlrand.Slope1, xmdlrand.Slope2, xmdlrand.Slope3, xmdlrand.Interc)

## Data: .
## Models:
## xmdlrand.Interc: LookingTime ~ Cond + Age + (1 | Subj) + (1 | Item)
## xmdlrand.Interc.Int: LookingTime ~ Cond * Age + (1 | Subj) + (1 | Item)
## xmdlrand.Slope1: LookingTime ~ Cond + Age + (1 + Cond | Subj) + (1 | Item)
## xmdlrand.Slope1.Int: LookingTime ~ Cond * Age + (1 + Cond | Subj) + (1 | Item)
## xmdlrand.Slope2: LookingTime ~ Cond + Age + (1 + Cond | Subj) + (1 + Cond | Item)
## xmdlrand.Slope2.Int: LookingTime ~ Cond * Age + (1 + Cond | Subj) + (1 + Cond | Item)
## xmdlrand.Slope3: LookingTime ~ Cond + Age + (1 + Cond | Subj) + (1 + Cond + Age | Item)
## xmdlrand.Slope3.Int: LookingTime ~ Cond * Age + (1 + Cond | Subj) + (1 + Cond * Age | Item)

## npar AIC BIC logLik -2*log(L) Chisq Df Pr(>Chisq)
## xmdlrand.Interc 6 42074 42110 -21031 42062
## xmdlrand.Interc.Int 7 42050 42093 -21018 42036 25.8359 1 3.717e-07
```
xmdlrand.Slope1 8 41834 41883 -20909 41818 217.8699 1 < 2.2e-16
xmdlrand.Slope1.Int 9 41833 41888 -20908 41815 3.0247 1 0.0820
xmdlrand.Slope2 10 41808 41869 -20894 41788 27.3253 1 1.719e-07
xmdlrand.Slope2.Int 11 41807 41874 -20892 41785 3.0149 1 0.0825
xmdlrand.Slope3 13 41780 41858 -20877 41754 31.2599 2 1.629e-07
xmdlrand.Slope3.Int 18 41786 41895 -20875 41750 3.3401 5 0.6477

xmdlrand.Interc
xmdlrand.Interc.Int ***
xmdlrand.Slope1 ***
xmdlrand.Slope1.Int .
xmdlrand.Slope2 ***
xmdlrand.Slope2.Int .
xmdlrand.Slope3 ***
xmdlrand.Slope3.Int

---
Signif. codes: 0 '**' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

The results above highlight that the model accounting for both by-subject and
by-item random intercepts and random slopes for Condition are improving the
model fit in comparison to a more complex model. We rerun the model with
REML = False

xmdl.Optimal <- dataCong %>
lmer(LookingTime ~ Cond + Age +
(1 + Cond | Subj) +
(1 + Cond + Age | Item), data = ., REML = TRUE,
control = lmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 1e5)))

3.3.2.5.1 Model criticism

hist(residuals(xmdl.Optimal))
3.3. LINEAR MIXED-EFFECTS MODELS. WHY RANDOM EFFECTS MATTER 195

Histogram of residuals(xmdl.Optimal)

<figure><img src="image_71.png" /></figure>

3.3.2.5.1.1 Histogram

residuals(xmdl.Optimal)

qqnorm(residuals(xmdl.Optimal)); qqline(residuals(xmdl.Optimal))

Normal Q-Q Plot

<figure><img src="image_72.png" /></figure>

3.3.2.5.1.2 QQ-plot

Theoretical Quantiles

plot(fitted(xmdl.Optimal), residuals(xmdl.Optimal), cex = 4)
<figure><img src="image_73.png" /><figcaption>fitted(xmdl.Optimal)</figcaption></figure>

### 3.3.2.5.1.3 Residuals vs Fitted

xmdl.Optimal %>
summary()

### 3.3.2.5.2 Summary

## Linear mixed model fit by REML ['lmerMod']

## Formula: LookingTime ~ Cond + Age + (1 + Cond | Subj) + (1 + Cond + Age | Item)

## Data: .

## Control: lmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 1e+05))

##

## REML criterion at convergence: 41724.6

##

## Scaled residuals:

## Min 1Q Median 3Q Max
-3.5337 -0.6485 -0.0054 0.6647 3.5358

##

## Random effects:

<table><thead><tr><th>Groups</th><th>Name</th><th>Variance</th><th>Std.Dev.</th><th>Corr</th></tr></thead><tbody><tr><td>Subj</td><td>(Intercept)</td><td>123480</td><td>351.40</td><td></td></tr><tr><td>Item</td><td>CondIncongruent</td><td>10746</td><td>103.66</td><td>-0.26</td></tr><tr><td>Subj</td><td>(Intercept)</td><td>38781</td><td>196.93</td><td></td></tr><tr><td>Item</td><td>CondIncongruent</td><td>1872</td><td>43.27</td><td>0.31</td></tr><tr><td>Subj</td><td>AgeOld</td><td>1851</td><td>43.03</td><td>-0.13 0.69</td></tr><tr><td>Item</td><td>AgeOld</td><td>22613</td><td>150.38</td><td></td></tr></tbody></table>

## Number of obs: 3200, groups: Subj, 40; Item, 40

##

## Fixed effects:
3.3. LINEAR MIXED-EFFECTS MODELS. WHY RANDOM EFFECTS MATTER197

## Estimate Std. Error t value
## (Intercept)   315.04      83.42   3.777
## CondIncongruent  504.35      18.54  27.204
## AgeOld         546.28     107.70   5.072
##
## Correlation of Fixed Effects:
##       (Intr) CndInc
## CndIncgrnt -0.120
## AgeOld       -0.646   0.016

Anova(xmdl.Optimal)

3.3.2.5.3 ANOVA

## Analysis of Deviance Table (Type II Wald chisquare tests)
##
## Response: LookingTime
## Chisq Df Pr(>Chisq)
## Cond 740.067 1 < 2.2e-16 ***
## Age 25.729 1 3.928e-07 ***
## ---
## Signif. codes: 0 '**' 0.001 '**' 0.01 '**' 0.05 '**' 0.1 ' ' 1

print tab_model(xmdl.Optimal, file = paste0("outputs/xmdl.Optimal.html")))
htmltools::includeHTML("outputs/xmdl.Optimal.html")

3.3.2.5.4 Model's fit

3.3.3 Plotting model's output

3.3.3.1 With ggstats

We use two functions from the package ggstats.

ggcoef_model(xmdl.Optimal)
<figure><img src="image_74.png" /></figure>

### 3.3.3.1.1 A plot

### 3.3.3.2 A plot + a table + 95% CI

ggcoef_table(xmdl.Optimal)

<figure><img src="image_75.png" /></figure>
3.3. LINEAR MIXED-EFFECTS MODELS. WHY RANDOM EFFECTS MATTER199

3 3 3 With ggstatsplot

ggcoefstats(xmdl.Optimal, point.args = list(color = paletteer_c("grDevices::rainbow", 13), stats.

## Warning in (function (mapping = NULL, data = NULL, stat = "identity", position
## = "identity", : Ignoring unknown parameters: `stats.label.colour`

## Warning: x Number of labels is greater than default palette color count.
## i Select another color `pulse` (and/or `package`).

<figure><img src="image_76.png" /></figure>

3.3.4 Exploring random effects

3 3 4 1 Subject random effects

randomEffects <- ranef(xmdl.Optimal) %>

pluck(1) %>

rownames_to_column() %>

rename(Subject = rowname, Intercept = "(Intercept)")

randomEffects %>

knitr::kable()
<table><thead><tr><th>Subject</th><th>Intercept</th><th>CondIncongruent</th></tr></thead><tbody><tr><td>Subj01</td><td>-404.45054</td><td>58.1953368</td></tr><tr><td>Subj02</td><td>164.05584</td><td>56.9126271</td></tr><tr><td>Subj03</td><td>-56.37438</td><td>-104.0600477</td></tr><tr><td>Subj04</td><td>-87.06837</td><td>43.7884729</td></tr><tr><td>Subj05</td><td>-55.65214</td><td>104.5323900</td></tr><tr><td>Subj06</td><td>-42.39999</td><td>-7.1394328</td></tr><tr><td>Subj07</td><td>-448.81496</td><td>124.6524549</td></tr><tr><td>Subj08</td><td>-171.75810</td><td>-105.4504187</td></tr><tr><td>Subj09</td><td>-587.74594</td><td>123.6911001</td></tr><tr><td>Subj10</td><td>-44.50407</td><td>-50.9618431</td></tr><tr><td>Subj11</td><td>-346.46288</td><td>1.6396966</td></tr><tr><td>Subj12</td><td>-550.49633</td><td>158.6524706</td></tr><tr><td>Subj13</td><td>417.66027</td><td>-169.1409700</td></tr><tr><td>Subj14</td><td>-11.45716</td><td>-30.0008252</td></tr><tr><td>Subj15</td><td>62.46659</td><td>-14.3520076</td></tr><tr><td>Subj16</td><td>-210.03389</td><td>-23.9077430</td></tr><tr><td>Subj17</td><td>124.19946</td><td>-122.7635167</td></tr><tr><td>Subj18</td><td>666.67147</td><td>-42.1836697</td></tr><tr><td>Subj19</td><td>815.78333</td><td>217.1615447</td></tr><tr><td>Subj20</td><td>-393.58521</td><td>26.1633665</td></tr><tr><td>Subj21</td><td>120.64645</td><td>37.9297097</td></tr><tr><td>Subj22</td><td>455.31816</td><td>-46.4925696</td></tr><tr><td>Subj23</td><td>42.42431</td><td>-54.4053551</td></tr><tr><td>Subj24</td><td>-496.29436</td><td>-31.7202386</td></tr><tr><td>Subj25</td><td>-552.91357</td><td>144.2714898</td></tr><tr><td>Subj26</td><td>-21.91509</td><td>-159.7897817</td></tr><tr><td>Subj27</td><td>65.14521</td><td>54.5212747</td></tr><tr><td>Subj28</td><td>373.40089</td><td>-166.0862255</td></tr><tr><td>Subj29</td><td>-132.82108</td><td>-21.8820276</td></tr><tr><td>Subj30</td><td>104.73419</td><td>-112.8914459</td></tr><tr><td>Subj31</td><td>-79.72260</td><td>125.0118699</td></tr><tr><td>Subj32</td><td>-182.30982</td><td>15.3898936</td></tr><tr><td>Subj33</td><td>-303.68384</td><td>-0.1957386</td></tr><tr><td>Subj34</td><td>215.98609</td><td>136.5078869</td></tr><tr><td>Subj35</td><td>-152.60397</td><td>76.5559812</td></tr><tr><td>Subj36</td><td>401.50547</td><td>-145.0045141</td></tr><tr><td>Subj37</td><td>274.61818</td><td>-114.4122298</td></tr><tr><td>Subj38</td><td>139.48473</td><td>-82.7958618</td></tr><tr><td>Subj39</td><td>733.87830</td><td>58.5575032</td></tr><tr><td>Subj40</td><td>155.08935</td><td>41.5013939</td></tr></tbody></table>
3.3. LINEAR MIXED-EFFECTS MODELS. WHY RANDOM EFFECTS MATTER201

3.3.4.2 Items random effects

random Effects <- ranef(xmdl.Optimal) %>
  pluck(2) %>
  rownames_to_column() %>
  rename(Items = rowname, Intercept = "(Intercept)")

random effects %>
  knitr::kable()
<table><thead><tr><th>Items</th><th>Intercept</th><th>CondIncongruent</th><th>AgeOld</th></tr></thead><tbody><tr><td>Item01</td><td>-247.414507</td><td>16.2991489</td><td>28.312990</td></tr><tr><td>Item02</td><td>-28.240445</td><td>20.6149279</td><td>37.267856</td></tr><tr><td>Item03</td><td>-27.548429</td><td>11.7099339</td><td>-3.218254</td></tr><tr><td>Item04</td><td>30.999046</td><td>32.2392558</td><td>32.548236</td></tr><tr><td>Item05</td><td>246.216859</td><td>38.0585978</td><td>2.963549</td></tr><tr><td>Item06</td><td>-135.583736</td><td>28.3151555</td><td>28.127356</td></tr><tr><td>Item07</td><td>75.461498</td><td>28.6715548</td><td>-2.095288</td></tr><tr><td>Item08</td><td>72.679400</td><td>69.1730999</td><td>73.479523</td></tr><tr><td>Item09</td><td>-180.071444</td><td>32.9237845</td><td>60.953057</td></tr><tr><td>Item10</td><td>-170.029328</td><td>8.4112590</td><td>23.865843</td></tr><tr><td>Item11</td><td>-278.857705</td><td>-39.6392919</td><td>-22.526611</td></tr><tr><td>Item12</td><td>114.001985</td><td>4.7652485</td><td>-15.353357</td></tr><tr><td>Item13</td><td>-137.533542</td><td>-49.5701246</td><td>-36.764423</td></tr><tr><td>Item14</td><td>-272.928912</td><td>-85.2576750</td><td>-45.340742</td></tr><tr><td>Item15</td><td>219.855541</td><td>-70.2475223</td><td>-83.121735</td></tr><tr><td>Item16</td><td>243.071753</td><td>13.0287924</td><td>-4.812872</td></tr><tr><td>Item17</td><td>210.792625</td><td>10.6898312</td><td>17.840004</td></tr><tr><td>Item18</td><td>328.737750</td><td>-36.9498461</td><td>-82.922663</td></tr><tr><td>Item19</td><td>-46.910049</td><td>28.2829527</td><td>22.930110</td></tr><tr><td>Item20</td><td>-107.870056</td><td>-25.5384308</td><td>-13.846115</td></tr><tr><td>Item21</td><td>-209.598744</td><td>-56.8339801</td><td>-29.482588</td></tr><tr><td>Item22</td><td>-190.253581</td><td>-3.0439700</td><td>20.502593</td></tr><tr><td>Item23</td><td>207.958662</td><td>34.4328035</td><td>33.373202</td></tr><tr><td>Item24</td><td>-371.211245</td><td>-46.1955836</td><td>1.751542</td></tr><tr><td>Item25</td><td>163.603914</td><td>15.0837752</td><td>-7.780876</td></tr><tr><td>Item26</td><td>-56.954235</td><td>-39.1972201</td><td>-59.652416</td></tr><tr><td>Item27</td><td>126.648406</td><td>7.5867262</td><td>-1.102683</td></tr><tr><td>Item28</td><td>48.176096</td><td>-0.4969082</td><td>1.358911</td></tr><tr><td>Item29</td><td>-76.699978</td><td>-27.4397677</td><td>-1.462473</td></tr><tr><td>Item30</td><td>-20.393146</td><td>33.1813806</td><td>36.286219</td></tr><tr><td>Item31</td><td>33.763413</td><td>-15.9993987</td><td>-14.400133</td></tr><tr><td>Item32</td><td>-15.979008</td><td>47.9237115</td><td>67.643383</td></tr><tr><td>Item33</td><td>64.451213</td><td>-8.2252951</td><td>-47.157817</td></tr><tr><td>Item34</td><td>102.286457</td><td>22.6554454</td><td>17.134672</td></tr><tr><td>Item35</td><td>319.882212</td><td>54.1470278</td><td>10.485257</td></tr><tr><td>Item36</td><td>115.886689</td><td>22.7596669</td><td>9.094458</td></tr><tr><td>Item37</td><td>93.471368</td><td>9.1514824</td><td>-17.490313</td></tr><tr><td>Item38</td><td>-523.293815</td><td>-46.1545897</td><td>-5.185309</td></tr><tr><td>Item39</td><td>287.858945</td><td>20.0462752</td><td>2.292928</td></tr><tr><td>Item40</td><td>-8.431927</td><td>-59.3622338</td><td>-34.495018</td></tr></tbody></table>

### 3.3.4.3 Plots

These plots below are produced with the sjPlot package.
3.3.4.3.1 Fixed effects

plot_model(xmdl.Optimal, type="pred", terms=c("Cond"), ci lvl = NA, dodge = 0) + themeBW() + ge

<figure><img src="image_77.png" /></figure>

3.3.4.3.1.1 Condition

plot_model(xmdl.Optimal, type="pred", terms=c("Age"), ci.lvl = NA, dodge = 0) + themeBW() + ge
<figure><img src="image_78.png" /><figcaption>3.3.4.3.1.2 Age</figcaption></figure>

plot_model(xmdl.Optimal, type="emm", terms=c("Cond", "Age"), ci lvl = NA, dodge = 0) +

3.3.4.3.1.3 Condition by Age

## Ignoring unknown labels:

## * linetype : "Age"

## * shape : "Age"
3.3. LINEAR MIXED-EFFECTS MODELS. WHY RANDOM EFFECTS MATTER205

<figure><img src="image_79.png" /></figure>

3.3.4.3.2 Random effects

plot_model(xmdl.Optimal, type="pred", terms=c("Subj"), pred.type="re", ci lvl = NA, dodge = 0) +

Predicted values of Looking Time

<figure><img src="image_80.png" /></figure>

3.3.4.3.2.1 Subject
plot_model(xmdl.Optimal, type="pred", terms=c("Cond", "Subj"), pred.type="re", ci lvl =

3.3.4.3.2.2 Subject by Condition

## Ignoring unknown labels:

## * linetype : "Subj"

## * shape : "Subj"

<figure><img src="image_81.png" /></figure>

plot_model(xmdl.Optimal, type="pred", terms=c("Age", "Subj"), pred.type="re", ci lvl =

3.3.4.3.2.3 Subject by Age

## Ignoring unknown labels:

## * linetype : "Subj"

## * shape : "Subj"
3.3. LINEAR MIXED-EFFECTS MODELS. WHY RANDOM EFFECTS MATTER207

<figure><img src="image_82.png" /></figure>

plot_model(xmdl.Optimal, type="pred", terms=c("Item"), pred.type="re", ci lvl = NA, dodge = 0) +

Predicted values of Looking Time

<figure><img src="image_83.png" /></figure>

3.3.4.3.2.4 Item
plot_model(xmdl.Optimal, type="pred", terms=c("Cond", "Item"), pred.type="re", ci lvl =

3.3.4.3.2.5 Item by Cond

## Ignoring unknown labels:

## * linetype : "Item"

## * shape : "Item"

<figure><img src="image_84.png" /></figure>

plot_model(xmdl.Optimal, type="pred", terms=c("Age", "Item"), pred.type="re", ci lvl =

3.3.4.3.2.6 Item by Age

## Ignoring unknown labels:

## * linetype : "Item"

## * shape : "Item"
3.3. LINEAR MIXED-EFFECTS MODELS. WHY RANDOM EFFECTS MATTER209

<figure><img src="image_85.png" /></figure>

plot_model(xmdl.Optimal, type="pred", terms=c("Cond", "Item", "Age"), pred.type="re", ci lvl = NA

3.3.4.3.2.7 Item by Cond facetted by Age

## Ignoring unknown labels:

## * linetype : "Item"

## * shape : "Item"
<figure><img src="image_86.png" /></figure>

plot_model(xmdl.Optimal, type="pred", terms=c("Subj", "Item"), pred.type="re", ci.lvl =

3.3.4.3.2.8 Subject by Item

## Ignoring unknown labels:

## * linetype : "Item"

## * shape : "Item"
3.3. LINEAR MIXED-EFFECTS MODELS. WHY RANDOM EFFECTS MATTER211

<figure><img src="image_87.png" /></figure>

plot_model(xmdl.Optimal, type="pred", terms=c("Subj", "Item", "Cond"), pred.type="re", ci lvl = 1

3.3.4.3.2.9 Subject by Item facetted by Cond

## Ignoring unknown labels:

## * linetype : "Item"

## * shape : "Item"
<figure><img src="image_88.png" /></figure>

plot_model(xmdl.Optimal, type="pred", terms=c("Subj", "Item", "Age"), pred.type="re",

3.3.4.3.2.10 Subject by Item facetted by Age

## Ignoring unknown labels:

## * linetype : "Item"

## * shape : "Item"
3.3. LINEAR MIXED-EFFECTS MODELS. WHY RANDOM EFFECTS MATTER213

<figure><img src="image_89.png" /></figure>

3.3.4.3.3 With Lattice

dotplot(ranef(xmdl.Optimal))$Subj[1]
Subj

<figure><img src="image_90.png" /></figure>

3.3.4.3.3.1 Subject Intercepts

dotplot(ranef(xmdl.Optimal), xlim = c(-350, 350))$Subj[2]

Subj

<figure><img src="image_91.png" /></figure>

3.3.4.3.3.2 Subject Slopes
3.3. LINEAR MIXED-EFFECTS MODELS. WHY RANDOM EFFECTS MATTER215

dotplot(ranef(xmdl.Optimal))$Item[1]

<figure><img src="image_92.png" /></figure>

3.3.4.3.3.3 Item Intercepts

dotplot(ranef(xmdl.Optimal), xlim = c(-150, 150))$Item[2]
Item

<figure><img src="image_93.png" /></figure>

3.3.4.3.3.4 Item Slopes for Cond

dotplot(ranef(xmdl.Optimal), xlim = c(-150, 150))$Item[3]

Item

<figure><img src="image_94.png" /></figure>

3.3.4.3.3.5 Item Slopes for Age

I hope this tutorial helped you to uncover the role of participants and items and
what they can tell us beyond the fixed effect!

### 3.3.5 Conclusion

In this simulated dataset, we showed how to use Linear Mixed-effects Models, and used a specific approach, named “maximal specification model”. This maximal specification model uses both random intercepts and random slopes. Usually, on any dataset, you are required to formally assess the need for Random slopes.

As a rule of thumb: Any within-subject (or within-item) should be tested for a potential inclusion as a random slope.

Fixed effects provide averages over all observations, even when using mixed effects regressions; we need to explore what random effects (intercepts and slopes) tell us.

In this example, we see that many subjects vary beyond the fixed effect; Standard Errors are not enough to quantify this type of variation. The same is true for items that are not explored routinely!

The approach above used a maximal specification model. This of course depends on the dataset you are working on and requires formal testing. See the package RePsychLing that is on github. The function RePCA is part of the package lme4. You can use it to verify if the model structure is appropriate. However, lme4 will give you directly a warning “is singular” that you can interpret as “over specified model”.

## 3.4 Generalised Linear Mixed-effects Models

Here we will look at an example when the outcome is binary. This simulated data is structured as follows. We asked one participant to listen to 165 sentences, and to judge whether these are “grammatical” or “ungrammatical”. There were 105 sentences that were “grammatical” and 60 “ungrammatical”. This fictitious example can apply in any other situation. Let’s think Geography: 165 lands: 105 “flat” and 60 “non-flat”, etc. This applies to any case where you need to “categorise” the outcome into two groups.

### 3.4.1 GLMM - Categorical predictors

Let’s run a first GLMM (Generalised Linear Model).

#### 3.4.1.1 Simulating a new dataset

```r
grammatical2 <- as.data.frame(
  cbind("participant" = c("participant" = rep("p1", 165), rep("p2", 165)),
        "grammaticality" = c("grammatical" = rep("grammatical", 105),
```
```
"ungrammatical" = rep("ungrammatical", 60),
"grammatical" = rep("grammatical", 105),
"ungrammatical" = rep("ungrammatical", 60)),
"response" = c("yes" = rep("yes", 100),
              "no" = rep("no", 5),
              "yes" = rep("yes", 10),
              "no" = rep("no", 50),
              "yes" = rep("yes", 90),
              "no" = rep("no", 15),
              "yes" = rep("yes", 30),
              "no" = rep("no", 30))),
row.names = FALSE)
grammatical2 %>
head(10)
```

### participant grammaticality response

<table><tr><td>## 1</td><td>p1</td><td>grammatical</td><td>yes</td></tr><tr><td>## 2</td><td>p1</td><td>grammatical</td><td>yes</td></tr><tr><td>## 3</td><td>p1</td><td>grammatical</td><td>yes</td></tr><tr><td>## 4</td><td>p1</td><td>grammatical</td><td>yes</td></tr><tr><td>## 5</td><td>p1</td><td>grammatical</td><td>yes</td></tr><tr><td>## 6</td><td>p1</td><td>grammatical</td><td>yes</td></tr><tr><td>## 7</td><td>p1</td><td>grammatical</td><td>yes</td></tr><tr><td>## 8</td><td>p1</td><td>grammatical</td><td>yes</td></tr><tr><td>## 9</td><td>p1</td><td>grammatical</td><td>yes</td></tr><tr><td>## 10</td><td>p1</td><td>grammatical</td><td>yes</td></tr></table>

### 3.4.1.2 Manipulations and a table

```
grammatical2 <- grammatical2 %>
mutate(response = factor(response, levels = c("no", "yes")),
        grammaticality = factor(grammaticality, levels = c("ungrammatical", "grammatical")))

grammatical2 %>
select(response, grammaticality) %>
group_by(response, grammaticality) %>
table()
```

### grammaticality

### response ungrammatical grammatical

### no 80 20

### yes 40 190
### 3.4.1.3 Model estimation and results

#### 3.4.1.3.1 Random Intercepts
The results below show the logodds for our model.

```
mdl.glmm <- grammatical2 %>

  glmer(response ~ grammaticality + (1 | participant), data = ., family = binomial)
summary(mdl.glmm)
```

```
## Generalized linear mixed model fit by maximum likelihood (Laplace
## Approximation) [glmerMod]
```

```
## Family: binomial ( logit )
## Formula: response ~ grammaticality + (1 | participant)
```

```
## Data: .
```

```
##
```

```
##      AIC      BIC   logLik -2*log(L)  df.resid
```

```
##      290.8    302.2  -142.4      284.8      327
```

```
##
```

```
## Scaled residuals:
```

```
##       Min      1Q   Median     3Q     Max
```

```
## -3.1221 -0.6985  0.3203  0.3280  1.4317
```

```
##
```

```
## Random effects:
```

```
##      Groups      Name          Variance Std.Dev.
```

```
## participant (Intercept) 0.005276 0.07264
```

```
## Number of obs: 330, groups: participant, 2
```

```
##
```

```
## Fixed effects:
```

```
##                 Estimate Std. Error z value Pr(>\|z\|)
```

```
## (Intercept)          -0.6940      0.2006  -3.459  0.000542 ***
```

```
## grammaticalitygrammatical  2.9475      0.3060   9.632  < 2e-16 ***
```

```
## ---
```

```
## Signif. codes: 0 '**' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
```

```
##
```

```
## Correlation of Fixed Effects:
```

```
##          (Intr)
```

```
## grmmtc1tygr -0.615
```

#### 3.4.1.3.2 Random Slopes
The results below show the logodds for our model.

```
mdl.glmmSlope <- grammatical2 %>

  glmer(response ~ grammaticality + (grammaticality | participant), data = ., family = binomial)
summary(mdl.glmmSlope)
```

```
## Generalized linear mixed model fit by maximum likelihood (Laplace
## Approximation) [glmerMod]
```

```
```
## Family: binomial ( logit )
## Formula: response ~ grammaticality + (grammaticality | participant)

## Data: .

##

##      AIC      BIC    logLik -2*log(L)  df.resid
##   280.3    299.2   -135.1     270.3      325

##

## Scaled residuals:

##      Min      1Q   Median      3Q     Max
## -4.2750 -0.4702  0.2339  0.3998  2.1269

##

## Random effects:

##      Groups Name                 Variance Std.Dev. Corr
##  participant (Intercept)        0.5992  0.774
##      grammaticalitygrammatical 1.8089  1.345  -1.00

## Number of obs: 330, groups: participant, 2

##

## Fixed effects:

##                 Estimate Std. Error z value Pr(>|z|)
## (Intercept)          -0.7951  0.5875  -1.353  0.17593
## grammaticalitygrammatical  3.1739  1.0099  3.143  0.00167 **

## ---

## Signif. codes: 0 '**' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

##

## Correlation of Fixed Effects:

##      (Intr)

## grmmtcltygr -0.955

## optimizer (Nelder_Mead) convergence code: 0 (OK)

## boundary (singular) fit: see help('isSingular')

### 3.4.1.3.3 Random Slopes decorrelated
The results below show the log-godds for our model.

mdl.glmmSlopeDec <- grammaticality2 %>%

glmer(response ~ grammaticality + (grammaticality | participant), data = ., family = glmerMod)
summary(mdl.glmmSlopeDec)

## Generalized linear mixed model fit by maximum likelihood (Laplace

## Approximation) [glmerMod]

## Family: binomial ( logit )

## Formula: response ~ grammaticality + (grammaticality || participant)

## Data: .

##

##      AIC      BIC    logLik -2*log(L)  df.resid
##   282.3    305.0   -135.1     270.3      324

##
## Scaled residuals:

Min 1Q Median 3Q Max
-4.2749 -0.4702 0.2339 0.3998 2.1269

##

## Random effects:

Groups Name Variance Std.Dev. Corr
participant (Intercept) 1.189e-10 1.091e-05
participant.1 grammaticalityungrammatical 5.992e-01 7.741e-01
grammaticalitygrammatical 3.259e-01 5.709e-01 -1.00
Number of obs: 330, groups: participant, 2

##

## Fixed effects:

Estimate Std. Error z value Pr(>|z|)
(Intercept) -0.7951 0.5874 -1.353 0.17591
grammaticalitygrammatical 3.1738 1.0098 3.143 0.00167 **

## ---

Signif. codes: 0 '**' 0.001 '**' 0.01 '**' 0.05 '**' 0.1 '**' 1

## Correlation of Fixed Effects:

(Intr)

grmmtbltygr -0.955

optimizer (Nelder_Mead) convergence code: 0 (OK)

boundary (singular) fit: see help('isSingular')

### 3.4.1.4 Model comparison

anova(mdl.glmm, mdl.glmmSlope)

## Data: .

## Models:

## mdl.glmm: response ~ grammaticality + (1 | participant)

## mdl.glmmSlope: response ~ grammaticality + (grammaticality | participant)

npar AIC BIC logLik -2*log(L) Chisq Df Pr(>Chisq)

## mdl.glmm 3 290.84 302.24 -142.42 284.84

## mdl.glmmSlope 5 280.25 299.25 -135.13 270.25 14.584 2 0.0006811 ***

## ---

Signif. codes: 0 '**' 0.001 '**' 0.01 '**' 0.05 '**' 0.1 '**' 1

anova(mdl.glmmSlope, mdl.glmmSlopeDec)

## Data: .

## Models:

## mdl.glmmSlope: response ~ grammaticality + (grammaticality | participant)

## mdl.glmmSlopeDec: response ~ grammaticality + (grammaticality || participant)

npar AIC BIC logLik -2*log(L) Chisq Df Pr(>Chisq)

## mdl.glmmSlope 5 280.25 299.25 -135.13 270.25
## mdl.glmmSlopeDec 6 282.25 305.05 -135.13 270.25 0 1 1

The model comparisons show that the model with both random intercepts and random slopes is improving the model fit. The `Is.Singular` message tells us that there is a chance there is a complete separation in the model.

### 3.4.1.5 Getting results

```
print tab_model(mdl.glmmSlope, file = paste0("outputs/mdl.glmmSlope.html")))
htmltools::includeHTML("outputs/mdl.glmmSlope.html")
```

#### 3.4.1.5.1 Model's fit

```
fixef(mdl.glmmSlope)
```

#### 3.4.1.5.2 Fixed effects

```
## (Intercept) grammatical
## -0.7950773 3.1738527
```

```
fixef(mdl.glmmSlope)[1]
```

```
## (Intercept)
## -0.7950773
```

```
fixef(mdl.glmmSlope)[2]
```

```
## grammatical
## 3.173853
```

```
coef(mdl.glmmSlope)$`participant`[1]
```

#### 3.4.1.5.3 Random effects

```
## (Intercept)
## p1 -1.50933642
## p2 -0.05609396
```

```
coef(mdl.glmmSlope)$`participant`[2]
```

```
## grammatical
## p1 4.414908
## p2 1.889839
```

#### 3.4.1.5.4 Logodds to Odd ratios
Logodds can be modified to talk about the odds of an event.
```
exp(fixef(mdl.glmmSlope)[1])
```

```
## (Intercept)
```

```
##   0.4515463
```

```
exp(fixef(mdl.glmmSlope)[1] + fixef(mdl.glmmSlope)[2])
```

```
## (Intercept)
```

```
##   10.79168
```

### 3.4.1.5.5 LogOdds to proportions

If you want to talk about the percentage "accuracy" of our model, then we can transform our loggoddos into proportions. This shows that the proportion of "grammatical" receiving a "yes" response increases by 99% (or 95% based on our "true" coefficients).

```
plogis(fixef(mdl.glmmSlope)[1])
```

```
## (Intercept)
```

```
##   0.3110795
```

```
plogis(fixef(mdl.glmmSlope)[1] + fixef(mdl.glmmSlope)[2])
```

```
## (Intercept)
```

```
##   0.9151944
```

```
grammatical2 <- grammatical2 %>%
```

```
mutate(prob = predict(mdl.glmmSlope, type = "response"))
```

```
grammatical2 %>%
```

```
ggplot(aes(x = as.numeric(grammaticality), y = prob)) +
```

```
geom_point() +
```

```
geomSmooth(method = "glm",
```

```
method.args = list(family = "binomial"),
```

```
se = T) + themeBW(base_size = 20) +
```

```
labs(y = "Probability", x = "") +
```

```
coordCartesian(ylim = c(0,1)) +
```

```
scale_x_discrete(limits = c("Ungrammatical", "Grammatical")) +
```

```
facet_grid(~ participant, margins = TRUE, scales = "free")
```
<figure><img src="image_95.png" /><figcaption>3.4.1.5.6 Plotting</figcaption></figure>

3.4.2 GLMM - Numeric predictors

In this example, we will run a GLM model using a similar technique to that used
in Al-Tamimi (2017) and Baumann & Winter (2018). We use the package
LanguageR and the dataset English.

In the model above, we used the equation as lm(RTlexdec ~ AgeSubject). We
were interested in examining the impact of age of subject on reaction time in
a lexical decision task. In this section, we are interested in understanding how
reaction time allows to differentiate the participants based on their age. We use
AgeSubject as our outcome and RTlexdec as our predictor using the equation
glm(AgeSubject ~ RTlexdec). We usually can use RTlexdec as is, but due to a
possible quasi separation and the fact that we may want to compare coefficients
using multiple acoustic metrics, we will z-score our predictor. We run below
two models, with and without z-scoring

For the `glm` model, we need to specify `family = "binomial"`.

3.4.2.1 Without z-scoring of predictor

3.4.2.1.1 Model estimation In the english dataset, we have a random factor: “Word”. We include it here.

english2 <- english %>%
  mutate(AgeSubject = factor(AgeSubject, levels = c("young", "old")))
mdl.glmm2 <- english2 %>%
```
glmer(AgeSubject ~ RTlexdec + (1|Word), data = ., family = "binomial")
summary(mdl.glmm2)
```

### 3.4.2.1.1.1 Random Intercepts

```
## Generalized linear mixed model fit by maximum likelihood (Laplace
## Approximation) [glmerMod]
## Family: binomial ( logit )
## Formula: AgeSubject ~ RTlexdec + (1 | Word)
## Data: .
##
## AIC          BIC      logLik  -2*log(L)  df.resid
## 3151.8       3171.1    -1572.9    3145.8      4565
##
## Scaled residuals:
## Min         1Q      Median     3Q      Max
## -26.3468    -0.3058   -0.0166    0.3893    4.0750
##
## Random effects:
## Groups Name      Variance  Std.Dev.
## Word (Intercept) 1.666e-15  4.082e-08
## Number of obs: 4568, groups: Word, 2197
##
## Fixed effects:
## Estimate Std. Error z value Pr(>z|t)
## (Intercept) -128.6308    3.7966   -33.88    <2e-16 ***
## RTlexdec     19.6497     0.5798    33.89    <2e-16 ***
## ---
## Signif. codes: 0 '**' 0.001 '.*' 0.01 '.*' 0.05 '.' 0.1 '' 1
##
## Correlation of Fixed Effects:
## (Intr)
## RTlexdec -1.000
## optimizer (Nelder_Mead) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')
```

```
mdl.glmmSlope2 <- english2 %>%
  glmer(AgeSubject ~ RTlexdec + (RTlexdec|Word), data = ., family = "binomial")
summary(mdl.glmmSlope2)
```

### 3.4.2.1.1.2 Random Slopes

```
## Generalized linear mixed model fit by maximum likelihood (Laplace
## Approximation) [glmerMod]
## Family: binomial ( logit )
```
## Formula: AgeSubject ~ RTlexdec + (RTlexdec | Word)

## Data: .

##

## AIC BIC logLik -2*log(L) df.resid

## 3075.6 3107.7 -1532.8 3065.6 4563

##

## Scaled residuals:

## Min 1Q Median 3Q Max

## -2.3923 -0.2133 -0.0024 0.2512 5.8061

##

## Random effects:

## Groups Name Variance Std.Dev. Corr

## Word (Intercept) 3325.68 57.669

## RTlexdec 80.01 8.945 -1.00

## Number of obs: 4568, groups: Word, 2197

##

## Fixed effects:

## Estimate Std. Error z value Pr(>z|)

## (Intercept) -179.980 10.482 -17.17 <2e-16 ***

## RTlexdec 27.535 1.607 17.13 <2e-16 ***

## ---

## Signif. codes: 0 '**' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

##

## Correlation of Fixed Effects:

## (Intr)

## RTlexdec -1.000

## optimizer (Nelder_Mead) convergence code: 0 (OK)

## boundary (singular) fit: see help('isSingular')

### 3.4.2.2 Model comparison

anova(mdl.glmm2, mdl.glmmSlope2)

## Data: .

## Models:

## mdl.glmm2: AgeSubject ~ RTlexdec + (1 | Word)

## mdl.glmmSlope2: AgeSubject ~ RTlexdec + (RTlexdec | Word)

## npar AIC BIC logLik -2*log(L) Chisq Df Pr(>Chisq)

## mdl.glmm2 3 3151.8 3171.1 -1572.9 3145.8

## mdl.glmmSlope2 5 3075.6 3107.7 -1532.8 3065.6 80.262 2 < 2.2e-16 ***

## ---

## Signif. codes: 0 '**' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

The model comparisons show that the model with both random intercepts and random slopes is improving the model fit. The `Is.Singular` message tells us that there is a chance there is a complete separation in the model.
### 3.4.2.3 Getting results

```r
print tab_model(mdl.glmmSlope2, file = paste0("outputs/mdl.glmmSlope2.html")))
htmltools::includeHTML("outputs/mdl.glmmSlope2.html")
```

#### 3.4.2.3.1 Model's fit

```r
fixef(mdl.glmmSlope2)
```

#### 3.4.2.3.2 Fixed effects

```r
## (Intercept)      RTlexdec
## -179.97997      27.53549
```

```r
fixef(mdl.glmmSlope2) [1]
```

```r
## (Intercept)
## -179.98
```

```r
fixef(mdl.glmmSlope2) [2]
```

```r
## RTlexdec
## 27.53549
```

```r
coef(mdl.glmmSlope2)$Word [1]
```

#### 3.4.2.3.3 Random effects

```r
## (Intercept)
## ace         -183.90593
## act         -194.45238
## add         -188.40333
## age         -187.46409
## aid         -181.03495
## aide        -158.07461
## ail         -123.55216
## aim         -190.10409
## air         -200.14396
## aisle       -174.27287
## ale         -180.30489
## angst       -165.78719
## ant         -191.28906
## ape         -187.24205
## arc         -126.77945
## arch        -184.42680
## are         -182.46607
```
<table>
  <tbody>
    <tr>
      <td>## arm</td>
      <td>-217.59076</td>
    </tr>
    <tr>
      <td>## art</td>
      <td>-189.04802</td>
    </tr>
    <tr>
      <td>## ash</td>
      <td>-182.98220</td>
    </tr>
    <tr>
      <td>## ask</td>
      <td>-196.70366</td>
    </tr>
    <tr>
      <td>## ass</td>
      <td>-183.23599</td>
    </tr>
    <tr>
      <td>## axe</td>
      <td>-181.94943</td>
    </tr>
    <tr>
      <td>## babe</td>
      <td>-188.70258</td>
    </tr>
    <tr>
      <td>## back</td>
      <td>-195.42039</td>
    </tr>
    <tr>
      <td>## badge</td>
      <td>-183.01595</td>
    </tr>
    <tr>
      <td>## bag</td>
      <td>-199.54314</td>
    </tr>
    <tr>
      <td>## bail</td>
      <td>-168.15030</td>
    </tr>
    <tr>
      <td>## bait</td>
      <td>-190.95479</td>
    </tr>
    <tr>
      <td>## bale</td>
      <td>-121.78656</td>
    </tr>
    <tr>
      <td>## ball</td>
      <td>-187.58021</td>
    </tr>
    <tr>
      <td>## ban</td>
      <td>-150.32497</td>
    </tr>
    <tr>
      <td>## band</td>
      <td>-182.62443</td>
    </tr>
    <tr>
      <td>## bang</td>
      <td>-196.73783</td>
    </tr>
    <tr>
      <td>## bank</td>
      <td>-193.70561</td>
    </tr>
    <tr>
      <td>## bar</td>
      <td>-200.25188</td>
    </tr>
    <tr>
      <td>## bard</td>
      <td>-117.84681</td>
    </tr>
    <tr>
      <td>## barge</td>
      <td>-141.73048</td>
    </tr>
    <tr>
      <td>## bark</td>
      <td>-196.61578</td>
    </tr>
    <tr>
      <td>## barn</td>
      <td>-200.39050</td>
    </tr>
    <tr>
      <td>## base</td>
      <td>-192.56565</td>
    </tr>
    <tr>
      <td>## bash</td>
      <td>-180.80001</td>
    </tr>
    <tr>
      <td>## bat</td>
      <td>-199.64365</td>
    </tr>
    <tr>
      <td>## batch</td>
      <td>-189.94741</td>
    </tr>
    <tr>
      <td>## bath</td>
      <td>-193.82412</td>
    </tr>
    <tr>
      <td>## bay</td>
      <td>-189.46411</td>
    </tr>
    <tr>
      <td>## beach</td>
      <td>-185.19024</td>
    </tr>
    <tr>
      <td>## bead</td>
      <td>-168.42383</td>
    </tr>
    <tr>
      <td>## beak</td>
      <td>-133.17528</td>
    </tr>
    <tr>
      <td>## beam</td>
      <td>-180.59024</td>
    </tr>
    <tr>
      <td>## bean</td>
      <td>-182.07824</td>
    </tr>
    <tr>
      <td>## bear</td>
      <td>-213.07935</td>
    </tr>
    <tr>
      <td>## beard</td>
      <td>-196.58612</td>
    </tr>
    <tr>
      <td>## beast</td>
      <td>-181.77336</td>
    </tr>
    <tr>
      <td>## beat</td>
      <td>-189.71515</td>
    </tr>
    <tr>
      <td>## beau</td>
      <td>-154.41186</td>
    </tr>
    <tr>
      <td>## beck</td>
      <td>-91.17832</td>
    </tr>
    <tr>
      <td>## bed</td>
      <td>-188.54683</td>
    </tr>
    <tr>
      <td>## bee</td>
      <td>-198.73653</td>
    </tr>
    <tr>
      <td>## beech</td>
      <td>-126.52901</td>
    </tr>
    <tr>
      <td>## beef</td>
      <td>-211.38709</td>
    </tr>
    <tr>
      <td>## beep</td>
      <td>-190.21971</td>
    </tr>
    <tr>
      <td>## beer</td>
      <td>-198.75869</td>
    </tr>
  </tbody>
</table>
<table><tr><td>## beet</td><td>-173.58986</td></tr><tr><td>## beg</td><td>-200.94583</td></tr><tr><td>## belch</td><td>-155.10294</td></tr><tr><td>## bell</td><td>-195.09608</td></tr><tr><td>## belt</td><td>-187.26488</td></tr><tr><td>## bench</td><td>-200.14864</td></tr><tr><td>## bend</td><td>-198.78979</td></tr><tr><td>## berth</td><td>-157.88188</td></tr><tr><td>## bet</td><td>-201.03313</td></tr><tr><td>## bib</td><td>-167.68854</td></tr><tr><td>## bid</td><td>-201.07976</td></tr><tr><td>## bide</td><td>-89.33357</td></tr><tr><td>## bile</td><td>-166.74646</td></tr><tr><td>## bilge</td><td>-99.16027</td></tr><tr><td>## bill</td><td>-189.36736</td></tr><tr><td>## bin</td><td>-159.06192</td></tr><tr><td>## bind</td><td>-150.49849</td></tr><tr><td>## binge</td><td>-173.11795</td></tr><tr><td>## birch</td><td>-158.44403</td></tr><tr><td>## bird</td><td>-192.34647</td></tr><tr><td>## bit</td><td>-197.94419</td></tr><tr><td>## bitch</td><td>-186.76026</td></tr><tr><td>## bite</td><td>-200.32906</td></tr><tr><td>## blade</td><td>-194.37973</td></tr><tr><td>## blame</td><td>-188.93559</td></tr><tr><td>## blanch</td><td>-125.38813</td></tr><tr><td>## blast</td><td>-186.24327</td></tr><tr><td>## blaze</td><td>-194.63239</td></tr><tr><td>## bleat</td><td>-157.35749</td></tr><tr><td>## bleed</td><td>-185.28387</td></tr><tr><td>## bleep</td><td>-132.46422</td></tr><tr><td>## blend</td><td>-191.20349</td></tr><tr><td>## bless</td><td>-186.61600</td></tr><tr><td>## blight</td><td>-165.14486</td></tr><tr><td>## blink</td><td>-180.49654</td></tr><tr><td>## bliss</td><td>-198.34652</td></tr><tr><td>## blitz</td><td>-171.79726</td></tr><tr><td>## bloat</td><td>-177.86001</td></tr><tr><td>## blob</td><td>-171.53996</td></tr><tr><td>## block</td><td>-192.29142</td></tr><tr><td>## bloke</td><td>-115.79912</td></tr><tr><td>## blood</td><td>-189.62162</td></tr><tr><td>## bloom</td><td>-196.43342</td></tr><tr><td>## blot</td><td>-184.07464</td></tr><tr><td>## blouse</td><td>-172.69882</td></tr><tr><td>## blow</td><td>-194.93018</td></tr></table>
<table>
  <tr>
    <td>## bluff</td>
    <td>-194.80366</td>
  </tr>
  <tr>
    <td>## blur</td>
    <td>-180.40574</td>
  </tr>
  <tr>
    <td>## blush</td>
    <td>-200.80527</td>
  </tr>
  <tr>
    <td>## boar</td>
    <td>-143.98103</td>
  </tr>
  <tr>
    <td>## board</td>
    <td>-193.40371</td>
  </tr>
  <tr>
    <td>## boast</td>
    <td>-190.16576</td>
  </tr>
  <tr>
    <td>## boat</td>
    <td>-200.62991</td>
  </tr>
  <tr>
    <td>## bob</td>
    <td>-143.95566</td>
  </tr>
  <tr>
    <td>## bog</td>
    <td>-163.01171</td>
  </tr>
  <tr>
    <td>## boil</td>
    <td>-187.41753</td>
  </tr>
  <tr>
    <td>## bolt</td>
    <td>-201.12835</td>
  </tr>
  <tr>
    <td>## bomb</td>
    <td>-187.14944</td>
  </tr>
  <tr>
    <td>## bond</td>
    <td>-193.50088</td>
  </tr>
  <tr>
    <td>## bone</td>
    <td>-199.94605</td>
  </tr>
  <tr>
    <td>## boo</td>
    <td>-183.41252</td>
  </tr>
  <tr>
    <td>## book</td>
    <td>-182.65017</td>
  </tr>
  <tr>
    <td>## boom</td>
    <td>-182.31854</td>
  </tr>
  <tr>
    <td>## boon</td>
    <td>-136.22257</td>
  </tr>
  <tr>
    <td>## boost</td>
    <td>-180.50187</td>
  </tr>
  <tr>
    <td>## boot</td>
    <td>-191.30090</td>
  </tr>
  <tr>
    <td>## booth</td>
    <td>-197.22089</td>
  </tr>
  <tr>
    <td>## booze</td>
    <td>-185.34293</td>
  </tr>
  <tr>
    <td>## bore</td>
    <td>-184.45599</td>
  </tr>
  <tr>
    <td>## boss</td>
    <td>-193.25143</td>
  </tr>
  <tr>
    <td>## bough</td>
    <td>-96.02206</td>
  </tr>
  <tr>
    <td>## bounce</td>
    <td>-200.88341</td>
  </tr>
  <tr>
    <td>## bound</td>
    <td>-185.03387</td>
  </tr>
  <tr>
    <td>## bout</td>
    <td>-140.82693</td>
  </tr>
  <tr>
    <td>## bowl</td>
    <td>-185.48560</td>
  </tr>
  <tr>
    <td>## box</td>
    <td>-181.85502</td>
  </tr>
  <tr>
    <td>## boy</td>
    <td>-197.94150</td>
  </tr>
  <tr>
    <td>## brace</td>
    <td>-188.09038</td>
  </tr>
  <tr>
    <td>## brad</td>
    <td>-93.89473</td>
  </tr>
  <tr>
    <td>## brag</td>
    <td>-188.95756</td>
  </tr>
  <tr>
    <td>## braid</td>
    <td>-179.85516</td>
  </tr>
  <tr>
    <td>## brain</td>
    <td>-195.29232</td>
  </tr>
  <tr>
    <td>## brake</td>
    <td>-200.99390</td>
  </tr>
  <tr>
    <td>## bran</td>
    <td>-84.22164</td>
  </tr>
  <tr>
    <td>## branch</td>
    <td>-183.72877</td>
  </tr>
  <tr>
    <td>## brand</td>
    <td>-185.22584</td>
  </tr>
  <tr>
    <td>## brass</td>
    <td>-198.41293</td>
  </tr>
  <tr>
    <td>## brat</td>
    <td>-182.01103</td>
  </tr>
  <tr>
    <td>## brawl</td>
    <td>-174.25434</td>
  </tr>
  <tr>
    <td>## brawn</td>
    <td>-82.04808</td>
  </tr>
  <tr>
    <td>## breach</td>
    <td>-140.02970</td>
  </tr>
  <tr>
    <td>## bread</td>
    <td>-200.46399</td>
  </tr>
</table>
<table><tr><td>## break</td><td>-190.42288</td></tr><tr><td>## breast</td><td>-183.88243</td></tr><tr><td>## breath</td><td>-188.84558</td></tr><tr><td>## breed</td><td>-189.48451</td></tr><tr><td>## breeze</td><td>-199.04383</td></tr><tr><td>## brew</td><td>-192.13872</td></tr><tr><td>## bribe</td><td>-192.44277</td></tr><tr><td>## brick</td><td>-183.68374</td></tr><tr><td>## bride</td><td>-193.32446</td></tr><tr><td>## bridge</td><td>-182.66701</td></tr><tr><td>## brig</td><td>-87.00210</td></tr><tr><td>## brim</td><td>-156.28506</td></tr><tr><td>## bring</td><td>-199.97936</td></tr><tr><td>## brink</td><td>-165.33005</td></tr><tr><td>## broach</td><td>-101.67591</td></tr><tr><td>## broad</td><td>-184.14711</td></tr><tr><td>## broil</td><td>-188.83623</td></tr><tr><td>## bronze</td><td>-194.90983</td></tr><tr><td>## brooch</td><td>-144.85307</td></tr><tr><td>## brood</td><td>-111.85702</td></tr><tr><td>## brook</td><td>-138.60347</td></tr><tr><td>## broom</td><td>-200.65621</td></tr><tr><td>## broth</td><td>-105.41151</td></tr><tr><td>## brow</td><td>-168.12982</td></tr><tr><td>## bruise</td><td>-184.30588</td></tr><tr><td>## brunt</td><td>-135.10110</td></tr><tr><td>## brush</td><td>-183.22355</td></tr><tr><td>## brute</td><td>-178.24258</td></tr><tr><td>## buck</td><td>-171.40396</td></tr><tr><td>## bud</td><td>-198.25589</td></tr><tr><td>## budge</td><td>-180.94456</td></tr><tr><td>## buff</td><td>-178.05972</td></tr><tr><td>## bug</td><td>-200.45603</td></tr><tr><td>## build</td><td>-195.49856</td></tr><tr><td>## bulb</td><td>-190.58618</td></tr><tr><td>## bulge</td><td>-181.62072</td></tr><tr><td>## bulk</td><td>-201.21282</td></tr><tr><td>## bull</td><td>-192.23010</td></tr><tr><td>## bum</td><td>-185.53349</td></tr><tr><td>## bump</td><td>-180.65765</td></tr><tr><td>## bun</td><td>-181.01941</td></tr><tr><td>## bunch</td><td>-194.60407</td></tr><tr><td>## bunk</td><td>-148.84434</td></tr><tr><td>## burn</td><td>-187.44693</td></tr><tr><td>## burr</td><td>-149.28860</td></tr><tr><td>## burst</td><td>-184.95025</td></tr></table>
<table>
  <tr>
    <td>bus</td>
    <td>-195.88880</td>
  </tr>
  <tr>
    <td>bush</td>
    <td>-187.16601</td>
  </tr>
  <tr>
    <td>bust</td>
    <td>-192.71986</td>
  </tr>
  <tr>
    <td>butt</td>
    <td>-185.85764</td>
  </tr>
  <tr>
    <td>buy</td>
    <td>-197.22608</td>
  </tr>
  <tr>
    <td>buzz</td>
    <td>-191.01296</td>
  </tr>
  <tr>
    <td>cab</td>
    <td>-189.31414</td>
  </tr>
  <tr>
    <td>cad</td>
    <td>-94.64563</td>
  </tr>
  <tr>
    <td>cage</td>
    <td>-196.05196</td>
  </tr>
  <tr>
    <td>cake</td>
    <td>-197.79401</td>
  </tr>
  <tr>
    <td>calf</td>
    <td>-189.19360</td>
  </tr>
  <tr>
    <td>call</td>
    <td>-199.38304</td>
  </tr>
  <tr>
    <td>cam</td>
    <td>-179.76373</td>
  </tr>
  <tr>
    <td>camp</td>
    <td>-186.84921</td>
  </tr>
  <tr>
    <td>can</td>
    <td>-194.03450</td>
  </tr>
  <tr>
    <td>cane</td>
    <td>-182.10092</td>
  </tr>
  <tr>
    <td>cant</td>
    <td>-165.08879</td>
  </tr>
  <tr>
    <td>cap</td>
    <td>-189.91369</td>
  </tr>
  <tr>
    <td>cape</td>
    <td>-185.06189</td>
  </tr>
  <tr>
    <td>car</td>
    <td>-199.84930</td>
  </tr>
  <tr>
    <td>card</td>
    <td>-187.43885</td>
  </tr>
  <tr>
    <td>care</td>
    <td>-187.49421</td>
  </tr>
  <tr>
    <td>cart</td>
    <td>-183.78949</td>
  </tr>
  <tr>
    <td>carve</td>
    <td>-187.96568</td>
  </tr>
  <tr>
    <td>case</td>
    <td>-183.55075</td>
  </tr>
  <tr>
    <td>cash</td>
    <td>-199.32521</td>
  </tr>
  <tr>
    <td>cask</td>
    <td>-150.36261</td>
  </tr>
  <tr>
    <td>cast</td>
    <td>-191.30003</td>
  </tr>
  <tr>
    <td>caste</td>
    <td>-146.56770</td>
  </tr>
  <tr>
    <td>cat</td>
    <td>-191.56693</td>
  </tr>
  <tr>
    <td>catch</td>
    <td>-200.53959</td>
  </tr>
  <tr>
    <td>cause</td>
    <td>-191.64140</td>
  </tr>
  <tr>
    <td>cave</td>
    <td>-194.45719</td>
  </tr>
  <tr>
    <td>cease</td>
    <td>-181.37334</td>
  </tr>
  <tr>
    <td>cell</td>
    <td>-186.90544</td>
  </tr>
  <tr>
    <td>cent</td>
    <td>-184.33529</td>
  </tr>
  <tr>
    <td>chafe</td>
    <td>-75.51498</td>
  </tr>
  <tr>
    <td>chain</td>
    <td>-181.65685</td>
  </tr>
  <tr>
    <td>chair</td>
    <td>-200.40358</td>
  </tr>
  <tr>
    <td>chaise</td>
    <td>-100.81512</td>
  </tr>
  <tr>
    <td>chalk</td>
    <td>-196.17666</td>
  </tr>
  <tr>
    <td>champ</td>
    <td>-191.66872</td>
  </tr>
  <tr>
    <td>chance</td>
    <td>-200.93094</td>
  </tr>
  <tr>
    <td>change</td>
    <td>-192.45362</td>
  </tr>
  <tr>
    <td>chant</td>
    <td>-185.03447</td>
  </tr>
  <tr>
    <td>chap</td>
    <td>-177.44020</td>
  </tr>
</table>
<table>
  <tr>
    <td>## char</td>
    <td>-68.46758</td>
  </tr>
  <tr>
    <td>## charge</td>
    <td>-194.79495</td>
  </tr>
  <tr>
    <td>## charm</td>
    <td>-200.86638</td>
  </tr>
  <tr>
    <td>## chart</td>
    <td>-197.81125</td>
  </tr>
  <tr>
    <td>## chase</td>
    <td>-200.24425</td>
  </tr>
  <tr>
    <td>## chat</td>
    <td>-189.45649</td>
  </tr>
  <tr>
    <td>## cheat</td>
    <td>-190.39801</td>
  </tr>
  <tr>
    <td>## check</td>
    <td>-198.39310</td>
  </tr>
  <tr>
    <td>## cheek</td>
    <td>-184.48965</td>
  </tr>
  <tr>
    <td>## cheer</td>
    <td>-200.34693</td>
  </tr>
  <tr>
    <td>## cheese</td>
    <td>-193.36714</td>
  </tr>
  <tr>
    <td>## chef</td>
    <td>-196.11278</td>
  </tr>
  <tr>
    <td>## chess</td>
    <td>-188.22427</td>
  </tr>
  <tr>
    <td>## chest</td>
    <td>-189.05611</td>
  </tr>
  <tr>
    <td>## chew</td>
    <td>-198.32585</td>
  </tr>
  <tr>
    <td>## chide</td>
    <td>-91.71206</td>
  </tr>
  <tr>
    <td>## chief</td>
    <td>-192.85386</td>
  </tr>
  <tr>
    <td>## child</td>
    <td>-195.18982</td>
  </tr>
  <tr>
    <td>## chime</td>
    <td>-184.57576</td>
  </tr>
  <tr>
    <td>## chin</td>
    <td>-181.01093</td>
  </tr>
  <tr>
    <td>## chip</td>
    <td>-199.00443</td>
  </tr>
  <tr>
    <td>## chive</td>
    <td>-123.44145</td>
  </tr>
  <tr>
    <td>## choice</td>
    <td>-197.97144</td>
  </tr>
  <tr>
    <td>## choir</td>
    <td>-192.00608</td>
  </tr>
  <tr>
    <td>## choke</td>
    <td>-186.05490</td>
  </tr>
  <tr>
    <td>## chomp</td>
    <td>-121.12000</td>
  </tr>
  <tr>
    <td>## choose</td>
    <td>-193.94850</td>
  </tr>
  <tr>
    <td>## chop</td>
    <td>-218.63852</td>
  </tr>
  <tr>
    <td>## chord</td>
    <td>-171.56332</td>
  </tr>
  <tr>
    <td>## chore</td>
    <td>-176.05107</td>
  </tr>
  <tr>
    <td>## chow</td>
    <td>-129.50781</td>
  </tr>
  <tr>
    <td>## chrome</td>
    <td>-172.35499</td>
  </tr>
  <tr>
    <td>## chuck</td>
    <td>-108.07041</td>
  </tr>
  <tr>
    <td>## chum</td>
    <td>-94.27296</td>
  </tr>
  <tr>
    <td>## chump</td>
    <td>-146.09800</td>
  </tr>
  <tr>
    <td>## chunk</td>
    <td>-181.15673</td>
  </tr>
  <tr>
    <td>## church</td>
    <td>-198.07686</td>
  </tr>
  <tr>
    <td>## churn</td>
    <td>-168.15092</td>
  </tr>
  <tr>
    <td>## chute</td>
    <td>-135.57633</td>
  </tr>
  <tr>
    <td>## cinch</td>
    <td>-132.48822</td>
  </tr>
  <tr>
    <td>## cite</td>
    <td>-169.39440</td>
  </tr>
  <tr>
    <td>## claim</td>
    <td>-183.59400</td>
  </tr>
  <tr>
    <td>## clam</td>
    <td>-183.37827</td>
  </tr>
  <tr>
    <td>## clamp</td>
    <td>-180.45165</td>
  </tr>
  <tr>
    <td>## clan</td>
    <td>-150.00296</td>
  </tr>
  <tr>
    <td>## lang</td>
    <td>-173.81098</td>
  </tr>
</table>
<table>
  <tr>
    <td>## clap</td>
    <td>-207.24220</td>
  </tr>
  <tr>
    <td>## clash</td>
    <td>-181.86249</td>
  </tr>
  <tr>
    <td>## class</td>
    <td>-193.98180</td>
  </tr>
  <tr>
    <td>## clause</td>
    <td>-133.02072</td>
  </tr>
  <tr>
    <td>## claw</td>
    <td>-187.57444</td>
  </tr>
  <tr>
    <td>## clay</td>
    <td>-196.65089</td>
  </tr>
  <tr>
    <td>## cleat</td>
    <td>-83.63746</td>
  </tr>
  <tr>
    <td>## clench</td>
    <td>-142.35169</td>
  </tr>
  <tr>
    <td>## clerk</td>
    <td>-183.34216</td>
  </tr>
  <tr>
    <td>## click</td>
    <td>-190.02281</td>
  </tr>
  <tr>
    <td>## cliff</td>
    <td>-195.01134</td>
  </tr>
  <tr>
    <td>## climb</td>
    <td>-199.07735</td>
  </tr>
  <tr>
    <td>## clinch</td>
    <td>-122.08349</td>
  </tr>
  <tr>
    <td>## cling</td>
    <td>-187.60078</td>
  </tr>
  <tr>
    <td>## clip</td>
    <td>-218.89310</td>
  </tr>
  <tr>
    <td>## cloak</td>
    <td>-184.24439</td>
  </tr>
  <tr>
    <td>## clock</td>
    <td>-194.97953</td>
  </tr>
  <tr>
    <td>## clod</td>
    <td>-130.05891</td>
  </tr>
  <tr>
    <td>## clog</td>
    <td>-147.25097</td>
  </tr>
  <tr>
    <td>## clot</td>
    <td>-180.13859</td>
  </tr>
  <tr>
    <td>## cloth</td>
    <td>-184.46511</td>
  </tr>
  <tr>
    <td>## cloud</td>
    <td>-187.55839</td>
  </tr>
  <tr>
    <td>## clout</td>
    <td>-174.13905</td>
  </tr>
  <tr>
    <td>## clove</td>
    <td>-131.16563</td>
  </tr>
  <tr>
    <td>## clown</td>
    <td>-196.03988</td>
  </tr>
  <tr>
    <td>## club</td>
    <td>-180.83260</td>
  </tr>
  <tr>
    <td>## cluck</td>
    <td>-124.64114</td>
  </tr>
  <tr>
    <td>## clump</td>
    <td>-139.14257</td>
  </tr>
  <tr>
    <td>## clutch</td>
    <td>-185.24986</td>
  </tr>
  <tr>
    <td>## coach</td>
    <td>-198.34055</td>
  </tr>
  <tr>
    <td>## coal</td>
    <td>-200.14164</td>
  </tr>
  <tr>
    <td>## coast</td>
    <td>-199.03566</td>
  </tr>
  <tr>
    <td>## coat</td>
    <td>-184.64238</td>
  </tr>
  <tr>
    <td>## coax</td>
    <td>-170.23921</td>
  </tr>
  <tr>
    <td>## cock</td>
    <td>-178.45820</td>
  </tr>
  <tr>
    <td>## cod</td>
    <td>-174.57753</td>
  </tr>
  <tr>
    <td>## code</td>
    <td>-180.97523</td>
  </tr>
  <tr>
    <td>## coil</td>
    <td>-181.77305</td>
  </tr>
  <tr>
    <td>## coin</td>
    <td>-193.51354</td>
  </tr>
  <tr>
    <td>## coke</td>
    <td>-187.51022</td>
  </tr>
  <tr>
    <td>## colt</td>
    <td>-164.12220</td>
  </tr>
  <tr>
    <td>## comb</td>
    <td>-194.19489</td>
  </tr>
  <tr>
    <td>## come</td>
    <td>-191.11122</td>
  </tr>
  <tr>
    <td>## cone</td>
    <td>-180.49716</td>
  </tr>
  <tr>
    <td>## cook</td>
    <td>-194.54499</td>
  </tr>
  <tr>
    <td>## coop</td>
    <td>-132.64990</td>
  </tr>
</table>
<table><tr><td>cop</td><td>-187.59229</td></tr><tr><td>cope</td><td>-190.58579</td></tr><tr><td>cord</td><td>-196.17560</td></tr><tr><td>core</td><td>-188.10518</td></tr><tr><td>cork</td><td>-199.57276</td></tr><tr><td>corn</td><td>-192.90891</td></tr><tr><td>corps</td><td>-164.00444</td></tr><tr><td>corpse</td><td>-189.23185</td></tr><tr><td>cost</td><td>-195.36964</td></tr><tr><td>cot</td><td>-156.64105</td></tr><tr><td>couch</td><td>-197.45139</td></tr><tr><td>cough</td><td>-187.03208</td></tr><tr><td>count</td><td>-217.84091</td></tr><tr><td>coup</td><td>-130.69606</td></tr><tr><td>coupe</td><td>-131.78313</td></tr><tr><td>course</td><td>-192.21289</td></tr><tr><td>court</td><td>-199.68152</td></tr><tr><td>cove</td><td>-174.66380</td></tr><tr><td>cow</td><td>-207.93440</td></tr><tr><td>cowl</td><td>-79.16103</td></tr><tr><td>cox</td><td>-185.92867</td></tr><tr><td>crab</td><td>-187.65680</td></tr><tr><td>crack</td><td>-190.65621</td></tr><tr><td>craft</td><td>-190.62081</td></tr><tr><td>crag</td><td>-133.96321</td></tr><tr><td>cram</td><td>-171.49642</td></tr><tr><td>cramp</td><td>-183.33555</td></tr><tr><td>crane</td><td>-179.95949</td></tr><tr><td>crank</td><td>-181.54295</td></tr><tr><td>crap</td><td>-186.18659</td></tr><tr><td>crash</td><td>-199.75401</td></tr><tr><td>crate</td><td>-160.10062</td></tr><tr><td>crave</td><td>-180.76333</td></tr><tr><td>crawl</td><td>-190.86481</td></tr><tr><td>craze</td><td>-184.42817</td></tr><tr><td>creak</td><td>-180.55221</td></tr><tr><td>cream</td><td>-190.42547</td></tr><tr><td>crease</td><td>-141.98035</td></tr><tr><td>creed</td><td>-187.18248</td></tr><tr><td>creek</td><td>-182.42283</td></tr><tr><td>creep</td><td>-193.43466</td></tr><tr><td>crepe</td><td>-126.11991</td></tr><tr><td>crest</td><td>-182.43332</td></tr><tr><td>crew</td><td>-191.06474</td></tr><tr><td>crime</td><td>-181.11049</td></tr><tr><td>croak</td><td>-161.38980</td></tr></table>
<table>
  <tr>
    <td>crone</td>
    <td>-165.66314</td>
  </tr>
  <tr>
    <td>crook</td>
    <td>-191.27333</td>
  </tr>
  <tr>
    <td>croon</td>
    <td>-78.44560</td>
  </tr>
  <tr>
    <td>crop</td>
    <td>-192.24369</td>
  </tr>
  <tr>
    <td>cross</td>
    <td>-188.28667</td>
  </tr>
  <tr>
    <td>crouch</td>
    <td>-180.25490</td>
  </tr>
  <tr>
    <td>crow</td>
    <td>-194.60014</td>
  </tr>
  <tr>
    <td>crowd</td>
    <td>-184.34005</td>
  </tr>
  <tr>
    <td>crown</td>
    <td>-196.03991</td>
  </tr>
  <tr>
    <td>crumb</td>
    <td>-196.51806</td>
  </tr>
  <tr>
    <td>crunch</td>
    <td>-180.84114</td>
  </tr>
  <tr>
    <td>crush</td>
    <td>-195.22073</td>
  </tr>
  <tr>
    <td>crust</td>
    <td>-200.53826</td>
  </tr>
  <tr>
    <td>crutch</td>
    <td>-179.71648</td>
  </tr>
  <tr>
    <td>crux</td>
    <td>-100.86016</td>
  </tr>
  <tr>
    <td>cry</td>
    <td>-189.14185</td>
  </tr>
  <tr>
    <td>crypt</td>
    <td>-178.51140</td>
  </tr>
  <tr>
    <td>cub</td>
    <td>-175.90026</td>
  </tr>
  <tr>
    <td>cube</td>
    <td>-197.38293</td>
  </tr>
  <tr>
    <td>cud</td>
    <td>-96.53218</td>
  </tr>
  <tr>
    <td>cue</td>
    <td>-187.12064</td>
  </tr>
  <tr>
    <td>cuff</td>
    <td>-155.37406</td>
  </tr>
  <tr>
    <td>cull</td>
    <td>-140.84171</td>
  </tr>
  <tr>
    <td>cult</td>
    <td>-178.16884</td>
  </tr>
  <tr>
    <td>cup</td>
    <td>-198.20140</td>
  </tr>
  <tr>
    <td>cur</td>
    <td>-180.14039</td>
  </tr>
  <tr>
    <td>curb</td>
    <td>-180.74474</td>
  </tr>
  <tr>
    <td>curd</td>
    <td>-146.87155</td>
  </tr>
  <tr>
    <td>cure</td>
    <td>-183.56937</td>
  </tr>
  <tr>
    <td>curl</td>
    <td>-196.35512</td>
  </tr>
  <tr>
    <td>curse</td>
    <td>-192.69476</td>
  </tr>
  <tr>
    <td>curve</td>
    <td>-194.28198</td>
  </tr>
  <tr>
    <td>cusp</td>
    <td>-149.77829</td>
  </tr>
  <tr>
    <td>cut</td>
    <td>-199.67885</td>
  </tr>
  <tr>
    <td>cyst</td>
    <td>-89.16689</td>
  </tr>
  <tr>
    <td>czar</td>
    <td>-91.18242</td>
  </tr>
  <tr>
    <td>dad</td>
    <td>-196.62455</td>
  </tr>
  <tr>
    <td>dale</td>
    <td>-105.53136</td>
  </tr>
  <tr>
    <td>dam</td>
    <td>-173.80358</td>
  </tr>
  <tr>
    <td>dame</td>
    <td>-162.49351</td>
  </tr>
  <tr>
    <td>damn</td>
    <td>-181.66803</td>
  </tr>
  <tr>
    <td>damp</td>
    <td>-209.91264</td>
  </tr>
  <tr>
    <td>dance</td>
    <td>-200.63086</td>
  </tr>
  <tr>
    <td>dare</td>
    <td>-200.39417</td>
  </tr>
  <tr>
    <td>darn</td>
    <td>-168.02181</td>
  </tr>
  <tr>
    <td>dash</td>
    <td>-190.99587</td>
  </tr>
</table>
<table>
  <tr>
    <td>## date</td>
    <td>-183.79488</td>
  </tr>
  <tr>
    <td>## daunt</td>
    <td>-133.97389</td>
  </tr>
  <tr>
    <td>## dawn</td>
    <td>-190.14072</td>
  </tr>
  <tr>
    <td>## deal</td>
    <td>-201.01035</td>
  </tr>
  <tr>
    <td>## dean</td>
    <td>-168.18573</td>
  </tr>
  <tr>
    <td>## dearth</td>
    <td>-148.41103</td>
  </tr>
  <tr>
    <td>## debt</td>
    <td>-193.93207</td>
  </tr>
  <tr>
    <td>## deck</td>
    <td>-201.15082</td>
  </tr>
  <tr>
    <td>## deed</td>
    <td>-191.01543</td>
  </tr>
  <tr>
    <td>## deem</td>
    <td>-91.13100</td>
  </tr>
  <tr>
    <td>## deer</td>
    <td>-196.33211</td>
  </tr>
  <tr>
    <td>## dell</td>
    <td>-80.69776</td>
  </tr>
  <tr>
    <td>## den</td>
    <td>-180.44026</td>
  </tr>
  <tr>
    <td>## dent</td>
    <td>-180.65280</td>
  </tr>
  <tr>
    <td>## desk</td>
    <td>-201.03569</td>
  </tr>
  <tr>
    <td>## dial</td>
    <td>-183.48571</td>
  </tr>
  <tr>
    <td>## dice</td>
    <td>-188.75710</td>
  </tr>
  <tr>
    <td>## die</td>
    <td>-189.10200</td>
  </tr>
  <tr>
    <td>## dig</td>
    <td>-197.56064</td>
  </tr>
  <tr>
    <td>## dike</td>
    <td>-94.58259</td>
  </tr>
  <tr>
    <td>## dill</td>
    <td>-137.67789</td>
  </tr>
  <tr>
    <td>## dime</td>
    <td>-182.62316</td>
  </tr>
  <tr>
    <td>## din</td>
    <td>-177.53529</td>
  </tr>
  <tr>
    <td>## dine</td>
    <td>-165.61647</td>
  </tr>
  <tr>
    <td>## dint</td>
    <td>-57.00731</td>
  </tr>
  <tr>
    <td>## dip</td>
    <td>-191.20058</td>
  </tr>
  <tr>
    <td>## dirge</td>
    <td>-163.84647</td>
  </tr>
  <tr>
    <td>## dirt</td>
    <td>-196.81738</td>
  </tr>
  <tr>
    <td>## disc</td>
    <td>-180.40030</td>
  </tr>
  <tr>
    <td>## dish</td>
    <td>-209.01026</td>
  </tr>
  <tr>
    <td>## ditch</td>
    <td>-181.87106</td>
  </tr>
  <tr>
    <td>## dive</td>
    <td>-185.07340</td>
  </tr>
  <tr>
    <td>## do</td>
    <td>-195.02990</td>
  </tr>
  <tr>
    <td>## dock</td>
    <td>-215.99127</td>
  </tr>
  <tr>
    <td>## dodge</td>
    <td>-184.76229</td>
  </tr>
  <tr>
    <td>## doe</td>
    <td>-161.63446</td>
  </tr>
  <tr>
    <td>## dog</td>
    <td>-194.18373</td>
  </tr>
  <tr>
    <td>## dole</td>
    <td>-171.96681</td>
  </tr>
  <tr>
    <td>## doll</td>
    <td>-181.98804</td>
  </tr>
  <tr>
    <td>## dome</td>
    <td>-179.91678</td>
  </tr>
  <tr>
    <td>## doom</td>
    <td>-181.66542</td>
  </tr>
  <tr>
    <td>## door</td>
    <td>-198.07026</td>
  </tr>
  <tr>
    <td>## dope</td>
    <td>-183.56799</td>
  </tr>
  <tr>
    <td>## dose</td>
    <td>-182.10807</td>
  </tr>
  <tr>
    <td>## doubt</td>
    <td>-191.71819</td>
  </tr>
  <tr>
    <td>## dough</td>
    <td>-190.01009</td>
  </tr>
</table>
<table>
  <tr>
    <td>## douse</td>
    <td>-87.93434</td>
  </tr>
  <tr>
    <td>## draft</td>
    <td>-185.61917</td>
  </tr>
  <tr>
    <td>## drag</td>
    <td>-199.16559</td>
  </tr>
  <tr>
    <td>## drain</td>
    <td>-186.91320</td>
  </tr>
  <tr>
    <td>## drake</td>
    <td>-128.99536</td>
  </tr>
  <tr>
    <td>## dram</td>
    <td>-61.66574</td>
  </tr>
  <tr>
    <td>## drape</td>
    <td>-170.05545</td>
  </tr>
  <tr>
    <td>## draught</td>
    <td>-176.00763</td>
  </tr>
  <tr>
    <td>## draw</td>
    <td>-186.86532</td>
  </tr>
  <tr>
    <td>## drawl</td>
    <td>-181.59201</td>
  </tr>
  <tr>
    <td>## dread</td>
    <td>-176.26934</td>
  </tr>
  <tr>
    <td>## dream</td>
    <td>-200.44281</td>
  </tr>
  <tr>
    <td>## dress</td>
    <td>-189.73487</td>
  </tr>
  <tr>
    <td>## drift</td>
    <td>-180.27390</td>
  </tr>
  <tr>
    <td>## drill</td>
    <td>-195.81357</td>
  </tr>
  <tr>
    <td>## drink</td>
    <td>-198.81291</td>
  </tr>
  <tr>
    <td>## drip</td>
    <td>-198.69315</td>
  </tr>
  <tr>
    <td>## drive</td>
    <td>-197.67095</td>
  </tr>
  <tr>
    <td>## drone</td>
    <td>-178.40936</td>
  </tr>
  <tr>
    <td>## droop</td>
    <td>-122.89942</td>
  </tr>
  <tr>
    <td>## drop</td>
    <td>-191.56759</td>
  </tr>
  <tr>
    <td>## dross</td>
    <td>-176.57875</td>
  </tr>
  <tr>
    <td>## drought</td>
    <td>-167.63177</td>
  </tr>
  <tr>
    <td>## drove</td>
    <td>-176.16415</td>
  </tr>
  <tr>
    <td>## drown</td>
    <td>-181.05452</td>
  </tr>
  <tr>
    <td>## drum</td>
    <td>-194.35796</td>
  </tr>
  <tr>
    <td>## duck</td>
    <td>-216.69012</td>
  </tr>
  <tr>
    <td>## duct</td>
    <td>-126.54745</td>
  </tr>
  <tr>
    <td>## dud</td>
    <td>-129.74875</td>
  </tr>
  <tr>
    <td>## duel</td>
    <td>-188.71094</td>
  </tr>
  <tr>
    <td>## dug</td>
    <td>-186.27951</td>
  </tr>
  <tr>
    <td>## duke</td>
    <td>-180.96454</td>
  </tr>
  <tr>
    <td>## dump</td>
    <td>-191.35165</td>
  </tr>
  <tr>
    <td>## dun</td>
    <td>-180.28043</td>
  </tr>
  <tr>
    <td>## dune</td>
    <td>-177.33480</td>
  </tr>
  <tr>
    <td>## dung</td>
    <td>-98.89113</td>
  </tr>
  <tr>
    <td>## dunk</td>
    <td>-151.71047</td>
  </tr>
  <tr>
    <td>## dusk</td>
    <td>-190.12137</td>
  </tr>
  <tr>
    <td>## dust</td>
    <td>-199.54212</td>
  </tr>
  <tr>
    <td>## dwarf</td>
    <td>-180.77459</td>
  </tr>
  <tr>
    <td>## dwell</td>
    <td>-172.50535</td>
  </tr>
  <tr>
    <td>## ear</td>
    <td>-196.88224</td>
  </tr>
  <tr>
    <td>## earl</td>
    <td>-157.48977</td>
  </tr>
  <tr>
    <td>## earn</td>
    <td>-187.52218</td>
  </tr>
  <tr>
    <td>## earth</td>
    <td>-195.82627</td>
  </tr>
  <tr>
    <td>## ease</td>
    <td>-180.98396</td>
  </tr>
</table>
<table>
  <tr>
    <td>east</td>
    <td>-171.11772</td>
  </tr>
  <tr>
    <td>eat</td>
    <td>-189.95817</td>
  </tr>
  <tr>
    <td>ebb</td>
    <td>-139.52032</td>
  </tr>
  <tr>
    <td>edge</td>
    <td>-194.51263</td>
  </tr>
  <tr>
    <td>eel</td>
    <td>-161.25098</td>
  </tr>
  <tr>
    <td>egg</td>
    <td>-199.67159</td>
  </tr>
  <tr>
    <td>elk</td>
    <td>-181.43786</td>
  </tr>
  <tr>
    <td>elm</td>
    <td>-182.60086</td>
  </tr>
  <tr>
    <td>end</td>
    <td>-181.59002</td>
  </tr>
  <tr>
    <td>err</td>
    <td>-117.43488</td>
  </tr>
  <tr>
    <td>eve</td>
    <td>-181.61675</td>
  </tr>
  <tr>
    <td>ewe</td>
    <td>-114.59184</td>
  </tr>
  <tr>
    <td>face</td>
    <td>-197.99366</td>
  </tr>
  <tr>
    <td>fact</td>
    <td>-199.51572</td>
  </tr>
  <tr>
    <td>fad</td>
    <td>-169.12056</td>
  </tr>
  <tr>
    <td>fade</td>
    <td>-188.69965</td>
  </tr>
  <tr>
    <td>fail</td>
    <td>-180.56733</td>
  </tr>
  <tr>
    <td>fair</td>
    <td>-192.27541</td>
  </tr>
  <tr>
    <td>faith</td>
    <td>-200.82745</td>
  </tr>
  <tr>
    <td>fake</td>
    <td>-183.14828</td>
  </tr>
  <tr>
    <td>fame</td>
    <td>-180.32311</td>
  </tr>
  <tr>
    <td>fan</td>
    <td>-181.44536</td>
  </tr>
  <tr>
    <td>fang</td>
    <td>-153.91650</td>
  </tr>
  <tr>
    <td>farce</td>
    <td>-128.83801</td>
  </tr>
  <tr>
    <td>fare</td>
    <td>-176.54643</td>
  </tr>
  <tr>
    <td>farm</td>
    <td>-200.43607</td>
  </tr>
  <tr>
    <td>fast</td>
    <td>-195.47234</td>
  </tr>
  <tr>
    <td>fate</td>
    <td>-199.77081</td>
  </tr>
  <tr>
    <td>fault</td>
    <td>-195.75784</td>
  </tr>
  <tr>
    <td>fawn</td>
    <td>-169.78123</td>
  </tr>
  <tr>
    <td>faze</td>
    <td>-161.37956</td>
  </tr>
  <tr>
    <td>fear</td>
    <td>-199.41411</td>
  </tr>
  <tr>
    <td>feast</td>
    <td>-198.80146</td>
  </tr>
  <tr>
    <td>feat</td>
    <td>-171.81362</td>
  </tr>
  <tr>
    <td>fee</td>
    <td>-176.63271</td>
  </tr>
  <tr>
    <td>feed</td>
    <td>-187.77635</td>
  </tr>
  <tr>
    <td>feel</td>
    <td>-200.76150</td>
  </tr>
  <tr>
    <td>feint</td>
    <td>-146.21897</td>
  </tr>
  <tr>
    <td>fell</td>
    <td>-217.53817</td>
  </tr>
  <tr>
    <td>fen</td>
    <td>-160.55269</td>
  </tr>
  <tr>
    <td>fence</td>
    <td>-193.26012</td>
  </tr>
  <tr>
    <td>fern</td>
    <td>-133.64212</td>
  </tr>
  <tr>
    <td>fetch</td>
    <td>-196.10547</td>
  </tr>
  <tr>
    <td>feud</td>
    <td>-177.24139</td>
  </tr>
  <tr>
    <td>fiend</td>
    <td>-100.06022</td>
  </tr>
  <tr>
    <td>fife</td>
    <td>-95.12509</td>
  </tr>
</table>
<table>
  <tbody>
    <tr><td>fig</td><td>-178.07028</td></tr>
    <tr><td>fight</td><td>-182.32497</td></tr>
    <tr><td>file</td><td>-191.68091</td></tr>
    <tr><td>fill</td><td>-175.68862</td></tr>
    <tr><td>film</td><td>-192.12628</td></tr>
    <tr><td>filth</td><td>-164.73944</td></tr>
    <tr><td>fin</td><td>-177.10972</td></tr>
    <tr><td>find</td><td>-189.25564</td></tr>
    <tr><td>fine</td><td>-181.82587</td></tr>
    <tr><td>fink</td><td>-128.19955</td></tr>
    <tr><td>fir</td><td>-160.69287</td></tr>
    <tr><td>fire</td><td>-199.86895</td></tr>
    <tr><td>firm</td><td>-197.81085</td></tr>
    <tr><td>fish</td><td>-198.30845</td></tr>
    <tr><td>fist</td><td>-160.05563</td></tr>
    <tr><td>fix</td><td>-199.19887</td></tr>
    <tr><td>flag</td><td>-198.46404</td></tr>
    <tr><td>flail</td><td>-84.08973</td></tr>
    <tr><td>flair</td><td>-167.02357</td></tr>
    <tr><td>flake</td><td>-177.85993</td></tr>
    <tr><td>flame</td><td>-194.72421</td></tr>
    <tr><td>flange</td><td>-77.78611</td></tr>
    <tr><td>flank</td><td>-165.52170</td></tr>
    <tr><td>flare</td><td>-193.75979</td></tr>
    <tr><td>flask</td><td>-186.04244</td></tr>
    <tr><td>flaw</td><td>-185.49454</td></tr>
    <tr><td>flax</td><td>-150.47932</td></tr>
    <tr><td>flea</td><td>-186.79512</td></tr>
    <tr><td>fleck</td><td>-114.79213</td></tr>
    <tr><td>flee</td><td>-179.89965</td></tr>
    <tr><td>fleet</td><td>-177.65238</td></tr>
    <tr><td>flesh</td><td>-190.19661</td></tr>
    <tr><td>flex</td><td>-186.41256</td></tr>
    <tr><td>flick</td><td>-178.21487</td></tr>
    <tr><td>flight</td><td>-181.29330</td></tr>
    <tr><td>fling</td><td>-183.60529</td></tr>
    <tr><td>flint</td><td>-179.31598</td></tr>
    <tr><td>flip</td><td>-182.12116</td></tr>
    <tr><td>flirt</td><td>-195.48457</td></tr>
    <tr><td>float</td><td>-184.83669</td></tr>
    <tr><td>flock</td><td>-187.60664</td></tr>
    <tr><td>floe</td><td>-124.83803</td></tr>
    <tr><td>flog</td><td>-172.28889</td></tr>
    <tr><td>flood</td><td>-201.00571</td></tr>
    <tr><td>floor</td><td>-194.93437</td></tr>
    <tr><td>flop</td><td>-166.74578</td></tr>
  </tbody>
</table>
<table>
  <tr>
    <td>## flour</td>
    <td>-196.72488</td>
  </tr>
  <tr>
    <td>## flow</td>
    <td>-180.73385</td>
  </tr>
  <tr>
    <td>## fluff</td>
    <td>-182.38838</td>
  </tr>
  <tr>
    <td>## fluke</td>
    <td>-183.47084</td>
  </tr>
  <tr>
    <td>## flush</td>
    <td>-189.89104</td>
  </tr>
  <tr>
    <td>## flute</td>
    <td>-182.08558</td>
  </tr>
  <tr>
    <td>## flux</td>
    <td>-167.27107</td>
  </tr>
  <tr>
    <td>## fly</td>
    <td>-217.99313</td>
  </tr>
  <tr>
    <td>## foal</td>
    <td>-146.96307</td>
  </tr>
  <tr>
    <td>## foam</td>
    <td>-186.60844</td>
  </tr>
  <tr>
    <td>## foe</td>
    <td>-186.51443</td>
  </tr>
  <tr>
    <td>## fog</td>
    <td>-185.98901</td>
  </tr>
  <tr>
    <td>## foil</td>
    <td>-186.45515</td>
  </tr>
  <tr>
    <td>## fold</td>
    <td>-199.14960</td>
  </tr>
  <tr>
    <td>## folk</td>
    <td>-191.49742</td>
  </tr>
  <tr>
    <td>## font</td>
    <td>-128.39289</td>
  </tr>
  <tr>
    <td>## food</td>
    <td>-192.46378</td>
  </tr>
  <tr>
    <td>## fool</td>
    <td>-200.77036</td>
  </tr>
  <tr>
    <td>## foot</td>
    <td>-198.20382</td>
  </tr>
  <tr>
    <td>## force</td>
    <td>-181.76007</td>
  </tr>
  <tr>
    <td>## ford</td>
    <td>-154.80240</td>
  </tr>
  <tr>
    <td>## forge</td>
    <td>-158.95721</td>
  </tr>
  <tr>
    <td>## fork</td>
    <td>-196.29043</td>
  </tr>
  <tr>
    <td>## form</td>
    <td>-182.59819</td>
  </tr>
  <tr>
    <td>## fort</td>
    <td>-148.53676</td>
  </tr>
  <tr>
    <td>## found</td>
    <td>-198.75044</td>
  </tr>
  <tr>
    <td>## fowl</td>
    <td>-199.62518</td>
  </tr>
  <tr>
    <td>## fox</td>
    <td>-200.83612</td>
  </tr>
  <tr>
    <td>## frame</td>
    <td>-176.34010</td>
  </tr>
  <tr>
    <td>## fraud</td>
    <td>-167.72184</td>
  </tr>
  <tr>
    <td>## fray</td>
    <td>-150.17128</td>
  </tr>
  <tr>
    <td>## freak</td>
    <td>-190.49511</td>
  </tr>
  <tr>
    <td>## freeze</td>
    <td>-184.41054</td>
  </tr>
  <tr>
    <td>## freight</td>
    <td>-175.58916</td>
  </tr>
  <tr>
    <td>## fret</td>
    <td>-118.61732</td>
  </tr>
  <tr>
    <td>## friend</td>
    <td>-192.71619</td>
  </tr>
  <tr>
    <td>## frieze</td>
    <td>-151.34849</td>
  </tr>
  <tr>
    <td>## fright</td>
    <td>-180.89830</td>
  </tr>
  <tr>
    <td>## frill</td>
    <td>-167.57179</td>
  </tr>
  <tr>
    <td>## fringe</td>
    <td>-176.32200</td>
  </tr>
  <tr>
    <td>## frock</td>
    <td>-139.43297</td>
  </tr>
  <tr>
    <td>## frog</td>
    <td>-193.45638</td>
  </tr>
  <tr>
    <td>## front</td>
    <td>-198.21653</td>
  </tr>
  <tr>
    <td>## frost</td>
    <td>-182.99339</td>
  </tr>
  <tr>
    <td>## froth</td>
    <td>-108.04893</td>
  </tr>
  <tr>
    <td>## frown</td>
    <td>-180.45973</td>
  </tr>
</table>
<table>
  <tr>
    <td>## fruit</td>
    <td>-197.51965</td>
  </tr>
  <tr>
    <td>## fry</td>
    <td>-207.23628</td>
  </tr>
  <tr>
    <td>## fuel</td>
    <td>-198.32659</td>
  </tr>
  <tr>
    <td>## full</td>
    <td>-194.13626</td>
  </tr>
  <tr>
    <td>## fun</td>
    <td>-192.26156</td>
  </tr>
  <tr>
    <td>## fund</td>
    <td>-182.25280</td>
  </tr>
  <tr>
    <td>## funk</td>
    <td>-175.44217</td>
  </tr>
  <tr>
    <td>## fur</td>
    <td>-193.97540</td>
  </tr>
  <tr>
    <td>## fuse</td>
    <td>-177.01873</td>
  </tr>
  <tr>
    <td>## fuss</td>
    <td>-182.68614</td>
  </tr>
  <tr>
    <td>## fuzz</td>
    <td>-149.71941</td>
  </tr>
  <tr>
    <td>## gab</td>
    <td>-142.05673</td>
  </tr>
  <tr>
    <td>## gag</td>
    <td>-153.90200</td>
  </tr>
  <tr>
    <td>## gain</td>
    <td>-181.93614</td>
  </tr>
  <tr>
    <td>## gait</td>
    <td>-128.41767</td>
  </tr>
  <tr>
    <td>## gal</td>
    <td>-123.49029</td>
  </tr>
  <tr>
    <td>## gale</td>
    <td>-156.99413</td>
  </tr>
  <tr>
    <td>## gall</td>
    <td>-157.17548</td>
  </tr>
  <tr>
    <td>## game</td>
    <td>-198.27914</td>
  </tr>
  <tr>
    <td>## gang</td>
    <td>-185.16851</td>
  </tr>
  <tr>
    <td>## gap</td>
    <td>-189.97582</td>
  </tr>
  <tr>
    <td>## garb</td>
    <td>-113.91571</td>
  </tr>
  <tr>
    <td>## gas</td>
    <td>-180.65589</td>
  </tr>
  <tr>
    <td>## gash</td>
    <td>-105.17302</td>
  </tr>
  <tr>
    <td>## gasp</td>
    <td>-180.73184</td>
  </tr>
  <tr>
    <td>## gate</td>
    <td>-177.42815</td>
  </tr>
  <tr>
    <td>## gauge</td>
    <td>-141.47216</td>
  </tr>
  <tr>
    <td>## gauze</td>
    <td>-135.20602</td>
  </tr>
  <tr>
    <td>## gay</td>
    <td>-181.83600</td>
  </tr>
  <tr>
    <td>## gaze</td>
    <td>-176.88690</td>
  </tr>
  <tr>
    <td>## gear</td>
    <td>-195.62551</td>
  </tr>
  <tr>
    <td>## gel</td>
    <td>-176.01706</td>
  </tr>
  <tr>
    <td>## gem</td>
    <td>-184.61844</td>
  </tr>
  <tr>
    <td>## gene</td>
    <td>-162.34573</td>
  </tr>
  <tr>
    <td>## get</td>
    <td>-192.14872</td>
  </tr>
  <tr>
    <td>## ghost</td>
    <td>-192.78995</td>
  </tr>
  <tr>
    <td>## ghoul</td>
    <td>-116.12786</td>
  </tr>
  <tr>
    <td>## gibe</td>
    <td>-152.77635</td>
  </tr>
  <tr>
    <td>## gift</td>
    <td>-200.60508</td>
  </tr>
  <tr>
    <td>## gig</td>
    <td>-121.14889</td>
  </tr>
  <tr>
    <td>## gill</td>
    <td>-77.93246</td>
  </tr>
  <tr>
    <td>## gilt</td>
    <td>-138.13176</td>
  </tr>
  <tr>
    <td>## gin</td>
    <td>-181.24206</td>
  </tr>
  <tr>
    <td>## gird</td>
    <td>-179.93736</td>
  </tr>
  <tr>
    <td>## girl</td>
    <td>-185.41349</td>
  </tr>
  <tr>
    <td>## gist</td>
    <td>-129.11464</td>
  </tr>
</table>
<table>
  <tr>
    <td>give</td>
    <td>-200.41921</td>
  </tr>
  <tr>
    <td>glance</td>
    <td>-187.06491</td>
  </tr>
  <tr>
    <td>gland</td>
    <td>-181.50379</td>
  </tr>
  <tr>
    <td>glare</td>
    <td>-199.90763</td>
  </tr>
  <tr>
    <td>glass</td>
    <td>-199.48135</td>
  </tr>
  <tr>
    <td>glaze</td>
    <td>-186.50647</td>
  </tr>
  <tr>
    <td>gleam</td>
    <td>-149.70623</td>
  </tr>
  <tr>
    <td>glean</td>
    <td>-78.15143</td>
  </tr>
  <tr>
    <td>glee</td>
    <td>-160.76827</td>
  </tr>
  <tr>
    <td>glen</td>
    <td>-138.05496</td>
  </tr>
  <tr>
    <td>glide</td>
    <td>-179.37727</td>
  </tr>
  <tr>
    <td>glimpse</td>
    <td>-181.60587</td>
  </tr>
  <tr>
    <td>glint</td>
    <td>-159.28343</td>
  </tr>
  <tr>
    <td>gloat</td>
    <td>-147.86417</td>
  </tr>
  <tr>
    <td>globe</td>
    <td>-175.12505</td>
  </tr>
  <tr>
    <td>gloom</td>
    <td>-192.23249</td>
  </tr>
  <tr>
    <td>gloss</td>
    <td>-197.04694</td>
  </tr>
  <tr>
    <td>glove</td>
    <td>-181.16216</td>
  </tr>
  <tr>
    <td>glow</td>
    <td>-180.92182</td>
  </tr>
  <tr>
    <td>glue</td>
    <td>-190.64795</td>
  </tr>
  <tr>
    <td>gnaw</td>
    <td>-148.13583</td>
  </tr>
  <tr>
    <td>gnome</td>
    <td>-105.86890</td>
  </tr>
  <tr>
    <td>go</td>
    <td>-187.69626</td>
  </tr>
  <tr>
    <td>goad</td>
    <td>-175.42550</td>
  </tr>
  <tr>
    <td>goal</td>
    <td>-196.93545</td>
  </tr>
  <tr>
    <td>goat</td>
    <td>-187.41293</td>
  </tr>
  <tr>
    <td>gob</td>
    <td>-92.92868</td>
  </tr>
  <tr>
    <td>god</td>
    <td>-180.44330</td>
  </tr>
  <tr>
    <td>gold</td>
    <td>-181.47352</td>
  </tr>
  <tr>
    <td>golf</td>
    <td>-179.63170</td>
  </tr>
  <tr>
    <td>gong</td>
    <td>-136.75768</td>
  </tr>
  <tr>
    <td>goon</td>
    <td>-82.58610</td>
  </tr>
  <tr>
    <td>goose</td>
    <td>-181.13527</td>
  </tr>
  <tr>
    <td>gore</td>
    <td>-113.73461</td>
  </tr>
  <tr>
    <td>gouge</td>
    <td>-113.02282</td>
  </tr>
  <tr>
    <td>gourd</td>
    <td>-112.04557</td>
  </tr>
  <tr>
    <td>gout</td>
    <td>-141.88418</td>
  </tr>
  <tr>
    <td>gown</td>
    <td>-176.09007</td>
  </tr>
  <tr>
    <td>grab</td>
    <td>-182.00879</td>
  </tr>
  <tr>
    <td>grace</td>
    <td>-192.65180</td>
  </tr>
  <tr>
    <td>grade</td>
    <td>-186.62191</td>
  </tr>
  <tr>
    <td>graft</td>
    <td>-154.77915</td>
  </tr>
  <tr>
    <td>grail</td>
    <td>-114.55579</td>
  </tr>
  <tr>
    <td>grain</td>
    <td>-184.09745</td>
  </tr>
  <tr>
    <td>gram</td>
    <td>-146.18919</td>
  </tr>
  <tr>
    <td>grant</td>
    <td>-191.43474</td>
  </tr>
</table>
<table>
  <tr>
    <td>grape</td>
    <td>-189.60298</td>
  </tr>
  <tr>
    <td>graph</td>
    <td>-185.83960</td>
  </tr>
  <tr>
    <td>grasp</td>
    <td>-185.26877</td>
  </tr>
  <tr>
    <td>grass</td>
    <td>-182.52369</td>
  </tr>
  <tr>
    <td>grate</td>
    <td>-166.38184</td>
  </tr>
  <tr>
    <td>grave</td>
    <td>-191.07284</td>
  </tr>
  <tr>
    <td>graze</td>
    <td>-176.97760</td>
  </tr>
  <tr>
    <td>grease</td>
    <td>-182.23696</td>
  </tr>
  <tr>
    <td>greed</td>
    <td>-186.00495</td>
  </tr>
  <tr>
    <td>greet</td>
    <td>-131.94855</td>
  </tr>
  <tr>
    <td>grid</td>
    <td>-179.17089</td>
  </tr>
  <tr>
    <td>grill</td>
    <td>-181.08284</td>
  </tr>
  <tr>
    <td>grille</td>
    <td>-98.32969</td>
  </tr>
  <tr>
    <td>grime</td>
    <td>-163.38482</td>
  </tr>
  <tr>
    <td>grin</td>
    <td>-174.34635</td>
  </tr>
  <tr>
    <td>grind</td>
    <td>-186.01090</td>
  </tr>
  <tr>
    <td>grip</td>
    <td>-180.26049</td>
  </tr>
  <tr>
    <td>gripe</td>
    <td>-149.76243</td>
  </tr>
  <tr>
    <td>grist</td>
    <td>-104.85385</td>
  </tr>
  <tr>
    <td>grit</td>
    <td>-133.28047</td>
  </tr>
  <tr>
    <td>groan</td>
    <td>-183.79673</td>
  </tr>
  <tr>
    <td>groin</td>
    <td>-159.07079</td>
  </tr>
  <tr>
    <td>groom</td>
    <td>-193.53931</td>
  </tr>
  <tr>
    <td>groove</td>
    <td>-183.85655</td>
  </tr>
  <tr>
    <td>grope</td>
    <td>-147.93012</td>
  </tr>
  <tr>
    <td>grouch</td>
    <td>-162.22721</td>
  </tr>
  <tr>
    <td>ground</td>
    <td>-197.96126</td>
  </tr>
  <tr>
    <td>group</td>
    <td>-190.42197</td>
  </tr>
  <tr>
    <td>grouse</td>
    <td>-157.99376</td>
  </tr>
  <tr>
    <td>grove</td>
    <td>-162.20875</td>
  </tr>
  <tr>
    <td>grow</td>
    <td>-201.06608</td>
  </tr>
  <tr>
    <td>growl</td>
    <td>-182.43694</td>
  </tr>
  <tr>
    <td>grub</td>
    <td>-121.92463</td>
  </tr>
  <tr>
    <td>grudge</td>
    <td>-175.96427</td>
  </tr>
  <tr>
    <td>grunt</td>
    <td>-177.67133</td>
  </tr>
  <tr>
    <td>guard</td>
    <td>-200.05251</td>
  </tr>
  <tr>
    <td>guess</td>
    <td>-187.26570</td>
  </tr>
  <tr>
    <td>guest</td>
    <td>-189.15319</td>
  </tr>
  <tr>
    <td>guide</td>
    <td>-200.88828</td>
  </tr>
  <tr>
    <td>guild</td>
    <td>-144.09297</td>
  </tr>
  <tr>
    <td>guile</td>
    <td>-126.39128</td>
  </tr>
  <tr>
    <td>guilt</td>
    <td>-182.63131</td>
  </tr>
  <tr>
    <td>guise</td>
    <td>-143.77007</td>
  </tr>
  <tr>
    <td>gulf</td>
    <td>-167.56129</td>
  </tr>
  <tr>
    <td>gull</td>
    <td>-120.08771</td>
  </tr>
  <tr>
    <td>gulp</td>
    <td>-185.41947</td>
  </tr>
</table>
<table><tr><td>gum</td><td>-181.88001</td></tr><tr><td>gun</td><td>-192.22397</td></tr><tr><td>gush</td><td>-162.54448</td></tr><tr><td>gust</td><td>-151.78338</td></tr><tr><td>gut</td><td>-175.50119</td></tr><tr><td>guy</td><td>-184.26441</td></tr><tr><td>gyp</td><td>-146.46216</td></tr><tr><td>hack</td><td>-178.47039</td></tr><tr><td>hag</td><td>-179.76685</td></tr><tr><td>hail</td><td>-199.05497</td></tr><tr><td>hair</td><td>-182.40259</td></tr><tr><td>hall</td><td>-187.63544</td></tr><tr><td>halt</td><td>-199.93177</td></tr><tr><td>ham</td><td>-200.91003</td></tr><tr><td>hand</td><td>-199.44050</td></tr><tr><td>hang</td><td>-194.70301</td></tr><tr><td>hank</td><td>-174.77663</td></tr><tr><td>hark</td><td>-176.38744</td></tr><tr><td>harm</td><td>-183.11507</td></tr><tr><td>harp</td><td>-193.61555</td></tr><tr><td>hart</td><td>-168.52174</td></tr><tr><td>hash</td><td>-176.20912</td></tr><tr><td>haste</td><td>-197.95679</td></tr><tr><td>hat</td><td>-187.99761</td></tr><tr><td>hatch</td><td>-193.38815</td></tr><tr><td>hate</td><td>-200.45732</td></tr><tr><td>haul</td><td>-200.91033</td></tr><tr><td>haunt</td><td>-157.99475</td></tr><tr><td>have</td><td>-196.13107</td></tr><tr><td>haw</td><td>-174.20030</td></tr><tr><td>hawk</td><td>-185.90661</td></tr><tr><td>hay</td><td>-200.81383</td></tr><tr><td>haze</td><td>-187.56525</td></tr><tr><td>head</td><td>-200.94795</td></tr><tr><td>heal</td><td>-187.82438</td></tr><tr><td>heap</td><td>-186.46627</td></tr><tr><td>hear</td><td>-194.58605</td></tr><tr><td>heart</td><td>-199.26918</td></tr><tr><td>hearth</td><td>-180.74902</td></tr><tr><td>heat</td><td>-195.54487</td></tr><tr><td>heave</td><td>-165.81451</td></tr><tr><td>heck</td><td>-172.10979</td></tr><tr><td>hedge</td><td>-173.64492</td></tr><tr><td>heed</td><td>-169.91193</td></tr><tr><td>heel</td><td>-185.83464</td></tr><tr><td>height</td><td>-188.06076</td></tr></table>
<table>
  <tr>
    <td>## heir</td>
    <td>-187.25315</td>
  </tr>
  <tr>
    <td>## hell</td>
    <td>-188.73324</td>
  </tr>
  <tr>
    <td>## helm</td>
    <td>-123.79796</td>
  </tr>
  <tr>
    <td>## help</td>
    <td>-201.01950</td>
  </tr>
  <tr>
    <td>## hem</td>
    <td>-162.33898</td>
  </tr>
  <tr>
    <td>## hen</td>
    <td>-181.48984</td>
  </tr>
  <tr>
    <td>## herb</td>
    <td>-178.17453</td>
  </tr>
  <tr>
    <td>## herd</td>
    <td>-185.34950</td>
  </tr>
  <tr>
    <td>## hick</td>
    <td>-177.52740</td>
  </tr>
  <tr>
    <td>## hide</td>
    <td>-218.47041</td>
  </tr>
  <tr>
    <td>## hike</td>
    <td>-193.76251</td>
  </tr>
  <tr>
    <td>## hill</td>
    <td>-199.53181</td>
  </tr>
  <tr>
    <td>## hilt</td>
    <td>-176.98041</td>
  </tr>
  <tr>
    <td>## hind</td>
    <td>-176.80490</td>
  </tr>
  <tr>
    <td>## hinge</td>
    <td>-180.36160</td>
  </tr>
  <tr>
    <td>## hint</td>
    <td>-194.41117</td>
  </tr>
  <tr>
    <td>## hip</td>
    <td>-198.84191</td>
  </tr>
  <tr>
    <td>## hire</td>
    <td>-191.31187</td>
  </tr>
  <tr>
    <td>## hiss</td>
    <td>-162.03448</td>
  </tr>
  <tr>
    <td>## hit</td>
    <td>-187.51734</td>
  </tr>
  <tr>
    <td>## hitch</td>
    <td>-148.42063</td>
  </tr>
  <tr>
    <td>## hive</td>
    <td>-171.91169</td>
  </tr>
  <tr>
    <td>## hob</td>
    <td>-181.48475</td>
  </tr>
  <tr>
    <td>## hoe</td>
    <td>-188.72219</td>
  </tr>
  <tr>
    <td>## hog</td>
    <td>-215.54434</td>
  </tr>
  <tr>
    <td>## hoist</td>
    <td>-182.30562</td>
  </tr>
  <tr>
    <td>## hold</td>
    <td>-196.56028</td>
  </tr>
  <tr>
    <td>## hole</td>
    <td>-197.40126</td>
  </tr>
  <tr>
    <td>## home</td>
    <td>-185.23380</td>
  </tr>
  <tr>
    <td>## hone</td>
    <td>-99.91129</td>
  </tr>
  <tr>
    <td>## hooch</td>
    <td>-178.09861</td>
  </tr>
  <tr>
    <td>## hood</td>
    <td>-194.60524</td>
  </tr>
  <tr>
    <td>## hoof</td>
    <td>-184.50822</td>
  </tr>
  <tr>
    <td>## hook</td>
    <td>-187.10417</td>
  </tr>
  <tr>
    <td>## hoop</td>
    <td>-182.79192</td>
  </tr>
  <tr>
    <td>## hoot</td>
    <td>-185.03854</td>
  </tr>
  <tr>
    <td>## hop</td>
    <td>-187.04028</td>
  </tr>
  <tr>
    <td>## hope</td>
    <td>-196.63149</td>
  </tr>
  <tr>
    <td>## horn</td>
    <td>-200.19922</td>
  </tr>
  <tr>
    <td>## horse</td>
    <td>-177.64210</td>
  </tr>
  <tr>
    <td>## hose</td>
    <td>-186.40822</td>
  </tr>
  <tr>
    <td>## host</td>
    <td>-195.40717</td>
  </tr>
  <tr>
    <td>## hound</td>
    <td>-183.13897</td>
  </tr>
  <tr>
    <td>## hour</td>
    <td>-185.18426</td>
  </tr>
  <tr>
    <td>## house</td>
    <td>-186.09944</td>
  </tr>
  <tr>
    <td>## howl</td>
    <td>-195.10912</td>
  </tr>
</table>
<table><tr><td>hub</td><td>-159.86107</td></tr><tr><td>hue</td><td>-182.83221</td></tr><tr><td>huff</td><td>-178.46191</td></tr><tr><td>hug</td><td>-196.04598</td></tr><tr><td>hulk</td><td>-193.74639</td></tr><tr><td>hull</td><td>-179.02064</td></tr><tr><td>hum</td><td>-180.51704</td></tr><tr><td>hump</td><td>-155.67932</td></tr><tr><td>hunch</td><td>-171.43643</td></tr><tr><td>hunk</td><td>-182.50043</td></tr><tr><td>hunt</td><td>-193.42263</td></tr><tr><td>hurl</td><td>-192.87159</td></tr><tr><td>hurt</td><td>-192.77434</td></tr><tr><td>hush</td><td>-181.81350</td></tr><tr><td>hut</td><td>-199.93621</td></tr><tr><td>hymn</td><td>-179.70837</td></tr><tr><td>ice</td><td>-200.58146</td></tr><tr><td>inch</td><td>-195.52191</td></tr><tr><td>ink</td><td>-201.02913</td></tr><tr><td>inn</td><td>-182.07870</td></tr><tr><td>ire</td><td>-174.74473</td></tr><tr><td>isle</td><td>-166.65097</td></tr><tr><td>itch</td><td>-152.99889</td></tr><tr><td>jab</td><td>-163.82217</td></tr><tr><td>jack</td><td>-194.88449</td></tr><tr><td>jade</td><td>-177.90244</td></tr><tr><td>jag</td><td>-169.33332</td></tr><tr><td>jail</td><td>-199.84984</td></tr><tr><td>jam</td><td>-199.41694</td></tr><tr><td>jape</td><td>-180.12428</td></tr><tr><td>jar</td><td>-190.68926</td></tr><tr><td>jaw</td><td>-191.43533</td></tr><tr><td>jazz</td><td>-188.97833</td></tr><tr><td>jeep</td><td>-197.29170</td></tr><tr><td>jeer</td><td>-182.32390</td></tr><tr><td>jerk</td><td>-191.06361</td></tr><tr><td>jest</td><td>-179.71290</td></tr><tr><td>jet</td><td>-194.42482</td></tr><tr><td>jig</td><td>-181.90520</td></tr><tr><td>job</td><td>-180.71905</td></tr><tr><td>jog</td><td>-200.74753</td></tr><tr><td>join</td><td>-182.70937</td></tr><tr><td>joke</td><td>-200.78251</td></tr><tr><td>jolt</td><td>-181.87755</td></tr><tr><td>jot</td><td>-175.23045</td></tr><tr><td>joust</td><td>-169.66294</td></tr></table>
<table>
  <tr>
    <td>## jowl</td>
    <td>-146.81413</td>
  </tr>
  <tr>
    <td>## joy</td>
    <td>-187.00519</td>
  </tr>
  <tr>
    <td>## judge</td>
    <td>-192.82922</td>
  </tr>
  <tr>
    <td>## jug</td>
    <td>-194.23844</td>
  </tr>
  <tr>
    <td>## juice</td>
    <td>-200.69223</td>
  </tr>
  <tr>
    <td>## jump</td>
    <td>-187.23337</td>
  </tr>
  <tr>
    <td>## junk</td>
    <td>-197.84974</td>
  </tr>
  <tr>
    <td>## jute</td>
    <td>-112.79893</td>
  </tr>
  <tr>
    <td>## kale</td>
    <td>-100.18255</td>
  </tr>
  <tr>
    <td>## keel</td>
    <td>-177.50475</td>
  </tr>
  <tr>
    <td>## keen</td>
    <td>-177.06191</td>
  </tr>
  <tr>
    <td>## keep</td>
    <td>-189.54046</td>
  </tr>
  <tr>
    <td>## keg</td>
    <td>-190.13366</td>
  </tr>
  <tr>
    <td>## kelp</td>
    <td>-97.03229</td>
  </tr>
  <tr>
    <td>## ken</td>
    <td>-173.00711</td>
  </tr>
  <tr>
    <td>## key</td>
    <td>-181.65476</td>
  </tr>
  <tr>
    <td>## kick</td>
    <td>-184.68939</td>
  </tr>
  <tr>
    <td>## kid</td>
    <td>-203.26627</td>
  </tr>
  <tr>
    <td>## kill</td>
    <td>-200.79462</td>
  </tr>
  <tr>
    <td>## kilt</td>
    <td>-133.20374</td>
  </tr>
  <tr>
    <td>## kin</td>
    <td>-179.01422</td>
  </tr>
  <tr>
    <td>## kind</td>
    <td>-188.54239</td>
  </tr>
  <tr>
    <td>## king</td>
    <td>-195.66770</td>
  </tr>
  <tr>
    <td>## kiss</td>
    <td>-199.94798</td>
  </tr>
  <tr>
    <td>## kit</td>
    <td>-183.92038</td>
  </tr>
  <tr>
    <td>## kite</td>
    <td>-196.93088</td>
  </tr>
  <tr>
    <td>## knack</td>
    <td>-123.44901</td>
  </tr>
  <tr>
    <td>## knead</td>
    <td>-183.49961</td>
  </tr>
  <tr>
    <td>## knee</td>
    <td>-199.65242</td>
  </tr>
  <tr>
    <td>## kneel</td>
    <td>-178.31363</td>
  </tr>
  <tr>
    <td>## knife</td>
    <td>-199.20108</td>
  </tr>
  <tr>
    <td>## knight</td>
    <td>-186.49948</td>
  </tr>
  <tr>
    <td>## knit</td>
    <td>-192.80352</td>
  </tr>
  <tr>
    <td>## knob</td>
    <td>-197.84757</td>
  </tr>
  <tr>
    <td>## knock</td>
    <td>-194.47701</td>
  </tr>
  <tr>
    <td>## knoll</td>
    <td>-151.90373</td>
  </tr>
  <tr>
    <td>## knot</td>
    <td>-199.87274</td>
  </tr>
  <tr>
    <td>## know</td>
    <td>-197.81408</td>
  </tr>
  <tr>
    <td>## lace</td>
    <td>-200.42146</td>
  </tr>
  <tr>
    <td>## lack</td>
    <td>-187.83600</td>
  </tr>
  <tr>
    <td>## lad</td>
    <td>-190.75025</td>
  </tr>
  <tr>
    <td>## lag</td>
    <td>-180.62334</td>
  </tr>
  <tr>
    <td>## lake</td>
    <td>-200.78604</td>
  </tr>
  <tr>
    <td>## lamb</td>
    <td>-183.68771</td>
  </tr>
  <tr>
    <td>## lame</td>
    <td>-200.63837</td>
  </tr>
  <tr>
    <td>## lamp</td>
    <td>-196.93251</td>
  </tr>
</table>
<table>
  <tr>
    <td>lance</td>
    <td>-145.86903</td>
  </tr>
  <tr>
    <td>land</td>
    <td>-195.33679</td>
  </tr>
  <tr>
    <td>lane</td>
    <td>-197.30552</td>
  </tr>
  <tr>
    <td>lap</td>
    <td>-216.39033</td>
  </tr>
  <tr>
    <td>lapse</td>
    <td>-186.91969</td>
  </tr>
  <tr>
    <td>lard</td>
    <td>-177.86885</td>
  </tr>
  <tr>
    <td>lark</td>
    <td>-184.39725</td>
  </tr>
  <tr>
    <td>lash</td>
    <td>-183.76214</td>
  </tr>
  <tr>
    <td>lass</td>
    <td>-106.43691</td>
  </tr>
  <tr>
    <td>last</td>
    <td>-176.23897</td>
  </tr>
  <tr>
    <td>latch</td>
    <td>-186.71549</td>
  </tr>
  <tr>
    <td>lath</td>
    <td>-71.31035</td>
  </tr>
  <tr>
    <td>lathe</td>
    <td>-178.61193</td>
  </tr>
  <tr>
    <td>laugh</td>
    <td>-187.55382</td>
  </tr>
  <tr>
    <td>launch</td>
    <td>-184.23064</td>
  </tr>
  <tr>
    <td>law</td>
    <td>-195.24692</td>
  </tr>
  <tr>
    <td>lawn</td>
    <td>-180.29152</td>
  </tr>
  <tr>
    <td>lay</td>
    <td>-191.58704</td>
  </tr>
  <tr>
    <td>laze</td>
    <td>-180.34278</td>
  </tr>
  <tr>
    <td>leaf</td>
    <td>-193.94081</td>
  </tr>
  <tr>
    <td>leak</td>
    <td>-200.79029</td>
  </tr>
  <tr>
    <td>lean</td>
    <td>-192.27152</td>
  </tr>
  <tr>
    <td>leap</td>
    <td>-181.08828</td>
  </tr>
  <tr>
    <td>learn</td>
    <td>-158.31850</td>
  </tr>
  <tr>
    <td>lease</td>
    <td>-200.55078</td>
  </tr>
  <tr>
    <td>leash</td>
    <td>-199.65926</td>
  </tr>
  <tr>
    <td>leave</td>
    <td>-196.83801</td>
  </tr>
  <tr>
    <td>ledge</td>
    <td>-181.67514</td>
  </tr>
  <tr>
    <td>lee</td>
    <td>-142.13595</td>
  </tr>
  <tr>
    <td>leg</td>
    <td>-179.99013</td>
  </tr>
  <tr>
    <td>lend</td>
    <td>-199.24896</td>
  </tr>
  <tr>
    <td>lens</td>
    <td>-183.66178</td>
  </tr>
  <tr>
    <td>let</td>
    <td>-180.71139</td>
  </tr>
  <tr>
    <td>lick</td>
    <td>-189.40868</td>
  </tr>
  <tr>
    <td>lid</td>
    <td>-192.57303</td>
  </tr>
  <tr>
    <td>lie</td>
    <td>-196.61014</td>
  </tr>
  <tr>
    <td>life</td>
    <td>-199.71842</td>
  </tr>
  <tr>
    <td>lift</td>
    <td>-192.01078</td>
  </tr>
  <tr>
    <td>light</td>
    <td>-200.24591</td>
  </tr>
  <tr>
    <td>like</td>
    <td>-199.73231</td>
  </tr>
  <tr>
    <td>lilt</td>
    <td>-181.08670</td>
  </tr>
  <tr>
    <td>limb</td>
    <td>-196.88088</td>
  </tr>
  <tr>
    <td>lime</td>
    <td>-184.93160</td>
  </tr>
  <tr>
    <td>limp</td>
    <td>-190.25819</td>
  </tr>
  <tr>
    <td>line</td>
    <td>-171.59602</td>
  </tr>
  <tr>
    <td>link</td>
    <td>-186.96680</td>
  </tr>
</table>
<table>
  <tr>
    <td>lint</td>
    <td>-175.89030</td>
  </tr>
  <tr>
    <td>lip</td>
    <td>-200.54641</td>
  </tr>
  <tr>
    <td>lisle</td>
    <td>-72.67327</td>
  </tr>
  <tr>
    <td>list</td>
    <td>-193.41954</td>
  </tr>
  <tr>
    <td>load</td>
    <td>-196.30199</td>
  </tr>
  <tr>
    <td>loaf</td>
    <td>-195.46059</td>
  </tr>
  <tr>
    <td>loan</td>
    <td>-193.83004</td>
  </tr>
  <tr>
    <td>lob</td>
    <td>-163.11344</td>
  </tr>
  <tr>
    <td>lobe</td>
    <td>-162.57905</td>
  </tr>
  <tr>
    <td>lock</td>
    <td>-198.67102</td>
  </tr>
  <tr>
    <td>lodge</td>
    <td>-195.13566</td>
  </tr>
  <tr>
    <td>loft</td>
    <td>-178.97956</td>
  </tr>
  <tr>
    <td>log</td>
    <td>-185.22078</td>
  </tr>
  <tr>
    <td>loin</td>
    <td>-180.45703</td>
  </tr>
  <tr>
    <td>look</td>
    <td>-200.89286</td>
  </tr>
  <tr>
    <td>loom</td>
    <td>-151.07758</td>
  </tr>
  <tr>
    <td>loon</td>
    <td>-152.26744</td>
  </tr>
  <tr>
    <td>loop</td>
    <td>-198.47144</td>
  </tr>
  <tr>
    <td>loot</td>
    <td>-184.21423</td>
  </tr>
  <tr>
    <td>lop</td>
    <td>-178.76689</td>
  </tr>
  <tr>
    <td>lope</td>
    <td>-179.87693</td>
  </tr>
  <tr>
    <td>lord</td>
    <td>-201.15254</td>
  </tr>
  <tr>
    <td>lore</td>
    <td>-173.11925</td>
  </tr>
  <tr>
    <td>lose</td>
    <td>-186.88681</td>
  </tr>
  <tr>
    <td>loss</td>
    <td>-194.38298</td>
  </tr>
  <tr>
    <td>lot</td>
    <td>-198.80471</td>
  </tr>
  <tr>
    <td>lounge</td>
    <td>-182.29248</td>
  </tr>
  <tr>
    <td>louse</td>
    <td>-138.15435</td>
  </tr>
  <tr>
    <td>love</td>
    <td>-200.33196</td>
  </tr>
  <tr>
    <td>low</td>
    <td>-198.61875</td>
  </tr>
  <tr>
    <td>luck</td>
    <td>-190.81330</td>
  </tr>
  <tr>
    <td>lug</td>
    <td>-185.59208</td>
  </tr>
  <tr>
    <td>lull</td>
    <td>-153.65927</td>
  </tr>
  <tr>
    <td>lump</td>
    <td>-196.41526</td>
  </tr>
  <tr>
    <td>lung</td>
    <td>-180.98134</td>
  </tr>
  <tr>
    <td>lurch</td>
    <td>-122.99627</td>
  </tr>
  <tr>
    <td>lure</td>
    <td>-181.35837</td>
  </tr>
  <tr>
    <td>lurk</td>
    <td>-179.32358</td>
  </tr>
  <tr>
    <td>lust</td>
    <td>-182.89164</td>
  </tr>
  <tr>
    <td>lute</td>
    <td>-180.48183</td>
  </tr>
  <tr>
    <td>lye</td>
    <td>-113.39506</td>
  </tr>
  <tr>
    <td>lymph</td>
    <td>-143.73762</td>
  </tr>
  <tr>
    <td>lynch</td>
    <td>-171.52063</td>
  </tr>
  <tr>
    <td>maid</td>
    <td>-198.09962</td>
  </tr>
  <tr>
    <td>mail</td>
    <td>-184.84235</td>
  </tr>
  <tr>
    <td>make</td>
    <td>-200.80781</td>
  </tr>
</table>
<table>
  <tr>
    <td>## mall</td>
    <td>-180.99489</td>
  </tr>
  <tr>
    <td>## malt</td>
    <td>-190.31519</td>
  </tr>
  <tr>
    <td>## man</td>
    <td>-200.79574</td>
  </tr>
  <tr>
    <td>## mane</td>
    <td>-178.15249</td>
  </tr>
  <tr>
    <td>## manse</td>
    <td>-179.99685</td>
  </tr>
  <tr>
    <td>## map</td>
    <td>-200.88926</td>
  </tr>
  <tr>
    <td>## mar</td>
    <td>-152.80806</td>
  </tr>
  <tr>
    <td>## march</td>
    <td>-208.94308</td>
  </tr>
  <tr>
    <td>## mare</td>
    <td>-153.04916</td>
  </tr>
  <tr>
    <td>## mark</td>
    <td>-183.89005</td>
  </tr>
  <tr>
    <td>## marsh</td>
    <td>-151.77141</td>
  </tr>
  <tr>
    <td>## mart</td>
    <td>-156.16528</td>
  </tr>
  <tr>
    <td>## mash</td>
    <td>-182.90075</td>
  </tr>
  <tr>
    <td>## mask</td>
    <td>-200.03227</td>
  </tr>
  <tr>
    <td>## mass</td>
    <td>-183.25182</td>
  </tr>
  <tr>
    <td>## mast</td>
    <td>-184.29974</td>
  </tr>
  <tr>
    <td>## mat</td>
    <td>-182.98022</td>
  </tr>
  <tr>
    <td>## match</td>
    <td>-193.21544</td>
  </tr>
  <tr>
    <td>## mate</td>
    <td>-189.31414</td>
  </tr>
  <tr>
    <td>## maw</td>
    <td>-180.44250</td>
  </tr>
  <tr>
    <td>## may</td>
    <td>-185.46891</td>
  </tr>
  <tr>
    <td>## maze</td>
    <td>-188.60828</td>
  </tr>
  <tr>
    <td>## mead</td>
    <td>-165.20365</td>
  </tr>
  <tr>
    <td>## meal</td>
    <td>-200.22039</td>
  </tr>
  <tr>
    <td>## mean</td>
    <td>-182.43837</td>
  </tr>
  <tr>
    <td>## meat</td>
    <td>-185.86031</td>
  </tr>
  <tr>
    <td>## meet</td>
    <td>-195.91554</td>
  </tr>
  <tr>
    <td>## meld</td>
    <td>-181.95453</td>
  </tr>
  <tr>
    <td>## melt</td>
    <td>-197.25873</td>
  </tr>
  <tr>
    <td>## mend</td>
    <td>-185.49384</td>
  </tr>
  <tr>
    <td>## merge</td>
    <td>-185.13662</td>
  </tr>
  <tr>
    <td>## mesh</td>
    <td>-185.50697</td>
  </tr>
  <tr>
    <td>## mess</td>
    <td>-176.37793</td>
  </tr>
  <tr>
    <td>## mew</td>
    <td>-93.25702</td>
  </tr>
  <tr>
    <td>## might</td>
    <td>-182.50529</td>
  </tr>
  <tr>
    <td>## mile</td>
    <td>-190.52918</td>
  </tr>
  <tr>
    <td>## milk</td>
    <td>-188.72240</td>
  </tr>
  <tr>
    <td>## mill</td>
    <td>-175.77660</td>
  </tr>
  <tr>
    <td>## mime</td>
    <td>-117.24062</td>
  </tr>
  <tr>
    <td>## mince</td>
    <td>-124.07608</td>
  </tr>
  <tr>
    <td>## mind</td>
    <td>-199.74716</td>
  </tr>
  <tr>
    <td>## mine</td>
    <td>-181.29971</td>
  </tr>
  <tr>
    <td>## mink</td>
    <td>-143.47992</td>
  </tr>
  <tr>
    <td>## mint</td>
    <td>-188.97949</td>
  </tr>
  <tr>
    <td>## mirth</td>
    <td>-160.28014</td>
  </tr>
  <tr>
    <td>## miss</td>
    <td>-189.59721</td>
  </tr>
</table>
<table>
  <tr>
    <td>## mist</td>
    <td>-193.40429</td>
  </tr>
  <tr>
    <td>## mite</td>
    <td>-140.20659</td>
  </tr>
  <tr>
    <td>## mitt</td>
    <td>-162.01465</td>
  </tr>
  <tr>
    <td>## mix</td>
    <td>-195.93078</td>
  </tr>
  <tr>
    <td>## moan</td>
    <td>-180.78331</td>
  </tr>
  <tr>
    <td>## mob</td>
    <td>-198.98451</td>
  </tr>
  <tr>
    <td>## mock</td>
    <td>-182.82260</td>
  </tr>
  <tr>
    <td>## mode</td>
    <td>-176.03664</td>
  </tr>
  <tr>
    <td>## mole</td>
    <td>-191.68787</td>
  </tr>
  <tr>
    <td>## moll</td>
    <td>-134.16861</td>
  </tr>
  <tr>
    <td>## mom</td>
    <td>-193.87945</td>
  </tr>
  <tr>
    <td>## monk</td>
    <td>-195.70333</td>
  </tr>
  <tr>
    <td>## month</td>
    <td>-198.53557</td>
  </tr>
  <tr>
    <td>## moo</td>
    <td>-169.34995</td>
  </tr>
  <tr>
    <td>## mood</td>
    <td>-187.67002</td>
  </tr>
  <tr>
    <td>## moon</td>
    <td>-181.15562</td>
  </tr>
  <tr>
    <td>## moose</td>
    <td>-185.85566</td>
  </tr>
  <tr>
    <td>## moot</td>
    <td>-154.24901</td>
  </tr>
  <tr>
    <td>## mop</td>
    <td>-193.99076</td>
  </tr>
  <tr>
    <td>## moss</td>
    <td>-186.95396</td>
  </tr>
  <tr>
    <td>## moth</td>
    <td>-144.23981</td>
  </tr>
  <tr>
    <td>## mould</td>
    <td>-154.46921</td>
  </tr>
  <tr>
    <td>## mount</td>
    <td>-194.34907</td>
  </tr>
  <tr>
    <td>## mourn</td>
    <td>-192.96060</td>
  </tr>
  <tr>
    <td>## mouse</td>
    <td>-186.28277</td>
  </tr>
  <tr>
    <td>## mouth</td>
    <td>-196.54941</td>
  </tr>
  <tr>
    <td>## move</td>
    <td>-195.40323</td>
  </tr>
  <tr>
    <td>## mow</td>
    <td>-170.08923</td>
  </tr>
  <tr>
    <td>## muck</td>
    <td>-127.07729</td>
  </tr>
  <tr>
    <td>## mud</td>
    <td>-199.67957</td>
  </tr>
  <tr>
    <td>## muff</td>
    <td>-157.43872</td>
  </tr>
  <tr>
    <td>## mug</td>
    <td>-197.36210</td>
  </tr>
  <tr>
    <td>## mulch</td>
    <td>-158.18027</td>
  </tr>
  <tr>
    <td>## mule</td>
    <td>-182.71257</td>
  </tr>
  <tr>
    <td>## mum</td>
    <td>-145.17176</td>
  </tr>
  <tr>
    <td>## munch</td>
    <td>-161.30880</td>
  </tr>
  <tr>
    <td>## muse</td>
    <td>-146.61355</td>
  </tr>
  <tr>
    <td>## mush</td>
    <td>-160.07077</td>
  </tr>
  <tr>
    <td>## must</td>
    <td>-191.94731</td>
  </tr>
  <tr>
    <td>## myth</td>
    <td>-180.64856</td>
  </tr>
  <tr>
    <td>## nab</td>
    <td>-129.49141</td>
  </tr>
  <tr>
    <td>## nail</td>
    <td>-181.13083</td>
  </tr>
  <tr>
    <td>## name</td>
    <td>-181.10521</td>
  </tr>
  <tr>
    <td>## nap</td>
    <td>-182.97976</td>
  </tr>
  <tr>
    <td>## nape</td>
    <td>-152.35898</td>
  </tr>
  <tr>
    <td>## naught</td>
    <td>-116.73088</td>
  </tr>
</table>
<table>
  <tr>
    <td>## neck</td>
    <td>-193.97846</td>
  </tr>
  <tr>
    <td>## need</td>
    <td>-198.85321</td>
  </tr>
  <tr>
    <td>## nerve</td>
    <td>-180.74974</td>
  </tr>
  <tr>
    <td>## nest</td>
    <td>-188.23496</td>
  </tr>
  <tr>
    <td>## news</td>
    <td>-195.08342</td>
  </tr>
  <tr>
    <td>## newt</td>
    <td>-154.34379</td>
  </tr>
  <tr>
    <td>## nick</td>
    <td>-110.02855</td>
  </tr>
  <tr>
    <td>## niece</td>
    <td>-182.17530</td>
  </tr>
  <tr>
    <td>## night</td>
    <td>-183.06171</td>
  </tr>
  <tr>
    <td>## nil</td>
    <td>-90.11699</td>
  </tr>
  <tr>
    <td>## nip</td>
    <td>-152.17400</td>
  </tr>
  <tr>
    <td>## nod</td>
    <td>-178.18764</td>
  </tr>
  <tr>
    <td>## node</td>
    <td>-168.31176</td>
  </tr>
  <tr>
    <td>## noise</td>
    <td>-194.50435</td>
  </tr>
  <tr>
    <td>## nonce</td>
    <td>-178.07127</td>
  </tr>
  <tr>
    <td>## nook</td>
    <td>-127.53759</td>
  </tr>
  <tr>
    <td>## noon</td>
    <td>-180.34609</td>
  </tr>
  <tr>
    <td>## noose</td>
    <td>-175.11994</td>
  </tr>
  <tr>
    <td>## norm</td>
    <td>-180.74248</td>
  </tr>
  <tr>
    <td>## north</td>
    <td>-186.63133</td>
  </tr>
  <tr>
    <td>## nose</td>
    <td>-183.30458</td>
  </tr>
  <tr>
    <td>## notch</td>
    <td>-175.82574</td>
  </tr>
  <tr>
    <td>## note</td>
    <td>-181.15978</td>
  </tr>
  <tr>
    <td>## noun</td>
    <td>-158.11040</td>
  </tr>
  <tr>
    <td>## nudge</td>
    <td>-161.41559</td>
  </tr>
  <tr>
    <td>## nun</td>
    <td>-180.75218</td>
  </tr>
  <tr>
    <td>## nurse</td>
    <td>-182.95022</td>
  </tr>
  <tr>
    <td>## nut</td>
    <td>-198.20571</td>
  </tr>
  <tr>
    <td>## nymph</td>
    <td>-176.22918</td>
  </tr>
  <tr>
    <td>## oak</td>
    <td>-200.34944</td>
  </tr>
  <tr>
    <td>## oath</td>
    <td>-181.48696</td>
  </tr>
  <tr>
    <td>## oil</td>
    <td>-200.78910</td>
  </tr>
  <tr>
    <td>## ooze</td>
    <td>-169.22253</td>
  </tr>
  <tr>
    <td>## orb</td>
    <td>-106.54526</td>
  </tr>
  <tr>
    <td>## ore</td>
    <td>-162.97071</td>
  </tr>
  <tr>
    <td>## ought</td>
    <td>-180.08220</td>
  </tr>
  <tr>
    <td>## ounce</td>
    <td>-180.72218</td>
  </tr>
  <tr>
    <td>## oust</td>
    <td>-120.36905</td>
  </tr>
  <tr>
    <td>## owl</td>
    <td>-200.70880</td>
  </tr>
  <tr>
    <td>## pace</td>
    <td>-186.45204</td>
  </tr>
  <tr>
    <td>## pack</td>
    <td>-200.03755</td>
  </tr>
  <tr>
    <td>## pact</td>
    <td>-194.62752</td>
  </tr>
  <tr>
    <td>## pad</td>
    <td>-196.85380</td>
  </tr>
  <tr>
    <td>## page</td>
    <td>-199.01848</td>
  </tr>
  <tr>
    <td>## pail</td>
    <td>-181.89363</td>
  </tr>
  <tr>
    <td>## pain</td>
    <td>-187.32906</td>
  </tr>
</table>
<table>
  <tr>
    <td>## paint</td>
    <td>-200.79098</td>
  </tr>
  <tr>
    <td>## pair</td>
    <td>-200.91533</td>
  </tr>
  <tr>
    <td>## pal</td>
    <td>-198.66856</td>
  </tr>
  <tr>
    <td>## pale</td>
    <td>-200.27561</td>
  </tr>
  <tr>
    <td>## pall</td>
    <td>-180.42405</td>
  </tr>
  <tr>
    <td>## palm</td>
    <td>-197.91769</td>
  </tr>
  <tr>
    <td>## pan</td>
    <td>-193.49579</td>
  </tr>
  <tr>
    <td>## pane</td>
    <td>-173.63898</td>
  </tr>
  <tr>
    <td>## pang</td>
    <td>-113.91692</td>
  </tr>
  <tr>
    <td>## pant</td>
    <td>-194.06427</td>
  </tr>
  <tr>
    <td>## pap</td>
    <td>-155.08604</td>
  </tr>
  <tr>
    <td>## par</td>
    <td>-150.55460</td>
  </tr>
  <tr>
    <td>## pare</td>
    <td>-141.23823</td>
  </tr>
  <tr>
    <td>## park</td>
    <td>-195.30045</td>
  </tr>
  <tr>
    <td>## part</td>
    <td>-197.76299</td>
  </tr>
  <tr>
    <td>## pass</td>
    <td>-185.08781</td>
  </tr>
  <tr>
    <td>## paste</td>
    <td>-193.96262</td>
  </tr>
  <tr>
    <td>## pat</td>
    <td>-201.02096</td>
  </tr>
  <tr>
    <td>## patch</td>
    <td>-195.48718</td>
  </tr>
  <tr>
    <td>## pate</td>
    <td>-180.54191</td>
  </tr>
  <tr>
    <td>## path</td>
    <td>-199.13137</td>
  </tr>
  <tr>
    <td>## paunch</td>
    <td>-128.71632</td>
  </tr>
  <tr>
    <td>## pause</td>
    <td>-195.08610</td>
  </tr>
  <tr>
    <td>## pave</td>
    <td>-176.88551</td>
  </tr>
  <tr>
    <td>## paw</td>
    <td>-185.47866</td>
  </tr>
  <tr>
    <td>## pawn</td>
    <td>-181.30552</td>
  </tr>
  <tr>
    <td>## pay</td>
    <td>-200.19722</td>
  </tr>
  <tr>
    <td>## pea</td>
    <td>-200.71782</td>
  </tr>
  <tr>
    <td>## peace</td>
    <td>-193.35666</td>
  </tr>
  <tr>
    <td>## peach</td>
    <td>-183.59653</td>
  </tr>
  <tr>
    <td>## peak</td>
    <td>-192.52925</td>
  </tr>
  <tr>
    <td>## peal</td>
    <td>-180.74111</td>
  </tr>
  <tr>
    <td>## pear</td>
    <td>-193.74897</td>
  </tr>
  <tr>
    <td>## pearl</td>
    <td>-200.70403</td>
  </tr>
  <tr>
    <td>## peat</td>
    <td>-149.20065</td>
  </tr>
  <tr>
    <td>## peck</td>
    <td>-191.99359</td>
  </tr>
  <tr>
    <td>## pee</td>
    <td>-178.43011</td>
  </tr>
  <tr>
    <td>## peel</td>
    <td>-193.00972</td>
  </tr>
  <tr>
    <td>## peep</td>
    <td>-182.76614</td>
  </tr>
  <tr>
    <td>## peer</td>
    <td>-194.61593</td>
  </tr>
  <tr>
    <td>## peg</td>
    <td>-190.32993</td>
  </tr>
  <tr>
    <td>## pelt</td>
    <td>-132.93315</td>
  </tr>
  <tr>
    <td>## pen</td>
    <td>-194.91945</td>
  </tr>
  <tr>
    <td>## perch</td>
    <td>-163.05019</td>
  </tr>
  <tr>
    <td>## perk</td>
    <td>-180.57165</td>
  </tr>
  <tr>
    <td>## pest</td>
    <td>-179.61735</td>
  </tr>
</table>
<table>
  <tr>
    <td>## pet</td>
    <td>-198.61936</td>
  </tr>
  <tr>
    <td>## pew</td>
    <td>-144.58374</td>
  </tr>
  <tr>
    <td>## phase</td>
    <td>-181.11181</td>
  </tr>
  <tr>
    <td>## phrase</td>
    <td>-181.60563</td>
  </tr>
  <tr>
    <td>## pick</td>
    <td>-196.88221</td>
  </tr>
  <tr>
    <td>## pie</td>
    <td>-198.30051</td>
  </tr>
  <tr>
    <td>## piece</td>
    <td>-187.93957</td>
  </tr>
  <tr>
    <td>## pier</td>
    <td>-181.77809</td>
  </tr>
  <tr>
    <td>## pierce</td>
    <td>-181.03272</td>
  </tr>
  <tr>
    <td>## pig</td>
    <td>-200.72493</td>
  </tr>
  <tr>
    <td>## pike</td>
    <td>-192.16181</td>
  </tr>
  <tr>
    <td>## pile</td>
    <td>-201.09305</td>
  </tr>
  <tr>
    <td>## pill</td>
    <td>-182.88186</td>
  </tr>
  <tr>
    <td>## pimp</td>
    <td>-182.37559</td>
  </tr>
  <tr>
    <td>## pin</td>
    <td>-181.37618</td>
  </tr>
  <tr>
    <td>## pinch</td>
    <td>-181.51707</td>
  </tr>
  <tr>
    <td>## pine</td>
    <td>-196.79650</td>
  </tr>
  <tr>
    <td>## pint</td>
    <td>-179.79235</td>
  </tr>
  <tr>
    <td>## pip</td>
    <td>-141.24310</td>
  </tr>
  <tr>
    <td>## pipe</td>
    <td>-200.79354</td>
  </tr>
  <tr>
    <td>## piss</td>
    <td>-180.38935</td>
  </tr>
  <tr>
    <td>## pit</td>
    <td>-189.26940</td>
  </tr>
  <tr>
    <td>## pitch</td>
    <td>-192.42438</td>
  </tr>
  <tr>
    <td>## pith</td>
    <td>-156.22479</td>
  </tr>
  <tr>
    <td>## place</td>
    <td>-200.16531</td>
  </tr>
  <tr>
    <td>## plaid</td>
    <td>-195.06602</td>
  </tr>
  <tr>
    <td>## plain</td>
    <td>-180.30771</td>
  </tr>
  <tr>
    <td>## plan</td>
    <td>-199.75163</td>
  </tr>
  <tr>
    <td>## plane</td>
    <td>-180.41347</td>
  </tr>
  <tr>
    <td>## plank</td>
    <td>-165.79725</td>
  </tr>
  <tr>
    <td>## plant</td>
    <td>-186.87654</td>
  </tr>
  <tr>
    <td>## plate</td>
    <td>-193.70710</td>
  </tr>
  <tr>
    <td>## play</td>
    <td>-199.25126</td>
  </tr>
  <tr>
    <td>## plea</td>
    <td>-187.86079</td>
  </tr>
  <tr>
    <td>## plead</td>
    <td>-197.54024</td>
  </tr>
  <tr>
    <td>## please</td>
    <td>-200.60511</td>
  </tr>
  <tr>
    <td>## pleat</td>
    <td>-139.96200</td>
  </tr>
  <tr>
    <td>## pledge</td>
    <td>-183.61700</td>
  </tr>
  <tr>
    <td>## plod</td>
    <td>-128.38135</td>
  </tr>
  <tr>
    <td>## plot</td>
    <td>-199.69360</td>
  </tr>
  <tr>
    <td>## plough</td>
    <td>-168.01326</td>
  </tr>
  <tr>
    <td>## pluck</td>
    <td>-187.01972</td>
  </tr>
  <tr>
    <td>## plug</td>
    <td>-184.80959</td>
  </tr>
  <tr>
    <td>## plum</td>
    <td>-201.15028</td>
  </tr>
  <tr>
    <td>## plume</td>
    <td>-147.75665</td>
  </tr>
  <tr>
    <td>## plunge</td>
    <td>-186.43705</td>
  </tr>
</table>
<table>
  <tr>
    <td>## plush</td>
    <td>-190.67227</td>
  </tr>
  <tr>
    <td>## poach</td>
    <td>-130.40642</td>
  </tr>
  <tr>
    <td>## pod</td>
    <td>-175.41735</td>
  </tr>
  <tr>
    <td>## point</td>
    <td>-199.14027</td>
  </tr>
  <tr>
    <td>## poise</td>
    <td>-182.14726</td>
  </tr>
  <tr>
    <td>## poke</td>
    <td>-186.77324</td>
  </tr>
  <tr>
    <td>## pole</td>
    <td>-189.42852</td>
  </tr>
  <tr>
    <td>## poll</td>
    <td>-186.57126</td>
  </tr>
  <tr>
    <td>## pomp</td>
    <td>-174.66773</td>
  </tr>
  <tr>
    <td>## pond</td>
    <td>-189.41429</td>
  </tr>
  <tr>
    <td>## pool</td>
    <td>-200.77211</td>
  </tr>
  <tr>
    <td>## pop</td>
    <td>-195.60487</td>
  </tr>
  <tr>
    <td>## pope</td>
    <td>-198.78767</td>
  </tr>
  <tr>
    <td>## porch</td>
    <td>-185.46070</td>
  </tr>
  <tr>
    <td>## pore</td>
    <td>-161.30291</td>
  </tr>
  <tr>
    <td>## pork</td>
    <td>-198.89400</td>
  </tr>
  <tr>
    <td>## port</td>
    <td>-172.58742</td>
  </tr>
  <tr>
    <td>## pose</td>
    <td>-189.27807</td>
  </tr>
  <tr>
    <td>## post</td>
    <td>-189.02343</td>
  </tr>
  <tr>
    <td>## pot</td>
    <td>-199.61732</td>
  </tr>
  <tr>
    <td>## pouch</td>
    <td>-181.26954</td>
  </tr>
  <tr>
    <td>## pound</td>
    <td>-217.75718</td>
  </tr>
  <tr>
    <td>## pour</td>
    <td>-187.31017</td>
  </tr>
  <tr>
    <td>## pout</td>
    <td>-145.10510</td>
  </tr>
  <tr>
    <td>## praise</td>
    <td>-189.95765</td>
  </tr>
  <tr>
    <td>## prank</td>
    <td>-186.43456</td>
  </tr>
  <tr>
    <td>## pray</td>
    <td>-191.62946</td>
  </tr>
  <tr>
    <td>## preach</td>
    <td>-153.30282</td>
  </tr>
  <tr>
    <td>## prep</td>
    <td>-171.84330</td>
  </tr>
  <tr>
    <td>## press</td>
    <td>-192.28828</td>
  </tr>
  <tr>
    <td>## prey</td>
    <td>-189.16135</td>
  </tr>
  <tr>
    <td>## price</td>
    <td>-201.04373</td>
  </tr>
  <tr>
    <td>## prick</td>
    <td>-180.63602</td>
  </tr>
  <tr>
    <td>## pride</td>
    <td>-200.82337</td>
  </tr>
  <tr>
    <td>## priest</td>
    <td>-173.18802</td>
  </tr>
  <tr>
    <td>## prime</td>
    <td>-191.51082</td>
  </tr>
  <tr>
    <td>## prince</td>
    <td>-180.70657</td>
  </tr>
  <tr>
    <td>## print</td>
    <td>-200.01290</td>
  </tr>
  <tr>
    <td>## prize</td>
    <td>-194.75454</td>
  </tr>
  <tr>
    <td>## probe</td>
    <td>-185.76816</td>
  </tr>
  <tr>
    <td>## prod</td>
    <td>-125.66617</td>
  </tr>
  <tr>
    <td>## prop</td>
    <td>-162.65597</td>
  </tr>
  <tr>
    <td>## prose</td>
    <td>-167.59682</td>
  </tr>
  <tr>
    <td>## prove</td>
    <td>-176.96261</td>
  </tr>
  <tr>
    <td>## prow</td>
    <td>-146.63555</td>
  </tr>
  <tr>
    <td>## prowl</td>
    <td>-184.17429</td>
  </tr>
</table>
<table>
  <tr>
    <td>## pry</td>
    <td>-168.89280</td>
  </tr>
  <tr>
    <td>## psalm</td>
    <td>-148.82510</td>
  </tr>
  <tr>
    <td>## pub</td>
    <td>-193.56240</td>
  </tr>
  <tr>
    <td>## puck</td>
    <td>-178.14789</td>
  </tr>
  <tr>
    <td>## puff</td>
    <td>-185.96955</td>
  </tr>
  <tr>
    <td>## puke</td>
    <td>-160.15354</td>
  </tr>
  <tr>
    <td>## pull</td>
    <td>-191.09319</td>
  </tr>
  <tr>
    <td>## pulp</td>
    <td>-184.67662</td>
  </tr>
  <tr>
    <td>## pulse</td>
    <td>-197.74325</td>
  </tr>
  <tr>
    <td>## pump</td>
    <td>-186.66700</td>
  </tr>
  <tr>
    <td>## pun</td>
    <td>-152.61996</td>
  </tr>
  <tr>
    <td>## punch</td>
    <td>-193.28535</td>
  </tr>
  <tr>
    <td>## punk</td>
    <td>-190.08833</td>
  </tr>
  <tr>
    <td>## punt</td>
    <td>-179.36237</td>
  </tr>
  <tr>
    <td>## pup</td>
    <td>-191.98187</td>
  </tr>
  <tr>
    <td>## purge</td>
    <td>-182.04486</td>
  </tr>
  <tr>
    <td>## purse</td>
    <td>-184.90220</td>
  </tr>
  <tr>
    <td>## pus</td>
    <td>-169.22419</td>
  </tr>
  <tr>
    <td>## push</td>
    <td>-180.66250</td>
  </tr>
  <tr>
    <td>## put</td>
    <td>-186.90231</td>
  </tr>
  <tr>
    <td>## putt</td>
    <td>-177.24050</td>
  </tr>
  <tr>
    <td>## pyre</td>
    <td>-132.51119</td>
  </tr>
  <tr>
    <td>## quack</td>
    <td>-182.74197</td>
  </tr>
  <tr>
    <td>## quake</td>
    <td>-170.45057</td>
  </tr>
  <tr>
    <td>## quart</td>
    <td>-179.25866</td>
  </tr>
  <tr>
    <td>## quartz</td>
    <td>-182.25666</td>
  </tr>
  <tr>
    <td>## quay</td>
    <td>-180.64819</td>
  </tr>
  <tr>
    <td>## queen</td>
    <td>-185.98573</td>
  </tr>
  <tr>
    <td>## quell</td>
    <td>-90.45914</td>
  </tr>
  <tr>
    <td>## quench</td>
    <td>-165.11305</td>
  </tr>
  <tr>
    <td>## quest</td>
    <td>-180.60952</td>
  </tr>
  <tr>
    <td>## queue</td>
    <td>-123.85789</td>
  </tr>
  <tr>
    <td>## quill</td>
    <td>-175.44450</td>
  </tr>
  <tr>
    <td>## quince</td>
    <td>-102.66350</td>
  </tr>
  <tr>
    <td>## quirk</td>
    <td>-177.83388</td>
  </tr>
  <tr>
    <td>## quiz</td>
    <td>-183.30790</td>
  </tr>
  <tr>
    <td>## quote</td>
    <td>-191.33133</td>
  </tr>
  <tr>
    <td>## race</td>
    <td>-198.11680</td>
  </tr>
  <tr>
    <td>## rack</td>
    <td>-183.32338</td>
  </tr>
  <tr>
    <td>## raft</td>
    <td>-178.53014</td>
  </tr>
  <tr>
    <td>## rag</td>
    <td>-182.64471</td>
  </tr>
  <tr>
    <td>## rage</td>
    <td>-199.89479</td>
  </tr>
  <tr>
    <td>## raid</td>
    <td>-197.15718</td>
  </tr>
  <tr>
    <td>## rail</td>
    <td>-183.15826</td>
  </tr>
  <tr>
    <td>## rain</td>
    <td>-194.15535</td>
  </tr>
  <tr>
    <td>## raise</td>
    <td>-187.57436</td>
  </tr>
</table>
<table>
  <tr>
    <td>## rake</td>
    <td>-194.48466</td>
  </tr>
  <tr>
    <td>## ram</td>
    <td>-155.21072</td>
  </tr>
  <tr>
    <td>## ranch</td>
    <td>-199.36573</td>
  </tr>
  <tr>
    <td>## range</td>
    <td>-193.20859</td>
  </tr>
  <tr>
    <td>## rank</td>
    <td>-181.84561</td>
  </tr>
  <tr>
    <td>## rant</td>
    <td>-150.87228</td>
  </tr>
  <tr>
    <td>## rap</td>
    <td>-184.78255</td>
  </tr>
  <tr>
    <td>## rape</td>
    <td>-187.57505</td>
  </tr>
  <tr>
    <td>## rash</td>
    <td>-198.11612</td>
  </tr>
  <tr>
    <td>## rasp</td>
    <td>-153.50488</td>
  </tr>
  <tr>
    <td>## rat</td>
    <td>-198.03964</td>
  </tr>
  <tr>
    <td>## rate</td>
    <td>-189.99350</td>
  </tr>
  <tr>
    <td>## rave</td>
    <td>-186.42459</td>
  </tr>
  <tr>
    <td>## ray</td>
    <td>-180.91672</td>
  </tr>
  <tr>
    <td>## reach</td>
    <td>-200.87196</td>
  </tr>
  <tr>
    <td>## realm</td>
    <td>-182.55186</td>
  </tr>
  <tr>
    <td>## ream</td>
    <td>-109.76483</td>
  </tr>
  <tr>
    <td>## reap</td>
    <td>-167.10909</td>
  </tr>
  <tr>
    <td>## rear</td>
    <td>-193.66365</td>
  </tr>
  <tr>
    <td>## reed</td>
    <td>-155.95166</td>
  </tr>
  <tr>
    <td>## reef</td>
    <td>-143.87663</td>
  </tr>
  <tr>
    <td>## reek</td>
    <td>-166.25755</td>
  </tr>
  <tr>
    <td>## reel</td>
    <td>-146.38460</td>
  </tr>
  <tr>
    <td>## reign</td>
    <td>-179.86878</td>
  </tr>
  <tr>
    <td>## rein</td>
    <td>-144.30895</td>
  </tr>
  <tr>
    <td>## rend</td>
    <td>-179.96963</td>
  </tr>
  <tr>
    <td>## rent</td>
    <td>-190.18766</td>
  </tr>
  <tr>
    <td>## rest</td>
    <td>-200.14005</td>
  </tr>
  <tr>
    <td>## retch</td>
    <td>-75.93226</td>
  </tr>
  <tr>
    <td>## rhyme</td>
    <td>-179.63498</td>
  </tr>
  <tr>
    <td>## rib</td>
    <td>-196.17855</td>
  </tr>
  <tr>
    <td>## rice</td>
    <td>-200.77392</td>
  </tr>
  <tr>
    <td>## ride</td>
    <td>-185.69574</td>
  </tr>
  <tr>
    <td>## ridge</td>
    <td>-178.83661</td>
  </tr>
  <tr>
    <td>## rift</td>
    <td>-156.90625</td>
  </tr>
  <tr>
    <td>## rig</td>
    <td>-170.59591</td>
  </tr>
  <tr>
    <td>## right</td>
    <td>-197.72986</td>
  </tr>
  <tr>
    <td>## rile</td>
    <td>-126.35545</td>
  </tr>
  <tr>
    <td>## rim</td>
    <td>-183.34697</td>
  </tr>
  <tr>
    <td>## rime</td>
    <td>-97.32187</td>
  </tr>
  <tr>
    <td>## rind</td>
    <td>-157.11220</td>
  </tr>
  <tr>
    <td>## ring</td>
    <td>-205.12959</td>
  </tr>
  <tr>
    <td>## rink</td>
    <td>-153.40127</td>
  </tr>
  <tr>
    <td>## rinse</td>
    <td>-194.99619</td>
  </tr>
  <tr>
    <td>## rip</td>
    <td>-182.49526</td>
  </tr>
  <tr>
    <td>## rise</td>
    <td>-200.97542</td>
  </tr>
</table>
<table>
  <tr>
    <td>## risk</td>
    <td>-191.45216</td>
  </tr>
  <tr>
    <td>## rite</td>
    <td>-161.96339</td>
  </tr>
  <tr>
    <td>## roach</td>
    <td>-185.43835</td>
  </tr>
  <tr>
    <td>## road</td>
    <td>-200.40120</td>
  </tr>
  <tr>
    <td>## roam</td>
    <td>-188.26786</td>
  </tr>
  <tr>
    <td>## roar</td>
    <td>-192.19867</td>
  </tr>
  <tr>
    <td>## roast</td>
    <td>-182.36657</td>
  </tr>
  <tr>
    <td>## rob</td>
    <td>-187.81765</td>
  </tr>
  <tr>
    <td>## robe</td>
    <td>-182.55108</td>
  </tr>
  <tr>
    <td>## rock</td>
    <td>-214.41192</td>
  </tr>
  <tr>
    <td>## rod</td>
    <td>-187.99830</td>
  </tr>
  <tr>
    <td>## roe</td>
    <td>-152.55200</td>
  </tr>
  <tr>
    <td>## role</td>
    <td>-190.78015</td>
  </tr>
  <tr>
    <td>## roll</td>
    <td>-181.86569</td>
  </tr>
  <tr>
    <td>## romp</td>
    <td>-167.51676</td>
  </tr>
  <tr>
    <td>## roof</td>
    <td>-200.64774</td>
  </tr>
  <tr>
    <td>## rook</td>
    <td>-138.88816</td>
  </tr>
  <tr>
    <td>## room</td>
    <td>-201.12960</td>
  </tr>
  <tr>
    <td>## roost</td>
    <td>-188.87526</td>
  </tr>
  <tr>
    <td>## root</td>
    <td>-195.84367</td>
  </tr>
  <tr>
    <td>## rope</td>
    <td>-193.25524</td>
  </tr>
  <tr>
    <td>## rose</td>
    <td>-199.24926</td>
  </tr>
  <tr>
    <td>## rot</td>
    <td>-182.31482</td>
  </tr>
  <tr>
    <td>## rouse</td>
    <td>-109.79916</td>
  </tr>
  <tr>
    <td>## rout</td>
    <td>-142.80674</td>
  </tr>
  <tr>
    <td>## rove</td>
    <td>-102.46965</td>
  </tr>
  <tr>
    <td>## rub</td>
    <td>-200.95492</td>
  </tr>
  <tr>
    <td>## rue</td>
    <td>-158.31063</td>
  </tr>
  <tr>
    <td>## rug</td>
    <td>-192.37161</td>
  </tr>
  <tr>
    <td>## rule</td>
    <td>-195.91589</td>
  </tr>
  <tr>
    <td>## rum</td>
    <td>-186.37569</td>
  </tr>
  <tr>
    <td>## rump</td>
    <td>-177.00272</td>
  </tr>
  <tr>
    <td>## run</td>
    <td>-182.39464</td>
  </tr>
  <tr>
    <td>## rung</td>
    <td>-155.71650</td>
  </tr>
  <tr>
    <td>## runt</td>
    <td>-118.33002</td>
  </tr>
  <tr>
    <td>## ruse</td>
    <td>-125.97785</td>
  </tr>
  <tr>
    <td>## rush</td>
    <td>-195.98513</td>
  </tr>
  <tr>
    <td>## rust</td>
    <td>-186.47713</td>
  </tr>
  <tr>
    <td>## rut</td>
    <td>-161.82767</td>
  </tr>
  <tr>
    <td>## rye</td>
    <td>-178.07559</td>
  </tr>
  <tr>
    <td>## sack</td>
    <td>-181.38431</td>
  </tr>
  <tr>
    <td>## sag</td>
    <td>-181.07131</td>
  </tr>
  <tr>
    <td>## sail</td>
    <td>-197.21202</td>
  </tr>
  <tr>
    <td>## saint</td>
    <td>-193.19800</td>
  </tr>
  <tr>
    <td>## sake</td>
    <td>-175.30860</td>
  </tr>
  <tr>
    <td>## sale</td>
    <td>-183.96642</td>
  </tr>
</table>
<table>
  <tr>
    <td>## salt</td>
    <td>-200.93684</td>
  </tr>
  <tr>
    <td>## salve</td>
    <td>-169.89094</td>
  </tr>
  <tr>
    <td>## sand</td>
    <td>-194.04721</td>
  </tr>
  <tr>
    <td>## sap</td>
    <td>-161.70408</td>
  </tr>
  <tr>
    <td>## sash</td>
    <td>-166.15555</td>
  </tr>
  <tr>
    <td>## sauce</td>
    <td>-194.25654</td>
  </tr>
  <tr>
    <td>## save</td>
    <td>-193.62868</td>
  </tr>
  <tr>
    <td>## saw</td>
    <td>-180.62980</td>
  </tr>
  <tr>
    <td>## sax</td>
    <td>-142.90758</td>
  </tr>
  <tr>
    <td>## say</td>
    <td>-184.19972</td>
  </tr>
  <tr>
    <td>## scald</td>
    <td>-132.74152</td>
  </tr>
  <tr>
    <td>## scale</td>
    <td>-189.65499</td>
  </tr>
  <tr>
    <td>## scalp</td>
    <td>-199.18851</td>
  </tr>
  <tr>
    <td>## scan</td>
    <td>-179.27390</td>
  </tr>
  <tr>
    <td>## scar</td>
    <td>-182.48437</td>
  </tr>
  <tr>
    <td>## scare</td>
    <td>-180.89106</td>
  </tr>
  <tr>
    <td>## scarf</td>
    <td>-183.69445</td>
  </tr>
  <tr>
    <td>## scene</td>
    <td>-186.47739</td>
  </tr>
  <tr>
    <td>## scent</td>
    <td>-198.97303</td>
  </tr>
  <tr>
    <td>## scheme</td>
    <td>-183.74242</td>
  </tr>
  <tr>
    <td>## school</td>
    <td>-187.36513</td>
  </tr>
  <tr>
    <td>## scoop</td>
    <td>-184.99389</td>
  </tr>
  <tr>
    <td>## scope</td>
    <td>-182.48244</td>
  </tr>
  <tr>
    <td>## score</td>
    <td>-193.73114</td>
  </tr>
  <tr>
    <td>## scorn</td>
    <td>-181.21660</td>
  </tr>
  <tr>
    <td>## scotch</td>
    <td>-175.97100</td>
  </tr>
  <tr>
    <td>## scour</td>
    <td>-164.89223</td>
  </tr>
  <tr>
    <td>## scourge</td>
    <td>-178.14822</td>
  </tr>
  <tr>
    <td>## scout</td>
    <td>-178.13461</td>
  </tr>
  <tr>
    <td>## scrap</td>
    <td>-180.07528</td>
  </tr>
  <tr>
    <td>## scrape</td>
    <td>-180.81134</td>
  </tr>
  <tr>
    <td>## scratch</td>
    <td>-182.85589</td>
  </tr>
  <tr>
    <td>## scream</td>
    <td>-181.03116</td>
  </tr>
  <tr>
    <td>## screech</td>
    <td>-156.68407</td>
  </tr>
  <tr>
    <td>## screen</td>
    <td>-183.02911</td>
  </tr>
  <tr>
    <td>## screw</td>
    <td>-198.49070</td>
  </tr>
  <tr>
    <td>## scribe</td>
    <td>-179.24772</td>
  </tr>
  <tr>
    <td>## script</td>
    <td>-200.85556</td>
  </tr>
  <tr>
    <td>## scrub</td>
    <td>-180.37167</td>
  </tr>
  <tr>
    <td>## scuff</td>
    <td>-125.06188</td>
  </tr>
  <tr>
    <td>## sea</td>
    <td>-195.16190</td>
  </tr>
  <tr>
    <td>## seal</td>
    <td>-182.82942</td>
  </tr>
  <tr>
    <td>## seam</td>
    <td>-134.86899</td>
  </tr>
  <tr>
    <td>## sear</td>
    <td>-138.84448</td>
  </tr>
  <tr>
    <td>## search</td>
    <td>-181.41687</td>
  </tr>
  <tr>
    <td>## seat</td>
    <td>-190.31345</td>
  </tr>
</table>
<table>
  <tr>
    <td>## sect</td>
    <td>-99.94390</td>
  </tr>
  <tr>
    <td>## see</td>
    <td>-191.78834</td>
  </tr>
  <tr>
    <td>## seed</td>
    <td>-188.68877</td>
  </tr>
  <tr>
    <td>## seek</td>
    <td>-200.85510</td>
  </tr>
  <tr>
    <td>## seem</td>
    <td>-181.75373</td>
  </tr>
  <tr>
    <td>## seep</td>
    <td>-141.27184</td>
  </tr>
  <tr>
    <td>## seize</td>
    <td>-195.57464</td>
  </tr>
  <tr>
    <td>## self</td>
    <td>-200.86794</td>
  </tr>
  <tr>
    <td>## sell</td>
    <td>-181.30148</td>
  </tr>
  <tr>
    <td>## send</td>
    <td>-187.14534</td>
  </tr>
  <tr>
    <td>## sense</td>
    <td>-189.31080</td>
  </tr>
  <tr>
    <td>## serf</td>
    <td>-152.05742</td>
  </tr>
  <tr>
    <td>## serge</td>
    <td>-147.29812</td>
  </tr>
  <tr>
    <td>## serve</td>
    <td>-182.59617</td>
  </tr>
  <tr>
    <td>## set</td>
    <td>-216.67293</td>
  </tr>
  <tr>
    <td>## sew</td>
    <td>-186.87950</td>
  </tr>
  <tr>
    <td>## sex</td>
    <td>-194.72305</td>
  </tr>
  <tr>
    <td>## shack</td>
    <td>-186.29230</td>
  </tr>
  <tr>
    <td>## shade</td>
    <td>-191.77651</td>
  </tr>
  <tr>
    <td>## shaft</td>
    <td>-181.66234</td>
  </tr>
  <tr>
    <td>## shag</td>
    <td>-160.94406</td>
  </tr>
  <tr>
    <td>## shah</td>
    <td>-147.18544</td>
  </tr>
  <tr>
    <td>## shake</td>
    <td>-193.82763</td>
  </tr>
  <tr>
    <td>## shall</td>
    <td>-177.64945</td>
  </tr>
  <tr>
    <td>## sham</td>
    <td>-159.27054</td>
  </tr>
  <tr>
    <td>## shame</td>
    <td>-185.77155</td>
  </tr>
  <tr>
    <td>## shank</td>
    <td>-137.77019</td>
  </tr>
  <tr>
    <td>## shape</td>
    <td>-197.14660</td>
  </tr>
  <tr>
    <td>## shard</td>
    <td>-129.99753</td>
  </tr>
  <tr>
    <td>## share</td>
    <td>-200.24253</td>
  </tr>
  <tr>
    <td>## shark</td>
    <td>-198.84384</td>
  </tr>
  <tr>
    <td>## shave</td>
    <td>-186.78454</td>
  </tr>
  <tr>
    <td>## shawl</td>
    <td>-160.77695</td>
  </tr>
  <tr>
    <td>## shay</td>
    <td>-168.85475</td>
  </tr>
  <tr>
    <td>## sheaf</td>
    <td>-134.71013</td>
  </tr>
  <tr>
    <td>## shear</td>
    <td>-174.93947</td>
  </tr>
  <tr>
    <td>## sheath</td>
    <td>-153.11711</td>
  </tr>
  <tr>
    <td>## shed</td>
    <td>-184.09195</td>
  </tr>
  <tr>
    <td>## sheen</td>
    <td>-138.83067</td>
  </tr>
  <tr>
    <td>## sheep</td>
    <td>-187.45273</td>
  </tr>
  <tr>
    <td>## sheer</td>
    <td>-173.79078</td>
  </tr>
  <tr>
    <td>## sheet</td>
    <td>-200.41153</td>
  </tr>
  <tr>
    <td>## shelf</td>
    <td>-194.14407</td>
  </tr>
  <tr>
    <td>## shell</td>
    <td>-199.56132</td>
  </tr>
  <tr>
    <td>## shield</td>
    <td>-199.55416</td>
  </tr>
  <tr>
    <td>## shift</td>
    <td>-187.21278</td>
  </tr>
</table>
<table>
  <tr>
    <td>## shin</td>
    <td>-147.15171</td>
  </tr>
  <tr>
    <td>## shine</td>
    <td>-180.82416</td>
  </tr>
  <tr>
    <td>## ship</td>
    <td>-195.32094</td>
  </tr>
  <tr>
    <td>## shirt</td>
    <td>-184.85724</td>
  </tr>
  <tr>
    <td>## shoal</td>
    <td>-132.34242</td>
  </tr>
  <tr>
    <td>## shock</td>
    <td>-184.36120</td>
  </tr>
  <tr>
    <td>## shoe</td>
    <td>-182.78819</td>
  </tr>
  <tr>
    <td>## shoot</td>
    <td>-190.72601</td>
  </tr>
  <tr>
    <td>## shop</td>
    <td>-193.30458</td>
  </tr>
  <tr>
    <td>## shore</td>
    <td>-182.16144</td>
  </tr>
  <tr>
    <td>## shot</td>
    <td>-182.83511</td>
  </tr>
  <tr>
    <td>## should</td>
    <td>-198.11266</td>
  </tr>
  <tr>
    <td>## shout</td>
    <td>-192.52303</td>
  </tr>
  <tr>
    <td>## shove</td>
    <td>-182.26475</td>
  </tr>
  <tr>
    <td>## show</td>
    <td>-188.95606</td>
  </tr>
  <tr>
    <td>## shred</td>
    <td>-180.62172</td>
  </tr>
  <tr>
    <td>## shrimp</td>
    <td>-188.37147</td>
  </tr>
  <tr>
    <td>## shrine</td>
    <td>-140.27048</td>
  </tr>
  <tr>
    <td>## shrink</td>
    <td>-184.59246</td>
  </tr>
  <tr>
    <td>## shrub</td>
    <td>-181.05770</td>
  </tr>
  <tr>
    <td>## shrug</td>
    <td>-165.70948</td>
  </tr>
  <tr>
    <td>## shuck</td>
    <td>-66.41085</td>
  </tr>
  <tr>
    <td>## shun</td>
    <td>-148.85423</td>
  </tr>
  <tr>
    <td>## shunt</td>
    <td>-88.92763</td>
  </tr>
  <tr>
    <td>## shut</td>
    <td>-181.15680</td>
  </tr>
  <tr>
    <td>## side</td>
    <td>-184.96325</td>
  </tr>
  <tr>
    <td>## siege</td>
    <td>-176.44916</td>
  </tr>
  <tr>
    <td>## sigh</td>
    <td>-168.48956</td>
  </tr>
  <tr>
    <td>## sight</td>
    <td>-185.19623</td>
  </tr>
  <tr>
    <td>## sign</td>
    <td>-182.02804</td>
  </tr>
  <tr>
    <td>## silk</td>
    <td>-182.17829</td>
  </tr>
  <tr>
    <td>## sill</td>
    <td>-97.09991</td>
  </tr>
  <tr>
    <td>## sin</td>
    <td>-182.22347</td>
  </tr>
  <tr>
    <td>## sine</td>
    <td>-118.70866</td>
  </tr>
  <tr>
    <td>## sing</td>
    <td>-198.64374</td>
  </tr>
  <tr>
    <td>## sink</td>
    <td>-192.16917</td>
  </tr>
  <tr>
    <td>## sip</td>
    <td>-196.58851</td>
  </tr>
  <tr>
    <td>## sir</td>
    <td>-177.99672</td>
  </tr>
  <tr>
    <td>## sit</td>
    <td>-198.01134</td>
  </tr>
  <tr>
    <td>## site</td>
    <td>-182.20435</td>
  </tr>
  <tr>
    <td>## size</td>
    <td>-197.90666</td>
  </tr>
  <tr>
    <td>## skate</td>
    <td>-194.54895</td>
  </tr>
  <tr>
    <td>## skeet</td>
    <td>-109.43309</td>
  </tr>
  <tr>
    <td>## sketch</td>
    <td>-182.82084</td>
  </tr>
  <tr>
    <td>## ski</td>
    <td>-183.35813</td>
  </tr>
  <tr>
    <td>## skid</td>
    <td>-167.38537</td>
  </tr>
</table>
<table>
  <tr>
    <td>skiff</td>
    <td>-180.61240</td>
  </tr>
  <tr>
    <td>skill</td>
    <td>-190.75874</td>
  </tr>
  <tr>
    <td>skin</td>
    <td>-180.88862</td>
  </tr>
  <tr>
    <td>skip</td>
    <td>-185.55312</td>
  </tr>
  <tr>
    <td>skirt</td>
    <td>-183.05175</td>
  </tr>
  <tr>
    <td>skit</td>
    <td>-192.00281</td>
  </tr>
  <tr>
    <td>skulk</td>
    <td>-179.31218</td>
  </tr>
  <tr>
    <td>skull</td>
    <td>-196.78044</td>
  </tr>
  <tr>
    <td>skunk</td>
    <td>-177.59173</td>
  </tr>
  <tr>
    <td>sky</td>
    <td>-200.66092</td>
  </tr>
  <tr>
    <td>slab</td>
    <td>-162.59690</td>
  </tr>
  <tr>
    <td>slam</td>
    <td>-183.43196</td>
  </tr>
  <tr>
    <td>slang</td>
    <td>-184.48607</td>
  </tr>
  <tr>
    <td>slant</td>
    <td>-179.90844</td>
  </tr>
  <tr>
    <td>slap</td>
    <td>-187.07268</td>
  </tr>
  <tr>
    <td>slash</td>
    <td>-180.14653</td>
  </tr>
  <tr>
    <td>slat</td>
    <td>-151.77343</td>
  </tr>
  <tr>
    <td>slate</td>
    <td>-171.99171</td>
  </tr>
  <tr>
    <td>slave</td>
    <td>-195.93577</td>
  </tr>
  <tr>
    <td>sleep</td>
    <td>-185.52574</td>
  </tr>
  <tr>
    <td>sleeve</td>
    <td>-196.70453</td>
  </tr>
  <tr>
    <td>slice</td>
    <td>-198.69686</td>
  </tr>
  <tr>
    <td>slide</td>
    <td>-188.20557</td>
  </tr>
  <tr>
    <td>slip</td>
    <td>-200.91955</td>
  </tr>
  <tr>
    <td>slit</td>
    <td>-176.38264</td>
  </tr>
  <tr>
    <td>slob</td>
    <td>-181.57825</td>
  </tr>
  <tr>
    <td>sloe</td>
    <td>-123.63302</td>
  </tr>
  <tr>
    <td>sloop</td>
    <td>-167.91262</td>
  </tr>
  <tr>
    <td>slop</td>
    <td>-138.09665</td>
  </tr>
  <tr>
    <td>slope</td>
    <td>-180.03767</td>
  </tr>
  <tr>
    <td>slot</td>
    <td>-185.55774</td>
  </tr>
  <tr>
    <td>slouch</td>
    <td>-169.68507</td>
  </tr>
  <tr>
    <td>slough</td>
    <td>-145.58308</td>
  </tr>
  <tr>
    <td>sludge</td>
    <td>-122.18314</td>
  </tr>
  <tr>
    <td>slug</td>
    <td>-180.66804</td>
  </tr>
  <tr>
    <td>sluice</td>
    <td>-92.79625</td>
  </tr>
  <tr>
    <td>slum</td>
    <td>-156.86831</td>
  </tr>
  <tr>
    <td>slump</td>
    <td>-183.36249</td>
  </tr>
  <tr>
    <td>smack</td>
    <td>-183.89882</td>
  </tr>
  <tr>
    <td>smart</td>
    <td>-190.89899</td>
  </tr>
  <tr>
    <td>smash</td>
    <td>-191.95488</td>
  </tr>
  <tr>
    <td>smear</td>
    <td>-198.17038</td>
  </tr>
  <tr>
    <td>smell</td>
    <td>-201.10669</td>
  </tr>
  <tr>
    <td>smelt</td>
    <td>-119.75341</td>
  </tr>
  <tr>
    <td>smile</td>
    <td>-198.52241</td>
  </tr>
  <tr>
    <td>smirk</td>
    <td>-178.61037</td>
  </tr>
</table>
<table>
  <tr>
    <td>smoke</td>
    <td>-199.91456</td>
  </tr>
  <tr>
    <td>snack</td>
    <td>-180.85241</td>
  </tr>
  <tr>
    <td>snag</td>
    <td>-187.81698</td>
  </tr>
  <tr>
    <td>snail</td>
    <td>-180.88456</td>
  </tr>
  <tr>
    <td>snake</td>
    <td>-189.01833</td>
  </tr>
  <tr>
    <td>snap</td>
    <td>-191.98350</td>
  </tr>
  <tr>
    <td>snare</td>
    <td>-183.00731</td>
  </tr>
  <tr>
    <td>snatch</td>
    <td>-181.81922</td>
  </tr>
  <tr>
    <td>sneak</td>
    <td>-185.82816</td>
  </tr>
  <tr>
    <td>sneer</td>
    <td>-183.88804</td>
  </tr>
  <tr>
    <td>sniff</td>
    <td>-180.79746</td>
  </tr>
  <tr>
    <td>snip</td>
    <td>-175.96218</td>
  </tr>
  <tr>
    <td>snob</td>
    <td>-182.07073</td>
  </tr>
  <tr>
    <td>snoop</td>
    <td>-181.84613</td>
  </tr>
  <tr>
    <td>snort</td>
    <td>-176.38866</td>
  </tr>
  <tr>
    <td>snout</td>
    <td>-168.95207</td>
  </tr>
  <tr>
    <td>snow</td>
    <td>-186.54855</td>
  </tr>
  <tr>
    <td>snug</td>
    <td>-180.52870</td>
  </tr>
  <tr>
    <td>soak</td>
    <td>-197.47777</td>
  </tr>
  <tr>
    <td>soap</td>
    <td>-200.16648</td>
  </tr>
  <tr>
    <td>sob</td>
    <td>-180.05082</td>
  </tr>
  <tr>
    <td>sock</td>
    <td>-183.37524</td>
  </tr>
  <tr>
    <td>sod</td>
    <td>-171.87157</td>
  </tr>
  <tr>
    <td>sole</td>
    <td>-186.57964</td>
  </tr>
  <tr>
    <td>solve</td>
    <td>-181.25563</td>
  </tr>
  <tr>
    <td>son</td>
    <td>-181.25279</td>
  </tr>
  <tr>
    <td>song</td>
    <td>-190.83791</td>
  </tr>
  <tr>
    <td>soot</td>
    <td>-119.54193</td>
  </tr>
  <tr>
    <td>soothe</td>
    <td>-170.16984</td>
  </tr>
  <tr>
    <td>sop</td>
    <td>-83.73826</td>
  </tr>
  <tr>
    <td>sort</td>
    <td>-186.53189</td>
  </tr>
  <tr>
    <td>soul</td>
    <td>-197.95492</td>
  </tr>
  <tr>
    <td>sound</td>
    <td>-198.28540</td>
  </tr>
  <tr>
    <td>soup</td>
    <td>-190.62453</td>
  </tr>
  <tr>
    <td>source</td>
    <td>-198.28720</td>
  </tr>
  <tr>
    <td>south</td>
    <td>-160.28872</td>
  </tr>
  <tr>
    <td>soy</td>
    <td>-175.16694</td>
  </tr>
  <tr>
    <td>spa</td>
    <td>-174.78612</td>
  </tr>
  <tr>
    <td>space</td>
    <td>-197.98746</td>
  </tr>
  <tr>
    <td>spade</td>
    <td>-185.49269</td>
  </tr>
  <tr>
    <td>span</td>
    <td>-180.64745</td>
  </tr>
  <tr>
    <td>spare</td>
    <td>-178.05934</td>
  </tr>
  <tr>
    <td>spark</td>
    <td>-197.20337</td>
  </tr>
  <tr>
    <td>spat</td>
    <td>-176.79567</td>
  </tr>
  <tr>
    <td>spate</td>
    <td>-111.00927</td>
  </tr>
  <tr>
    <td>speak</td>
    <td>-183.95416</td>
  </tr>
</table>
<table>
  <tr>
    <td>## spear</td>
    <td>-189.72435</td>
  </tr>
  <tr>
    <td>## speck</td>
    <td>-139.14799</td>
  </tr>
  <tr>
    <td>## speech</td>
    <td>-189.36852</td>
  </tr>
  <tr>
    <td>## speed</td>
    <td>-192.29385</td>
  </tr>
  <tr>
    <td>## spell</td>
    <td>-216.32293</td>
  </tr>
  <tr>
    <td>## spend</td>
    <td>-200.73796</td>
  </tr>
  <tr>
    <td>## sphere</td>
    <td>-181.48721</td>
  </tr>
  <tr>
    <td>## sphinx</td>
    <td>-179.94986</td>
  </tr>
  <tr>
    <td>## spice</td>
    <td>-181.51850</td>
  </tr>
  <tr>
    <td>## spike</td>
    <td>-200.21480</td>
  </tr>
  <tr>
    <td>## spill</td>
    <td>-200.79293</td>
  </tr>
  <tr>
    <td>## spin</td>
    <td>-200.44847</td>
  </tr>
  <tr>
    <td>## spine</td>
    <td>-186.52253</td>
  </tr>
  <tr>
    <td>## spire</td>
    <td>-158.62391</td>
  </tr>
  <tr>
    <td>## spit</td>
    <td>-187.10866</td>
  </tr>
  <tr>
    <td>## spite</td>
    <td>-166.83537</td>
  </tr>
  <tr>
    <td>## splash</td>
    <td>-191.04130</td>
  </tr>
  <tr>
    <td>## spleen</td>
    <td>-119.16819</td>
  </tr>
  <tr>
    <td>## splice</td>
    <td>-141.89796</td>
  </tr>
  <tr>
    <td>## split</td>
    <td>-191.21046</td>
  </tr>
  <tr>
    <td>## splurge</td>
    <td>-149.94453</td>
  </tr>
  <tr>
    <td>## spoil</td>
    <td>-190.85156</td>
  </tr>
  <tr>
    <td>## spoke</td>
    <td>-199.23057</td>
  </tr>
  <tr>
    <td>## spoof</td>
    <td>-140.69350</td>
  </tr>
  <tr>
    <td>## spool</td>
    <td>-200.30228</td>
  </tr>
  <tr>
    <td>## spoon</td>
    <td>-183.00642</td>
  </tr>
  <tr>
    <td>## sport</td>
    <td>-189.72236</td>
  </tr>
  <tr>
    <td>## spot</td>
    <td>-187.75947</td>
  </tr>
  <tr>
    <td>## spouse</td>
    <td>-184.65006</td>
  </tr>
  <tr>
    <td>## spout</td>
    <td>-180.21159</td>
  </tr>
  <tr>
    <td>## sprawl</td>
    <td>-180.95358</td>
  </tr>
  <tr>
    <td>## spray</td>
    <td>-180.97595</td>
  </tr>
  <tr>
    <td>## spread</td>
    <td>-182.45691</td>
  </tr>
  <tr>
    <td>## spree</td>
    <td>-128.06103</td>
  </tr>
  <tr>
    <td>## sprig</td>
    <td>-115.04485</td>
  </tr>
  <tr>
    <td>## spring</td>
    <td>-190.76488</td>
  </tr>
  <tr>
    <td>## sprite</td>
    <td>-139.41579</td>
  </tr>
  <tr>
    <td>## sprout</td>
    <td>-185.85706</td>
  </tr>
  <tr>
    <td>## spur</td>
    <td>-181.05877</td>
  </tr>
  <tr>
    <td>## spurt</td>
    <td>-150.35849</td>
  </tr>
  <tr>
    <td>## spy</td>
    <td>-188.31844</td>
  </tr>
  <tr>
    <td>## squad</td>
    <td>-180.87106</td>
  </tr>
  <tr>
    <td>## squall</td>
    <td>-150.39662</td>
  </tr>
  <tr>
    <td>## square</td>
    <td>-183.61698</td>
  </tr>
  <tr>
    <td>## squash</td>
    <td>-181.76710</td>
  </tr>
  <tr>
    <td>## squat</td>
    <td>-168.49604</td>
  </tr>
</table>
<table>
  <tr>
    <td>## squaw</td>
    <td>-131.41016</td>
  </tr>
  <tr>
    <td>## squawk</td>
    <td>-148.36055</td>
  </tr>
  <tr>
    <td>## squeak</td>
    <td>-182.72143</td>
  </tr>
  <tr>
    <td>## squeal</td>
    <td>-181.00388</td>
  </tr>
  <tr>
    <td>## squeeze</td>
    <td>-185.02157</td>
  </tr>
  <tr>
    <td>## squint</td>
    <td>-182.96653</td>
  </tr>
  <tr>
    <td>## squire</td>
    <td>-159.63536</td>
  </tr>
  <tr>
    <td>## squirm</td>
    <td>-183.28023</td>
  </tr>
  <tr>
    <td>## squirt</td>
    <td>-181.15936</td>
  </tr>
  <tr>
    <td>## stab</td>
    <td>-182.63028</td>
  </tr>
  <tr>
    <td>## stack</td>
    <td>-184.97646</td>
  </tr>
  <tr>
    <td>## staff</td>
    <td>-196.70820</td>
  </tr>
  <tr>
    <td>## stag</td>
    <td>-192.24276</td>
  </tr>
  <tr>
    <td>## stage</td>
    <td>-189.04541</td>
  </tr>
  <tr>
    <td>## stain</td>
    <td>-180.92342</td>
  </tr>
  <tr>
    <td>## stair</td>
    <td>-185.67162</td>
  </tr>
  <tr>
    <td>## stake</td>
    <td>-176.17801</td>
  </tr>
  <tr>
    <td>## stalk</td>
    <td>-183.83687</td>
  </tr>
  <tr>
    <td>## stall</td>
    <td>-195.48424</td>
  </tr>
  <tr>
    <td>## stamp</td>
    <td>-186.02846</td>
  </tr>
  <tr>
    <td>## stance</td>
    <td>-177.40536</td>
  </tr>
  <tr>
    <td>## stanch</td>
    <td>-180.56654</td>
  </tr>
  <tr>
    <td>## stand</td>
    <td>-192.21776</td>
  </tr>
  <tr>
    <td>## star</td>
    <td>-190.12507</td>
  </tr>
  <tr>
    <td>## starch</td>
    <td>-188.25042</td>
  </tr>
  <tr>
    <td>## stare</td>
    <td>-185.37834</td>
  </tr>
  <tr>
    <td>## start</td>
    <td>-186.51462</td>
  </tr>
  <tr>
    <td>## starve</td>
    <td>-183.12461</td>
  </tr>
  <tr>
    <td>## state</td>
    <td>-187.50172</td>
  </tr>
  <tr>
    <td>## staunch</td>
    <td>-123.61598</td>
  </tr>
  <tr>
    <td>## stave</td>
    <td>-142.97567</td>
  </tr>
  <tr>
    <td>## stay</td>
    <td>-198.67878</td>
  </tr>
  <tr>
    <td>## stead</td>
    <td>-155.95756</td>
  </tr>
  <tr>
    <td>## steak</td>
    <td>-181.94464</td>
  </tr>
  <tr>
    <td>## steal</td>
    <td>-197.20840</td>
  </tr>
  <tr>
    <td>## steam</td>
    <td>-180.82404</td>
  </tr>
  <tr>
    <td>## steed</td>
    <td>-145.20281</td>
  </tr>
  <tr>
    <td>## steel</td>
    <td>-184.23585</td>
  </tr>
  <tr>
    <td>## steer</td>
    <td>-181.12372</td>
  </tr>
  <tr>
    <td>## stem</td>
    <td>-181.08883</td>
  </tr>
  <tr>
    <td>## stench</td>
    <td>-147.23064</td>
  </tr>
  <tr>
    <td>## step</td>
    <td>-200.63404</td>
  </tr>
  <tr>
    <td>## stew</td>
    <td>-201.07644</td>
  </tr>
  <tr>
    <td>## stick</td>
    <td>-191.94924</td>
  </tr>
  <tr>
    <td>## still</td>
    <td>-197.13322</td>
  </tr>
  <tr>
    <td>## stilt</td>
    <td>-133.62956</td>
  </tr>
</table>
<table><tr><td>sting</td><td>-181.41850</td></tr><tr><td>stink</td><td>-183.02114</td></tr><tr><td>stint</td><td>-179.08701</td></tr><tr><td>stir</td><td>-200.52346</td></tr><tr><td>stitch</td><td>-159.49679</td></tr><tr><td>stock</td><td>-200.79501</td></tr><tr><td>stole</td><td>-197.24021</td></tr><tr><td>stone</td><td>-182.69565</td></tr><tr><td>stool</td><td>-200.61709</td></tr><tr><td>stoop</td><td>-147.13250</td></tr><tr><td>stop</td><td>-191.18680</td></tr><tr><td>store</td><td>-190.57167</td></tr><tr><td>stork</td><td>-183.89560</td></tr><tr><td>storm</td><td>-190.51947</td></tr><tr><td>stout</td><td>-179.12409</td></tr><tr><td>stove</td><td>-187.92919</td></tr><tr><td>stow</td><td>-149.30680</td></tr><tr><td>strafe</td><td>-147.84157</td></tr><tr><td>strain</td><td>-189.56632</td></tr><tr><td>strand</td><td>-177.70036</td></tr><tr><td>strap</td><td>-181.55636</td></tr><tr><td>straw</td><td>-198.46284</td></tr><tr><td>stray</td><td>-195.30999</td></tr><tr><td>streak</td><td>-185.23098</td></tr><tr><td>stream</td><td>-180.72229</td></tr><tr><td>street</td><td>-184.65560</td></tr><tr><td>stress</td><td>-199.67422</td></tr><tr><td>stretch</td><td>-184.51075</td></tr><tr><td>stride</td><td>-189.82378</td></tr><tr><td>strife</td><td>-168.19173</td></tr><tr><td>strike</td><td>-199.54882</td></tr><tr><td>string</td><td>-185.42961</td></tr><tr><td>strip</td><td>-197.04012</td></tr><tr><td>stripe</td><td>-188.38282</td></tr><tr><td>strive</td><td>-180.66683</td></tr><tr><td>stroke</td><td>-184.98133</td></tr><tr><td>stroll</td><td>-181.33207</td></tr><tr><td>strut</td><td>-150.71254</td></tr><tr><td>stub</td><td>-176.97839</td></tr><tr><td>stud</td><td>-188.61372</td></tr><tr><td>stuff</td><td>-191.09976</td></tr><tr><td>stump</td><td>-186.63559</td></tr><tr><td>stunt</td><td>-180.22994</td></tr><tr><td>style</td><td>-201.26577</td></tr><tr><td>sub</td><td>-101.36317</td></tr><tr><td>suck</td><td>-181.09018</td></tr></table>
<table>
  <tr>
    <td>## sue</td>
    <td>-174.48489</td>
  </tr>
  <tr>
    <td>## suit</td>
    <td>-188.74239</td>
  </tr>
  <tr>
    <td>## suite</td>
    <td>-185.04973</td>
  </tr>
  <tr>
    <td>## sulk</td>
    <td>-151.02667</td>
  </tr>
  <tr>
    <td>## sum</td>
    <td>-183.32057</td>
  </tr>
  <tr>
    <td>## sun</td>
    <td>-184.45041</td>
  </tr>
  <tr>
    <td>## sup</td>
    <td>-180.40743</td>
  </tr>
  <tr>
    <td>## surf</td>
    <td>-182.64958</td>
  </tr>
  <tr>
    <td>## surge</td>
    <td>-173.12654</td>
  </tr>
  <tr>
    <td>## swamp</td>
    <td>-181.09198</td>
  </tr>
  <tr>
    <td>## swan</td>
    <td>-180.87991</td>
  </tr>
  <tr>
    <td>## swap</td>
    <td>-163.73536</td>
  </tr>
  <tr>
    <td>## swarm</td>
    <td>-182.43298</td>
  </tr>
  <tr>
    <td>## swath</td>
    <td>-132.62905</td>
  </tr>
  <tr>
    <td>## sway</td>
    <td>-182.26333</td>
  </tr>
  <tr>
    <td>## swear</td>
    <td>-192.45090</td>
  </tr>
  <tr>
    <td>## sweat</td>
    <td>-191.82664</td>
  </tr>
  <tr>
    <td>## sweep</td>
    <td>-182.57891</td>
  </tr>
  <tr>
    <td>## swell</td>
    <td>-200.14393</td>
  </tr>
  <tr>
    <td>## swerve</td>
    <td>-180.52031</td>
  </tr>
  <tr>
    <td>## swig</td>
    <td>-150.03192</td>
  </tr>
  <tr>
    <td>## swim</td>
    <td>-190.68509</td>
  </tr>
  <tr>
    <td>## swine</td>
    <td>-183.51823</td>
  </tr>
  <tr>
    <td>## swing</td>
    <td>-200.76315</td>
  </tr>
  <tr>
    <td>## swipe</td>
    <td>-181.79668</td>
  </tr>
  <tr>
    <td>## swirl</td>
    <td>-180.64481</td>
  </tr>
  <tr>
    <td>## switch</td>
    <td>-185.40017</td>
  </tr>
  <tr>
    <td>## swoop</td>
    <td>-156.86835</td>
  </tr>
  <tr>
    <td>## sword</td>
    <td>-198.07333</td>
  </tr>
  <tr>
    <td>## tab</td>
    <td>-185.34020</td>
  </tr>
  <tr>
    <td>## tack</td>
    <td>-176.33899</td>
  </tr>
  <tr>
    <td>## tact</td>
    <td>-192.71237</td>
  </tr>
  <tr>
    <td>## tag</td>
    <td>-184.71081</td>
  </tr>
  <tr>
    <td>## tail</td>
    <td>-184.72629</td>
  </tr>
  <tr>
    <td>## taint</td>
    <td>-181.81677</td>
  </tr>
  <tr>
    <td>## take</td>
    <td>-197.70277</td>
  </tr>
  <tr>
    <td>## tale</td>
    <td>-190.42637</td>
  </tr>
  <tr>
    <td>## talk</td>
    <td>-184.25487</td>
  </tr>
  <tr>
    <td>## tamp</td>
    <td>-167.22869</td>
  </tr>
  <tr>
    <td>## tan</td>
    <td>-184.36062</td>
  </tr>
  <tr>
    <td>## tang</td>
    <td>-149.54766</td>
  </tr>
  <tr>
    <td>## tank</td>
    <td>-180.64483</td>
  </tr>
  <tr>
    <td>## tape</td>
    <td>-195.05470</td>
  </tr>
  <tr>
    <td>## tar</td>
    <td>-192.36391</td>
  </tr>
  <tr>
    <td>## tart</td>
    <td>-180.99382</td>
  </tr>
  <tr>
    <td>## task</td>
    <td>-199.74630</td>
  </tr>
</table>
<table>
  <tr>
    <td>## taste</td>
    <td>-197.67704</td>
  </tr>
  <tr>
    <td>## taunt</td>
    <td>-180.87142</td>
  </tr>
  <tr>
    <td>## tax</td>
    <td>-197.43834</td>
  </tr>
  <tr>
    <td>## tea</td>
    <td>-199.77953</td>
  </tr>
  <tr>
    <td>## teach</td>
    <td>-191.02274</td>
  </tr>
  <tr>
    <td>## teak</td>
    <td>-180.01711</td>
  </tr>
  <tr>
    <td>## team</td>
    <td>-198.86440</td>
  </tr>
  <tr>
    <td>## tease</td>
    <td>-192.64858</td>
  </tr>
  <tr>
    <td>## tech</td>
    <td>-87.81492</td>
  </tr>
  <tr>
    <td>## tee</td>
    <td>-184.37757</td>
  </tr>
  <tr>
    <td>## teens</td>
    <td>-180.63114</td>
  </tr>
  <tr>
    <td>## tell</td>
    <td>-194.65882</td>
  </tr>
  <tr>
    <td>## tempt</td>
    <td>-195.21268</td>
  </tr>
  <tr>
    <td>## tend</td>
    <td>-180.67394</td>
  </tr>
  <tr>
    <td>## tense</td>
    <td>-190.90087</td>
  </tr>
  <tr>
    <td>## tent</td>
    <td>-199.59222</td>
  </tr>
  <tr>
    <td>## test</td>
    <td>-193.52204</td>
  </tr>
  <tr>
    <td>## text</td>
    <td>-198.24629</td>
  </tr>
  <tr>
    <td>## thank</td>
    <td>-196.56181</td>
  </tr>
  <tr>
    <td>## thaw</td>
    <td>-182.35136</td>
  </tr>
  <tr>
    <td>## theft</td>
    <td>-184.26332</td>
  </tr>
  <tr>
    <td>## theme</td>
    <td>-184.80672</td>
  </tr>
  <tr>
    <td>## thief</td>
    <td>-183.78822</td>
  </tr>
  <tr>
    <td>## thigh</td>
    <td>-198.10655</td>
  </tr>
  <tr>
    <td>## thin</td>
    <td>-189.50346</td>
  </tr>
  <tr>
    <td>## thing</td>
    <td>-187.31531</td>
  </tr>
  <tr>
    <td>## think</td>
    <td>-201.13984</td>
  </tr>
  <tr>
    <td>## thirst</td>
    <td>-200.45240</td>
  </tr>
  <tr>
    <td>## thong</td>
    <td>-156.36849</td>
  </tr>
  <tr>
    <td>## thorn</td>
    <td>-201.22369</td>
  </tr>
  <tr>
    <td>## thought</td>
    <td>-189.60407</td>
  </tr>
  <tr>
    <td>## thrash</td>
    <td>-178.27401</td>
  </tr>
  <tr>
    <td>## thread</td>
    <td>-193.55186</td>
  </tr>
  <tr>
    <td>## threat</td>
    <td>-182.45323</td>
  </tr>
  <tr>
    <td>## thrift</td>
    <td>-185.10653</td>
  </tr>
  <tr>
    <td>## thrill</td>
    <td>-184.75849</td>
  </tr>
  <tr>
    <td>## thrive</td>
    <td>-183.50624</td>
  </tr>
  <tr>
    <td>## throat</td>
    <td>-200.86763</td>
  </tr>
  <tr>
    <td>## throne</td>
    <td>-164.71494</td>
  </tr>
  <tr>
    <td>## throng</td>
    <td>-123.56174</td>
  </tr>
  <tr>
    <td>## throw</td>
    <td>-183.93492</td>
  </tr>
  <tr>
    <td>## thrush</td>
    <td>-141.05116</td>
  </tr>
  <tr>
    <td>## thrust</td>
    <td>-178.71562</td>
  </tr>
  <tr>
    <td>## thud</td>
    <td>-165.84814</td>
  </tr>
  <tr>
    <td>## thug</td>
    <td>-180.18185</td>
  </tr>
  <tr>
    <td>## thumb</td>
    <td>-200.85400</td>
  </tr>
</table>