Appendix G: Statistical Procedures

Appendix G, Section 1: Expanded Summary

All statistics for the MMT protocols were done with StatCHARRMS (Statistical analysis of 

Chemistry, Histopathology, And Reproduction endpoints including Repeated measures and Multigeneration Studies), a SAS (SAS Institute, Cary, NC)-based program developed for the MidContinent Ecology Division of the USEPA, NHEEL by John Green (Dupont Applied Statistics 

Group, Newark, DE). Generally speaking, StatCHARRMS analyzes data of three different types: 1) 

continuous data that is not a repeated measure (fecundity and fertility are the only repeated 

measures) hereby termed ‘endpoint’ data, 2) fecundity and fertility data which is a repeated 

measure, and 3) histopathology data, which usually is in the form of severity scores. For these three 

types, StatCHARRMS analyzes the data in a distinct fashion for each.

In a multi-generation study for a continuous response measured only once per subject, such 

as liver weight, there are only two main effects, treatment and generation. If the generation-bytreatment interaction is significant at the 0.05 level, then generations are compared within treatments 

and treatments are compared within generations at the 0.05 significance level through contrasts 

without further adjustment to the p-values. If the interaction is not significant, then such contrasts 

are still tested but Bonferroni-Holm adjusted p-values are used, with separate adjustments for 

generation and treatment comparisons. A main effects test for generation is done with no adjustment 

and there is only one comparison made unless the F0 generation is included. Main effects tests for 

treatment use Dunnett’s test, which requires no further adjustment.

In a one-generation study, treatment is the only factor and Dunnett’s test can be used to test 

for treatment effects for a continuous response. Alternatively, the step-down Jonckheere-Terpstra 

test can be used. The Jonckheere-Terpstra test is appropriate if the data are consistent with a 

monotone concentration-response. Otherwise, Dunnett’s test is used.

Egg production can be analyzed as a continuous response by a repeated measures ANOVA, 

with week (or day) the repeated factor and treatment and generation as fixed effect factors. 

Generation is not a repeated factor for two primary reasons. First, no individual is measured in more 

than one generation. Second, while in the abstract it might be possible to make the vessel the unit of 

analysis if the same vessel were used for the F0 generation and for all progeny of the F0 parents in 

that vessel and all progeny of the resulting F1 generation, the logistics of such a design are 

inefficient. In fact, the eggs from the F0 generation are randomized into new vessels to form the F1 

generation and the eggs from F1 are randomized to form F2. Thus, there is no discernible 

experimental unit that is being measured repeatedly over generations. 

Usually, only the F1 and F2 generations are analyzed, as both of these generations were 

exposed to the chemical throughout their entire lives, whereas the F0 generation was first exposed in 

the egg state or later.

Tests for differences across generations and differences across weeks within each 

generation, as well as treatment effects within and across generations are done using contrasts. The 

analysis begins with evaluations of the requirements for ANOVA, namely normality (Shapiro-Wilk 

and Anderson-Darling tests) and variance homogeneity (Levene test). Transformations of variables 

are applied to achieve these requirements where the original data do not. Where no other 

transformation is found, analysis is based on a normalized rank-order transform.

The analysis with all generations included tests for differences (1) between generations 

averaged across weeks and groups, (2) between groups averaged across generations and weeks, (3) 

between weeks averaged across generations and groups, (4) between groups within the same 

generation, (5) between groups within the same generation and week, (6) between weeks within the 

same group and generation, and (7) between generations within the same group and week. If every 

such comparison is made with a 5% false positive rate, there is a very high probability of some false 

positives occurring. To control the false positive rate, some adjustment is needed for the number of 

comparisons. However, it is not appropriate to use a crude Bonferroni or Bonferroni-Holm type 

adjustment for all comparisons simultaneously, for this would grossly inflate the false negative rate.
The adjustments are primarily based on the ANOVA F-tests, except main effects of 

treatment are tested using the Dunnett test, which adjusts for the number of comparisons

independent of any F-test. For the main effect of generation or week, there is no “control” level and 

every pair of levels is a comparison of possible interest. For these two main effects, if the F-test for 

the main effect is significant at the 0.05 level, then the pairwise comparisons across levels of that 

factor can then be tested at the 0.05 level without further adjustment.

However, the model includes two- and three-factor interactions, so that a main effect for, 

say, generation, may not be significant even though generation has a significant impact on results. 

Thus, if a two- or three-factor interaction involving generation is significant at the 0.05 level, then 

comparisons of levels of generation at the 0.05 significance level are done without further 

adjustment. Similar statements can be made for week.

Next are F-tests for significance of treatment within weeks and generations, the so-called 

‘slices’ in the ANOVA table. If, for example, the slice for treatment within generation F1 and week 

12 is significant at the 0.05 level, then the pairwise comparisons for treatment within that generation 

and week are made at the 0.05 level without further adjustment. Similar statements apply to tests for 

week within a generation and treatment and for generation within a week and treatment.

Finally, for comparisons not covered by a significant slice F-test, comparisons are adjusted 

using the Bonferroni-Holm adjustment to p-values. Separate adjustments are made for tests of each 

factor.

The model includes all main effects, two-factor interactions, and the three-factor interaction. 

It is quite likely that some of these interactions and main effects will not be significant. It is 

possible to implement a scheme that would first eliminate the three-factor interaction if it is not 

significant, then eliminate the least significant two-factor interaction (if not significant at the .05 

level) and continue in sequential fashion until only significant factors and interactions remain in the 

model. Only if no interaction involving a factor is significant, would a non-significant main effect 

be eliminated.

There are several problems with the above procedure. First, eliminating a term at step 3, for 

example, might make a term eliminated at step 2 now significant. Thus a stepwise procedure might 

be adopted, such as used in stepwise regression. This can be done if the model is formulated 

carefully, though it can be tedious and can produce misleading results. There is another problem that 

arises from the need to make multiple comparisons beyond the ANOVA F-tests. It can be quite 

challenging to determine how to test a comparison of interest when some interactions are eliminated 

from the model. The most straightforward procedure is to leave all terms in the model so as to 

accommodate the various comparisons of interest. There is nothing wrong with retaining a nonsignificant term in the final model. This could be a problem with a very complex model with a large 

number of potential explanatory variables that should be reduced to a manageable number. In the 

present case, there are only three basic model terms, generation, week, and treatment, all of which 

have very clear meaning and do not overlap. Moreover, it is entirely plausible for all factors to be 

important, and for egg production to vary across weeks within the same treatment group and for 

different generations to show different responses to the treatments. It thus is justifiable to retain all 

model terms. This will also allow easier comparisons of chemicals, as all are modeled in the same 

way.

The same general procedure can be followed if a single generation is analyzed. In this case, 

there are two main effects, treatment and week, and a single two-factor interaction. Dunnett’s test 

still controls the false positive rate for comparisons of treatment main effects, i.e., treatments 

averaged across weeks. For main effects of weeks, i.e., comparisons of weeks averaged across 

treatments, if either the week main effect or the week-by-treatment interaction is significant at the 

0.05 level, then the comparisons of weeks averaged across treatments or within a treatment are done 

at the 0.05 level with no further adjustment. Similarly, if the two-factor interaction is significant at 

the 0.05 level, then treatments within the same week are compared at the 0.05 level without further 

adjustment to the p-values. If the two-factor interaction is not significant, then comparisons of 

weeks within a treatment or treatments within a week are compared using Bonferroni-Holm adjusted 

p-values.
The histopathological data is analyzed by StatCHARRMS with a novel approach termed 

RSCABS (Rao-Scott Cochran-Armitage by Slices) developed by John Green (DuPont), Timothy 

Springer (Wildlife International, Easton, MD), and Amy Saulnier (The Franklin Company, City, 

State). RSCABS incorporates the replicate vessel (aquarium) experimental design and the 

biological expectation that severity of effect will tend to increase with increasing concentrations of 

an EDC. In addition, RSCABS retains the individual subject scores (severity score) thus revealing 

the severity of any effect found statistically significant. RSCABS can be implemented for both 

single and multiple generational comparisons. The advantages of RSCABS over the typical 

histopathological analysis done in aquatic toxicology tests is 2-fold: 1) it provides an objective, 

defensible analysis of the data determining effect concentrations, and 2) it provides information on 

the severity of the effect at any particular concentration of EDC, and therefore a context to the 

effect(s) observed. 

RSCABS involves, iteratively, the following steps for each pathological observation: Step 1: 

For each replicate, count the number of fish in that replicate with severity 1 or greater and the 

number with score 0 (no pathology), thereby changing the score to an incidence table. Apply the 

step-down Rao-Scott Cochran-Armitage test to these counts. This will establish a LOEC1 and 

NOEC1 for increased severity, where both exceed the highest test concentration if no effect is found. 

Step 2: For each replicate, count the number of fish in that replicate with severity 2 or greater and 

the number with score <2, thereby changing the score to a new incidence table. Apply step-down 

Rao-Scott Cochran-Armitage test to these counts. This will establish a LOEC2 and NOEC2 for test 

concentrations producing severity level 2 or higher, where both exceed the highest test concentration 

if no effect is found. Step K: For each replicate, count the number of fish in that replicate with 

severity K or greater and the number with score <K, thereby changing the score to a new incidence 

table. Apply stepdown Rao-Scott Cochran-Armitage test to these counts. This will establish a 

LOECK and NOECK for test concentrations producing severity level K or higher, where both exceed 

the highest test concentration if no effect is found. The lowest test concentration which is LOECK 

for some K>0 is the LOEC for the response under investigation and the value of K indicates the 

severity of the effect at that concentration. Furthermore, individual LOECK values indicate where 

effects of severity K are observed.

Appendix G, Section 2: Detailed Statistics Description

The following was provided by John Green, Dupont Biostatistics group as a description of 

the methodology used within the StatCHARRMS program.

Statistical Analysis of Responses from Toxicity Experiments

A basic principle in selecting statistical methods is to attempt to use underlying statistical models 

that are consistent with the actual experimental design and underlying biology. This principle has 

historically been tempered by widely adopted conventions. For example, it is traditional in 

ecotoxicological studies to analyze the same response measured at different time points separately 

by time point, although in many cases unified analysis methods may be available. The 

appropriateness of this convention will not be pursued in this discussion, but it does underlie the 

methodology in the ANOVA component of the EPA catalog. Instead, discussion will be restricted 

to the most appropriate analysis of a response at a single time point. Attention is further restricted to 

situations where all other relevant factors, such as sex, are fixed at a single value. It is entirely 

possible to use a statistical model that incorporates and accounts for differences in sex, time of 

measurement, and other pertinent factors. However, this is not common in ecotoxicity and is not 

pursued it in this software.

The ANOVA procedure is restricted to hypothesis testing methods to determine a so-called No 

Observed Effects Concentration (NOEC). 
The NOEC is defined in terms of the LOEC, or Lowest Observed Effects Concentration. The LOEC 

is the lowest tested concentration that results in a statistically significant adverse effect. The NOEC 

is defined as the highest test concentration below the LOEC. Thus, the LOEC and NOEC are tested 

concentrations and experiments with different sets of tested concentrations will produce different 

NOEC and LOEC values. The ANOVA component of the EPA catalog does not provide LOEC 

values directly, though they are readily discernable from the NOEC and tested concentrations. A 

related concept that is used in risk assessment is the MATC or Maximum Allowable Toxic 

Concentration, which is the geometric mean of the NOEC and LOEC. That is, 

Equivalently, the MATC is the antilog of the mean of the logarithms of the NOEC and LOEC. This 

concept can probably best be understood from the fact that traditionally, the effect of a toxic 

chemical was expected to increase linearly with the logarithm of concentration. On a log scale, the 

MATC is midway between a NOEC and a LOEC and MATC is a compromise between those 

wanting to base risk assessment on the lowest observed effects concentration and those wanting to 

base risk assessment on the highest concentration in which no adverse effect was observed. The 

idea is that since the NOEC and LOEC are tested concentrations subject to the “whim” of 

experimental design, there may be concentrations below the LOEC that produce adverse effects and 

there may be concentrations above the NOEC that do not. The midpoint (on the log scale) is a best 

guess at where the “true” dividing point is between adverse effect and non-adverse effect.

How accurate is the NOEC? It must be understood that the NOEC is not an estimate of the threshold 

of toxicity. One cannot provide a confidence interval for the NOEC. It is possible to provide a 

confidence interval for the absolute or percent effect at the NOEC. The ANOVA procedure does not 

do this directly, but the standard error of the treatment means is reported, so that the user can 

construct simple confidence intervals should that be needed.

The statistical test that is used depends on the hypothesis tested, the associated statistical model, and 

the distribution of the values (e.g., are data normally distributed?). Thus, it is necessary to determine 

the appropriate statistical model and specify the hypotheses to be tested before selecting the test 

procedure. 

All methods of statistical assessment (regression and hypothesis testing alike) assume a statistical 

model. The hypothesis testing approach to evaluation of toxicity data is based in part on keeping to a 

reasonable number the untestable or difficult-to-test assumptions, particularly those regarding the 

statistical model, that will be used in reaching conclusions. The models used in regression-based 

methods use stronger assumptions (such as specifing a definite parametric form for the doseresponse shape) than the models used in the hypothesis testing approach, but result in more 

quantitative conclusions. 

Statistical Model for NOEC

The simplest statistical model generally used in hypothesis testing assumes only that the 

distributions of responses within these populations are identical except for a location parameter 

(e.g., the mean or median of the distribution of values from each group). The basic hypothesis (in 1-

sided form) can be stated as follows:

H0 : μ0=μ1=μ2=...=μk vs H1 : μ0>μi for at least one i, (1)

where μi, i=0, 1, 2, 3, ..., k denote the means (or medians) of the control and test populations, 

respectively. Thus, one tests the null hypothesis of no differences among the population means 

against the alternative that at least one population mean is smaller than the control mean. There is no 

investigation of differences among the treatment means, only whether treatment means differ from 

MATC = NOEC * LOEC
the control mean. To apply this procedure, one tests the null hypothesis of no trend against the 

alternative at the 0.05 level. If the null hypothesis is not rejected, then testing stops and the NOEC 

exceeds the highest concentration. If the alternative hypothesis is accepted, then the high 

concentration is omitted and the test is repeated (still at the 0.05 significance level) with the 

remaining concentrations. This process continues until the null hypothesis of no trend is first not 

rejected. The NOEC is the highest concentration remaining at this stage. All of these tests are 

conducted at the 0.05 significance level, which is the false positive rate for the entire procedure. 

Further discussion of this is given in Hochberg and Tamhane (1987), Westfall (1999), Westfall et al.

(1999), Marcus et al. (1976), Rom et al. (1995).

In this formulation, an adverse effect is one that reduces the population mean response. This will 

generally be appropriate for responses such as size, biomass, and reproduction. Where an adverse 

effect is indicated by an increase in the population mean response, the inequality (1) is reversed. 

In some situations, any change, i.e., either an increase or decrease, in the mean response is indicative 

of an adverse effect. In these situations, a 2-sided alternative hypothesis is appropriate. Then the 

alternative is

H1 : μ0≠μi for at least one i.

The test statistics for the above hypotheses are based on comparing each treatment to the control, 

independent of the other treatments. Many tests have been developed for this approach, some of 

which will be discussed in this course. Most such tests were developed for experiments in which 

treatments are qualitatively different, as, for example, in comparing various new therapies or drug 

formulations to a standard.

In toxicology, the treatment groups generally differ only in the exposure concentration (or dose) of a 

single chemical. It is further often true that biology and experience suggest that if the chemical is 

toxic, then as the level of exposure is increased, the magnitude of effect will tend to increase.

Depending on what response is measured, the effect of increasing exposure may show up as an 

increase or as a decrease in the measured response, but not both. The statistical model underlying 

this biological expectation is what will be called a trend model or a model assuming monotonicity of 

the population means:

μ0 ≥ μ1 ≥ μ2 ≥ μ3 ≥. . . ≥ μk (or with inequalities reversed). (Model 2)

The null and alternative hypotheses can then be stated as

H02 : μ0=μ1=μ2=...=μk vs H12 : μ0 ≥ μ1 ≥ μ2 ≥ μ3 ≥. . . ≥ μk , with μ0 > μk .

Note that μ0 > μk is equivalent, under the alternative, to μ0 > μi for at least one i. If this monotone 

model is accepted as representing the true responses of test organisms to exposure to toxicants, it is 

not possible for, say, μ3 to be smaller than μ0 and μ6 not to be smaller. 

Under the trend model and tests designed for that model, if tests of hypotheses H02 vs H12 reveal that 

μ3 is different from μ0, but μ2 is not, the NOEC has been determined (i.e. it is the test concentration 

associated with μ2), and there is no need to test whether μ1 differs from μ0. Also, finding that μ3

differs from μ0 implies that a significant trend exists across the span of doses including μ0 and μ3, 

the span including μ0 and μ4, and so on. For the majority of toxicological studies, a test of the trend 

hypothesis based on model (2) is consistent with the basic expectations for a model for doseresponse. In addition, statistical tests for trend tend to be more powerful than alternative non-trend 

tests, and should be the preferred tests if they are applicable. Thus, a necessary early step in the 

analysis of results from a study is to consider each endpoint, decide whether a trend model is 
appropriate, and then choose the initial statistical test based on that decision. Only after it is 

concluded trend is not appropriate do specific pairwise comparisons make sense to illuminate 

sources of variability.

Toxicologists sometimes do not know whether a compound will cause measurements of continuous 

variables such as growth or weight to increase or decrease, but they are confident it will act in only 

one direction. For such endpoints, the 2-sided trend test is appropriate. One difference between 

implementing step-down procedures for quantal data and continuous data is that two-sided tests are 

much more likely to be of interest for continuous variables. Such a model is rarely appropriate for 

quantal data, as only increased incidence rate above background (control) incidence are of interest in 

toxicology. The two-sided version of the step-down procedure is based on the underlying model:

μ0 ≥ μ1 ≥ μ2 ≥ μ3 ≥ . . . ≥ μk

or

μ0 ≤ μ1 ≤ μ2 ≤ μ3 ≤ . . . ≤ μk.

Under this model, in testing the hypothesis that all population means are equal against the 

alternative that at least one inequality is strict, one first tests separately each 1-sided alternative at 

the 0.025-level of significance with all doses present. If neither of these tests is significant, the 

NOEC is higher than the highest concentration. If both of these tests are significant, a trend-based 

procedure should not be used, as the direction of the trend is unclear. If exactly one of these tests 

with all the data is significant, then the direction of all further tests is in the direction of the

significant test with all groups. Thereafter, the procedure is as in the 1-sided test, except all tests are 

at the 0.025 significance level to maintain the overall 0.05 false positive rate. 

Where it is biologically sensible, it is preferable to test the one-sided hypothesis, because random 

variation in one direction can be ignored, and as a result, statistical tests of the one-sided hypothesis 

are more powerful than tests of the two-sided hypothesis.

Note that a hypothesis test based on model 2 assumes only a monotone dose-response rather than a 

precise mathematical form, such as is required for regression methods.

Comparisons of single-step (pairwise comparisons) to step-down trend tests to determine the 

NOEC 

In general, determining the NOEC for a study involves multiple tests of hypotheses (i.e., a family of 

hypotheses is tested), either pairwise comparisons of treatment groups, or a sequence of tests of the 

significance of trend. Statisticians have developed tests to control the family-wise error rate, FWE, 

(the probability that one or more of the null hypotheses in the family will be rejected incorrectly) in 

the multiple comparisons performed to identify the NOEC. The method of controlling the familywise error rate has important implications for the power of the test. There are two general 

approaches that will be discussed: single-step procedures and step-down procedures. 

Single-step procedures amount to performing all possible comparisons of treatment groups to the 

control. Multiple comparisons to the control may be made, but there is no ordered set of hypotheses 

to test, and no use of the sequence of outcomes in deciding which comparisons to make. Examples 

of the single-step approach include the use of the Fisher’s exact test, the Mann-Whitney, Dunnett 

and Dunn tests. Since many comparisons to the control are made, some adjustment must be made 

for the number of such comparisons to keep the family-wise error (FWE) rate at a fixed level, 

generally 0.05. 

With tests that are inherently single comparison tests, such as Fisher’s exact and Mann-Whitney, a 

Bonferroni adjustment can be made: a study with k treatment levels would be analyzed by 

performing the pair-wise comparisons of each of the treatment groups to the control group, each 
performed at a significance level of α/k instead of α. (This is the Bonferroni adjustment.) The 

Bonferroni adjustment is generally overly conservative, especially for large k. Modifications reduce 

the conservatism while preserving the FWE at 0.05 or less.

Bonferroni-Holm adjustment to p-values

For the Holm modification (Holm, (1979)) of the Bonferroni adjustment, arrange the k unadjusted pvalues for all comparisons of treatments to control in rank order, i.e., p(1)≤ p(2)≤ p(3)≤ ... ≤ p(k) . 

Beginning with p(1), compare p(i) with α/(k –i+1), stopping at the first non-significant comparison. If 

the smallest i for which p(i) exceeds α/(k –i+1) is i=j, then all comparisons with i>j are judged nonsignificant without further comparisons. It is helpful (Wright (1992)) to report adjusted p-values 

rather than the above comparisons. Thus, report p*(1) = p(1)*(k-i+1) and then compare each adjusted 

p-value to α. In the case of ties among the unadjusted p-values, all adjustments are the same as for 

the smallest rank of those p-values. Table 1 illustrates the advantage of the Bonferroni-Holm 

method. In this hypothetical example, only the comparison of treatment 4 with the control would be 

significant it the Bonferroni adjustment is used, whereas all comparisons except the comparison of 

the Control with treatment 1 would be significant if the Bonferroni-Holm adjustment is used. Holm 

modification to the Bonferroni is implemented in the ANOVA and Quantal NOEC procedures for 

the Mann-Whitney of Fisher Exact tests. Dunn’s test, used in ANOVA, uses a Bonferroni 

adjustment. The paper by Dunn (1964) uses that approach applied only to the specific comparisons 

of interest to toxicity studies.

Comparison Unadjusted p

value

Bonferroni-Holm 

Adjusted p value

p *(i)

α/k 

(Bonferroni 

Adjustment of α)

Control – Treatment 4 p (1) =0.002 0.002*4=0.008 0.05/4=0.0125

Control – Treatment 2 p (2) =0.013 0.013*3=0.039 0.05/4=0.0125

Control – Treatment 3 p (3) =0.020 0.020*2=0.040 0.05/4=0.0125

Control – Treatment 1 p (4) =0.310 0.310*1=0.310 0.05/4=0.0125

Table 1 Comparison of Adjusted and Unadjusted P-Values

The Bonferroni and Bonferroni-Holm adjustment guarantee that the family-wise error rate is less 

than α, but they are conservative. 

The Dunnett test, has a “built-in” adjustment for the number of comparisons made and are less 

conservative (hence, more powerful). There is no additional adjustment for the number of 

comparisons. Step-down tests, discussed below, do not require an adjustment for the number of 

comparisons.

Step-down procedures are generally preferred where they are applicable. All step-down procedures 

discussed are based on a sequential process consisting of testing an ordered set of hypotheses 

concerning means, ranks, or trend. A step-down procedure based on trend (for example) works as 

follows: First, the hypothesis that there is no trend in response with increasing dose is tested when 

the control and all dose groups are included in the test. Then, if the test for trend is significant, the 

high dose group is dropped from the data set, and the hypothesis that there is no trend in the reduced 

data set is tested. This process of dropping treatment groups and testing is continued until the first 

time the trend test is non-significant. The highest dose in the reduced data set at that stage is then 

declared to be the NOEC. Distinguishing features of step-down procedures are that the tests of 

hypothesis must be performed in a given order, and that the outcome of each hypothesis test is 

evaluated before deciding whether to test the next hypothesis in the ordered sequence of hypotheses. 

It is these two aspects of these procedures that account for controlling the family-wise error (FWE) 

rate.
A step-down method typically uses a critical level larger than that used in single-step procedures, 

and seeks to limit the number of comparisons that need to be made. Indeed, the special class of 

“fixed-sequence” tests we will describe fix the critical level at 0.05 for each comparison but bound 

the FWE rate at 0.05. Thus, step-down methods are generally preferable to the single-step methods 

as long as the response means are monotonic. 

Tests based on trend are logically consistent with the anticipated monotone pattern of responses in 

toxicity tests. Step-down procedures make use of this ordered alternative by ordering the tests of 

hypotheses. This minimizes the number of comparisons that need to be made, and in all the methods 

discussed here, a trend model is explicitly assumed (and tested) as a part of the procedure.

Procedures that employ step-down trend tests have more power than procedures that rely on 

multiple pairwise comparisons when there is a monotone dose-response because they make more 

use of the biology and experimental design being analyzed. When there is a monotone doseresponse, procedures that compare single treatment means or medians against the control, 

independent of the results in other treatments (i.e. single-step procedures), ignore important and 

relevant information, and suffer power loss as a result.

The trend models used in the step-down procedures do not assume a particular precise mathematical 

relationship between dose and response, but rather use only monotonicity of the dose-response 

relationship. The underlying statistical model assumes a monotone dose-response in the population

means, not the observed means.

Rejection of the null hypothesis (i.e., rejecting the hypothesis that all group means, or medians, or 

distributions are equal) in favor of the stated alternative implies that the high dose is significantly 

different from the control. The same logic applies at each stage in the step-down application of the 

test to imply, whenever the test is significant, that the high dose remaining at that stage is 

significantly different from the control. These tests are all applied in a 1-sided manner with the 

direction of the alternative hypothesis always the same. Moreover, this methodology is general, and 

applies to any legitimate test of the stated hypotheses under the stated model. That is, one can use 

this fixed-sequence approach with the Cochran-Armitage test on quantal data or the JonckheereTerpstra (Jonckheere (1954)) test of trend on continuous data. Other tests of trend can also be used 

in this manner, but are not implemented in the ANOVA component of the EPA catalog. 

Deciding between pairwise and trend-based comparisons 

The first consideration is biological. Do we expect a monotone dose-response? If not, then tests 

based on monotonicity should not be used. USEPA (1995) recommends the use of step-down trend 

tests to establish NOECs for both quantal (incidence) and continuous responses. (USEPA (1995) 

recommends the Mantel-Haenszel test instead of the almost equivalent Cochran-Armitage test for 

incidence data and Jonckheere-Terpstra test for continuous data to establish the NOEC.)

Even if we expect a monotone dose-response, it is important to assess the data for consistency with 

that judgment. There are several reasons for this. Bauer (1997) has shown that certain tests based 

on a monotone dose-response can have poor power properties or error rates when the monotone 

assumption is wrong. Davis and Svendsgaard (1990) and others have suggested that departures from 

monotonicity may be more common than previously thought. These results suggest that a need for 

caution exists. 

On the positive side, Odeh (1972), Odeh (1971), Poon (1980), Potter and Sturm (1981), Potthoff and 

Whittinghill (1966) and Puri (1965) all discuss the favorable performance of this test compared to 

various others and USEPA (1995) recommends this test.
Both formal tests and visual inspection are recommended to determine whether there is significant 

departure from monotonicity. The ANOVA component of the EPA catalog uses such a “negative” 

test for departure from monotonicity (sets of orthogonal contrasts for continuous responses and a 

decomposition of the chi-square test of independence for quantal responses) and proceeds unless 

there is evidence of non-monotonicity. Details on these procedures are given later. This approach is 

grounded in the idea that monotonicity is the rule and that it should take strong evidence to depart 

from this rule. However, the procedures in the ANOVA component of the EPA catalog allow expert 

judgment to override this presumption of monotonicity. This is done by selecting pairwise 

comparisons only.

Formal tests for monotonicity are especially desirable in a highly automated test environment. The 

ANOVA procedure uses linear and quadratic contrasts of normalized rank statistics (to avoid the 

complications that can arise from non-normal or heterogeneous data). If the linear contrast is not 

significant and the quadratic contrast is significant, there is evidence of possible non-monotonicity 

that calls for closer examination of the data or pairwise comparison methods. By default, the 

program refuses to do the Jonckheere test under this condition, though the user can force that action. 

Otherwise, a trend-based analysis is used. 

Where expert judgment is used, formal tests for monotonicity or its lack may be replaced by visual 

inspection of the data, especially of the mean or median responses. The same concept applies to 

assessing normality and variance homogeneity. The ANOVA procedure does not provide graphical 

displays of the data. 

Normality

Non-monotonic dose-response data should be assessed using an appropriate pairwise comparison 

procedure. These can be categorized according whether they require the data be normally distributed 

or homogeneous. Dunnett’s test is appropriate if the data are normally distributed with 

homogeneous variance. For normally distributed but heterogeneous data, the Tamhane-Dunnett (T3) 

method (Hochberg and Tamhane (1988); Tamhane (1979); Dunnett (1980); Tamhane and Dunnett, 

(1998)) can be used. Non-normal data can be analyzed by using Dunn or Mann-Whitney tests with 

Bonferroni-Holm adjustment. Of course, a variance stabilizing or normalizing transform, if found, 

can be employed to make the response fit one of tests requiring these features. Normality is formally 

assessed in the ANOVA procedure using the Shapiro-Wilk test (Shapiro and Wilk (1965).

Parametric versus non-parametric tests – (Continuous data)

Dunnett’s test requires the data to be approximately normally distributed with homogeneous withintreatment variances. The Tamhane-Dunnett test is for normally distributed data with heterogeneous 

within-treatment variances. Parametric tests have desirable properties when these assumptions are 

met. Failure of the data to meet assumptions can sometimes be corrected by transforming the data 

and transformations are available in the ANOVA procedure and discussed below. Some nonparametric tests are almost as powerful as their parametric counterparts when the assumptions of 

normality and homogeneity of variances are met and may be much more powerful if the 

assumptions are not met. Furthermore, a test based on trend is generally more powerful than a 

pairwise test. A decision to use a parametric or non-parametric test should be based on which best 

describes the physical, biological and statistical properties of a given experiment.

If the data are found non-normally distributed, then the ANOVA procedure uses a non-parametric 

test. Ordinarily, for pairwise comparisons, this is Dunn’s test configured only to compare groups to 

control. Under some conditions, Mann-Whitney tests with a Bonferroni-Holm adjustment to the pvalues is used. This is discussed further under Exact Permutation Tests below.

Regardless of normality and variance homogeneity considerations, if a step-down trend test is used, 

the ANOVA procedure uses the Jonckheere-Terpstra test. The primary parametric alternative to the 
Jonckheere test is Williams’ test, which is not implemented in the ANOVA component of the EPA 

catalog at this time but is expected to be available in the next release. Power simulation studies 

carried out at DuPont and some publications (see Poon (1980), Potter and Sturm (1981), Puri

(1965), for example) indicate these two tests have similar power characteristics under normal, 

homogeneous conditions and the Jonckheere test tends to be superior to Williams’ when these 

conditions are not met.

Outliers 

Outliers that relate to an experimental unit may arise due to the fact that such a unit differed 

systematically from the other groups by some (usually unknown) experimental factor(s). For 

instance, the organisms in the various experimental units were held in different aquaria, and one of 

them contained an infection. Or, the organisms in the different experimental units were treated in a 

specific order (with respect to feeding, time of observation, etc). Detection of this type of outliers 

typically cannot be enforced by any formal statistical method, and one has to rely on visual 

inspection, judgment and experience. 

Obviously, experimental unit or treatment group outliers are highly undesirable, since they directly 

interfere with the effect that one wishes to measure, thereby increasing the probability of both false 

positive and false negative results. For example, a NOEC may be assessed at a level where 

substantial effects do occur, or a LOEC may be assessed at a level without real effects (i.e. from the 

chemical). The best way to reduce the chance of an outlier at the group or replicate level is a design 

that is perfectly randomized with respect to all experimental actions that may potentially influence 

the (observed response of) the biological system. In practical biological studies, however, perfect 

randomization is hard to realize. Therefore, it is important to make the study design relatively 

insensitive to potential outliers, i.e., by randomized replicated dose groups, and/or by increasing the 

number of different doses.

Outliers at the individual level can be detected in continuous data. When a particular distribution is 

assumed for the scatter in the data, the judgment of outliers may be based on a specific, small 

probability that any single data point could occur. This implies that the judgment of outliers can 

depend quite strongly on the assumed distribution. For example, values that appear to be extremely 

high when assuming a normal distribution may be judged as non-extreme when assuming a 

lognormal distribution. On the other hand, low values may be judged as extremes when assuming a 

lognormal distribution, but not so when a normal distribution is assumed.

The statistical analysis of the data is sensitive to individual outliers, although less dramatically than 

to group outliers. On the one hand, individual outliers may result in biased estimates of the effect 

(either too small or too large). On the other hand, the estimate of the residual variance (the “noise”) 

will be increased, implying that statistical tests tend to be less powerful, and estimated parameters 

(e.g. ECx) less precise. Therefore, if biological reasons can be found explaining the outliers, it is 

preferable to delete them from the analysis. As a reality check, one can also repeat the analysis with 

the outliers omitted. If this does not change the conclusions, one may have greater confidence in the 

result if no biological justification for omitting the outliers is found. This is a helpful step before 

expending great effort to find a reason for omitting an observation. In the ANOVA procedure, the 

repetition of analysis with outliers removed is done automatically and is shown in the output Lis file 

described below. The outlier omitted analysis is not reflected in the summary table, also described 

below.

In addition to plots and visual inspection, there are formal outlier rules that are useful, particularly 

when a large volume of data must be processed in a short period of time. The Tukey (1977) outlier 

rule (described in the next paragraph) is practical, useful and implemented in the ANOVA 

procedure. Furthermore, it is not itself sensitive to the effects outliers, which makes it a decided 

improvement over methods based on standard deviations, which are quite sensitive to the effects of 
outliers. Tukey’s outlier rule is used as a formal test with outliers being assessed from residuals 

(results of subtracting treatment means from individual values) to avoid confounding outliers and 

treatment effects. 

Any response more than 1.5 times the interquartile range above the third quartile (75th percentile) or 

below the first quartile (25th percentile) is considered an outlier by Tukey’s rule. Such outliers are 

reported with the results of the analysis. The entire analysis of a given endpoint is repeated with 

outliers omitted to determine whether the outliers affected the conclusion. While it is true that 

nonparametric analyses are less sensitive to outliers than parametric analyses, omission of outliers 

can still change conclusions, especially when sample sizes are small or outliers are numerous.

Although non-detectable, individual outliers can also occur in quantal data and affect the analysis. 

For example, when just one of the individuals in the controls shows a response, but is in fact an 

outlier, this outlier may have quite an impact on the statistical analysis. Being non-detectable, 

individual outliers are a larger problem in quantal than in continuous data. 

Heterogeneous variances 

Visual inspection may also be used to explore the general pattern of the scatter around (continuous) 

data. Thus, one may find out if the scatter around the mean response appears to be symmetrical or 

skew, and if the scatter is more or less homogenous. Heterogeneity of variance (scatter) may have a 

biological basis i.e. the individual organisms (units) respond differently to the chemical. However, 

an apparent increase of decrease in the scatter may also be related to the statistical distribution of the 

data, e.g. the scatter increases with the mean response. This distinction is important, both for the 

analysis, and for the interpretation of results, and some further clarification is given below. 

When the plotted data show scatter that is correlated with the mean response, such pattern may be 

related to the underlying distribution of the data. Such plots are provided by the ECx procedure. For 

example, in lognormally or gamma distributed data it may be expected theoretically that the 

standard deviation increases proportionally with the mean (or, equivalently, the Coefficient of 

Variation, CV, is homogenous). When a particular dataset (such as weights, concentrations) show 

scatter that increases with the mean, one may plot such data on the log-scale, which may make the 

scatter independent from the means. In addition, when the scatter is relatively large (say, CV larger 

than 20%), the scatter may be skewed on the original scale, but not on the log-scale. The latter 

would confirm that the pattern in the scatter is a result from the underlying distribution.

As another example, counts (such as number of live young) may follow a Poisson distribution. Here 

the variances are expected to be equal to the means (or, proportional to them). Such a pattern should 

vanish when the data are plotted on square root scale. 

Finally, in quantal data with replicated dose groups, it is expected a priori that the scatter between 

the replicates depend on the mean response (this follows directly from the properties of frequencies). 

Here, one may plot the frequencies after the transformation arcsin(√p), where p is the observed 

frequency (fraction). Such a transform should remove the (theoretical) relationship between the 

variance and the mean frequency (assuming a binomial distribution).

Heterogeneity in the scatter might be caused by the treatment (the applied chemical) itself, i.e. some 

individuals exhibit greater responses to the chemical than others. In most toxicity tests, however, the 

organisms used are genetically homogenous, and real (biological) heterogeneity in response to the 

chemical will, in those cases, not be very likely.

Residual plots (plot of the residuals vs. the predicted values) and formal tests of heterogeneity of 

variance can be used to find heterogeneity or dismiss it as a problem. Of the latter, the ANOVA 
procedure utilizes Levene’s test (Box, 1953), since it is not as sensitive to outliers and other data 

issues such as non-normality as some alternatives such as those of Bartlett or Hartley. 

When heterogeneity of variances appears to be due to real biological heterogeneity in responses 

among individual organisms, then more care must be taken. For example, when the organisms (or 

experimental units) consist of two distinct subpopulations, one responding, and the other not, an 

estimated change in mean response has no useful meaning unless the subpopulations can be 

distinguished from known causes, such as sex. In that event, the appropriate way to proceed is to 

analyze the subpopulations separately, or using the subpopulation identity or value as a covariate.

Heterogeneity of variances may be a matter of scaling that can be removed by the right 

transformation. Another approach is to omit the transformation, and use methods that are directly 

based on the assumed distribution (i.e. generalized linear models). If no such distribution or 

transformation can be found or is readily available, then nonparametric procedures can be used.

Transformation of data

Many standard parametric methods assume normally distributed data and homogenous variances. 

Data often deviate from these assumptions, and if so, the inferences resulting from these standard 

methods can be unreliable. If a variance-stabilizing transformation can be found, then the statistical 

analysis can be done on the transformed data. 

For a variance-stabilizing transformation to exist, there must be a relationship between the 

population means and variances. In many cases, the theoretical distribution of the response variable 

can guide the choice of a transformation. For example, if the underlying distribution is assumed to 

be Poisson, the square root transformation, yi’ = (yi

1⁄2) or yi’ = ((yi +1)1⁄2) or [yi’=(yi+1)1⁄2+ (yi1⁄2) ], 

might be used. If the underlying data are lognormal, the log-transformation, yi’ = log(yi), is often 

used. For proportions with binomial distributions, the arc-sin square-root [yi’=arcsin(yi

1⁄2)] and 

Freeman-Tukey transformations are often used. If the underlying theoretical distribution is 

unknown, a data-based procedure (Box-Cox transformation) can be used (Box and Cox, 1964).

The use of transformations will often simplify the data analysis, in that the more familiar and 

traditional data analysis methods can be used, but care must be taken in interpreting the results of 

this data analysis. 

If a transformation is used, it is also necessary to back-transform the means and confidence intervals 

back to the original scale, when reporting results. As to confidence intervals, one must backtransform the bounds of the interval, not back-transform the standard errors. It must also be 

understand that the back-transformed means generally differ from the arithmetic means of the 

original data. These back-transformed means should be interpreted as estimates of the median of the 

underlying data distribution, if the transformed data are normally (or at least symmetrically) 

distributed. In the special case of a log-transformation, the back-transformed mean is the geometric 

mean of the original data, and this value estimates the median of the underlying lognormal 

distribution. 

When a transformation is not used in the data analysis, the difference in the means is a logical 

measure for the size of an effect. This difference is interpreted as an absolute change in the original 

units (e.g., a decrease of 1.2 grams). The back-transformed difference in means (of the transformed 

data) however has another, usually more difficult, interpretation. In the special case of a logtransformation, the difference between the back-transformed means does allow a simple 

interpretation: it estimates the ratio (or percent change) of the median responses. 

1

, 1 1

+

+

+

+ =

i

i i

i

i i

i

n

n y arsin

n

n y

y arsin
In addition, transformations may not maintain additivity of effects (interactions among factors, e.g., 

test substance, sex, age, in the experiment). Other possible consequences of using transformations 

are that they change the interpretation of outliers and that they affect the value of r (Pearson 

correlation coefficient) and R2

. 

Transformation of the response especially complicates regression methods to estimate an ECx, since 

an x% change in the untransformed response does not correspond to an x% change in the 

transformed response. Great care must be taken to estimate a meaningful quantity after a transform. 

This is less of a problem with hypothesis testing, since we are only inquiring whether a response 

mean or median (or other measure of location) differs from the control. It is not necessary to 

quantify the amount of change to determine the NOEC.

All of the transformations discussed above and others can be peformed in the ANOVA procedure, 

using one of two methods which are described in the program syntax below. References on 

transformations include Box and Cox (1964), Box and Hill (1974), Box and Tidwell (1962), Draper 

and Cox (1969).

Exact Permutation Tests

Not all data problems can be fixed by transformation of the response. For example, if a large

percentage of the responses have the same measured value (ties), no transformation will address that 

issue. In the case of very small samples, say less than three per concentration for most 

concentrations, it is may not be possible to assess in a meaningful way the distribution of responses. 

One can either use an assumed distribution on faith or treat this situation in the same way as data 

with massive ties. Exact permutation methodology is an appropriate tool to use in these cases. The 

ANOVA component of the EPA catalog automatically uses exact methods when deemed 

appropriate. In particular, the Jonckheere-Terpstra, Mann-Whitney and Cochran-Armitage tests 

discussed later all have exact versions that are implemented in the ANOVA component of the EPA 

catalog. In the ANOVA procedure, there are two conditions under which exact methods are used: 

(1) There are no more than three experimental units in any treatment group and non-parametric 

procedures are found appropriate. (2) There are “massive ties” in the responses, i.e., 25% or more of 

the experimental units have the same response or 40% or more have one of only two response values 

or 65% or more have one of only three response values. An exact version of the JonckheereTerpstra test is used for step-down trend test and an exact version of the Mann-Whitney test with 

Bonferroni-Holm adjusted p-values is used in place of Dunn’s test. 

Weighted ANOVA

There are two selections that affect whether and how a weighted analysis is done in the ANOVA 

procedure. These are the Pick weight/frequency variable button and the Var(btwn)/Var(wthn) Ratio

scroll menu. Weighted analysis is generally meaningful only when there two or more sources of 

variability in the data, typically resulting from a nested experimental design, with multiple 

replicates(tanks, beakers, pots, plots) per treatment and multiple subjects (fish, daphnid, plants, 

plants) per replicate.

When there are two (or more) sources of variability in the data, some caution is needed to ensure a 

proper analysis. A situation common in ecotoxicity studies is to have replicate vessels each 

comprised of multiple organisms. For example, in a fish or daphnid experiment, at each 

concentration tested, there may be two or more tanks or beakers, each with 10-20 subjects. In a nontarget plant study, there may be replicate tubs or plots, each containing 5-10 individual plants. 

Usually, the vessel (tank, tub, beaker, plot) is considered the experimental unit in this experimental 

set-up. 
It is possible to analyze such data in several ways. Some statistical models use only the replicate 

means, justifying this on the theory that the replicate is the experimental unit. However, as 

demonstrated below, this is only appropriate when the number of subjects in all replicates is the 

same in every replicate vessel. While experiments are often designed with such equal sample sizes, 

differential mortality often occurs during the course of the experiment, so that at study end, when 

data are collected for analysis, there are unequal numbers of surviving subjects in different replicate 

vessels. If the disparities in number of survivors is small, differing by no more than 10-20%, there 

is usually little penalty in modeling replicate means without further refinement. However, when 

final sample sizes differ more than that, substantial error can be incurred when following this 

practice. For this reason, the best practice is to analyze the individual subjects using an appropriate 

model, such as described below.

Alternatively, if individual data are not available or there is limited ability to carry out such an 

analysis, then a weighted ANOVA can be done. First, the need for a weighted ANOVA will be 

shown. Then, a method for carrying out such an analysis will be described. References on weighted 

ANOVA include Milliken and Johnson (1984), Hocking (1985). The second of these is also 

valuable for the following discussion on variance ratios.

An appropriate model incorporating terms for subject and replicate as well as concentration is 

simple to state. In this analysis, the ANOVA model can be written as follows:

ijk i j i ijk y = Conc + rep (Conc) + e ( )

where the eijk correspond to individual subjects and 

* * *

* * *

cov( , ) 0 * *

12 0

12

* * *

if ijk i j k

if ij i j and k k

y y if i i or j j ijk i j k

= + =

= = ≠

= ≠ ≠

φ φ

φ

Variance Ratio

The variance of a replicate mean is given by















 = +















 = + = +

ij ij ij

ij n

r

n n

y

1 1 var( ) 0

0

12

0

0

. 12 φ φ

φ φ φ φ

where nij is the number of subjects in rep j of concentration i. Thus, the variance of the rep mean is 

a function of both the rep sample size and the ratio of variance components. 

If there is little variation in sample sizes, then the variance ratio and weights can probably be 

ignored. If the between-rep variance component, φ12 , is large compared to the within-rep 

contribution, φ0 /nij, then weighted ANOVA is of little value. This happens, for example, when the 

variance ratio is larger than 1.5, that is, the between-rep variance is 50% larger than the within-rep 

variance. From the table, it also happens when the minimum sample size exceeds 5. In other 

situations, both the variance ratio and sample size can have significant effects on the variance of the 

replicate means and should not be ignored.

TABLE: Effect of Sample Size and Variance ratio on Variance of Replicate mean

Value in table is variance of replicate mean.

 Size 1 2 3 4 5 6 7 8 9 10

VRatio

0 1.00 0.50 0.33 0.25 0.20 0.17 0.14 0.13 0.11 0.10
0.1 1.10 0.60 0.43 0.35 0.30 0.27 0.24 0.23 0.21 0.20

0.2 1.20 0.70 0.53 0.45 0.40 0.37 0.34 0.33 0.31 0.30

0.3 1.30 0.80 0.63 0.55 0.50 0.47 0.44 0.43 0.41 0.40

0.4 1.40 0.90 0.73 0.65 0.60 0.57 0.54 0.53 0.51 0.50

0.5 1.50 1.00 0.83 0.75 0.70 0.67 0.64 0.63 0.61 0.60

0.6 1.60 1.10 0.93 0.85 0.80 0.77 0.74 0.73 0.71 0.70

0.7 1.70 1.20 1.03 0.95 0.90 0.87 0.84 0.83 0.81 0.80

0.8 1.80 1.30 1.13 1.05 1.00 0.97 0.94 0.93 0.91 0.90

0.9 1.90 1.40 1.23 1.15 1.10 1.07 1.04 1.03 1.01 1.00

1 2.00 1.50 1.33 1.25 1.20 1.17 1.14 1.13 1.11 1.10

1.1 2.10 1.60 1.43 1.35 1.30 1.27 1.24 1.23 1.21 1.20

1.2 2.20 1.70 1.53 1.45 1.40 1.37 1.34 1.33 1.31 1.30

1.3 2.30 1.80 1.63 1.55 1.50 1.47 1.44 1.43 1.41 1.40

1.4 2.40 1.90 1.73 1.65 1.60 1.57 1.54 1.53 1.51 1.50

1.5 2.50 2.00 1.83 1.75 1.70 1.67 1.64 1.63 1.61 1.60

1.6 2.60 2.10 1.93 1.85 1.80 1.77 1.74 1.73 1.71 1.70

1.7 2.70 2.20 2.03 1.95 1.90 1.87 1.84 1.83 1.81 1.80

1.8 2.80 2.30 2.13 2.05 2.00 1.97 1.94 1.93 1.91 1.90

1.9 2.90 2.40 2.23 2.15 2.10 2.07 2.04 2.03 2.01 2.00

2 3.00 2.50 2.33 2.25 2.20 2.17 2.14 2.13 2.11 2.10

That is, it is clear that the variances of the sample means can vary greatly if there are great variations 

in sample size and the variation is greater as the variance ratio increases. It is not immediately 

obvious from the formula above that conclusions from the ANOVA can vary significantly as a result 

of these unequal variances. However, such is indisputably true. 

If we have the individual data, then the nested variance component structure is no problem. If we 

have only the rep means, we cannot estimate the two variance components. However, if the sample 

sizes nij are all the same, there is no problem is analyzing replicate means, since in this instance, the 

(population) variances of all replicate means are the same. If the sample sizes are not all the same, 

then one should use weights proportional to the inverse of the variance. Thus, weights should be 

proportional to 

ij

ij

ij

rn

n

n

r

+ =

+

1 1

1

To use weights proportional to nij alone is seen to be equivalent to assuming r=0, which is 

unrealistic. 

By using historical data to estimate the variance ratio, one can give a better weight. This can be 

verified by running two models, one with individual observations and the indicated nested variance 

structure and the other by using the indicated weights. Validation of this approach to weighted 

ANOVA included using this idea.

Historical data was used in developing the ANOVA component of the EPA catalog. For non-target 

plants, the median value of the variance ratio r was found to be 0.33. However, a default variance 

ratio of zero is set in the ANOVA program. The reason is the expectation that the ANOVA program 

will be used for a greater variety of datasets and a default value of zero will correspond to what 

many knowledgeable users will expect. Other values of r can be selected by the user if, for a 

particular species or study, one has a better estimate for this ratio.

Appendix , Section 3: Analysis of Continuous Responses, Repeated Measure 

(Fecundity/Fertility)
The following was provided by John Green, Dupont Biostatistics group as a description of the 

methodology used within the StatCHARRMS program.

Egg production can be analyzed as a continuous response by a repeated measures ANOVA, with 

week (or day) the repeated factor and treatment and generation as fixed effect factors. Generation is 

not a repeated factor for two primary reasons. First, no individual is measured in more than one 

generation. Second, while in the abstract it might be possible to make the vessel the unit of analysis 

if the same vessel were used for the F0 generation and for all progeny of the F0 parents in that 

vessel and all progeny of the resulting F1 generation, the logistics of such a design are inefficient. In 

fact, the eggs from the F0 generation are randomized into new vessels to form the F1 generation and 

the eggs from F1 are randomized to form F2. Thus, there is no discernible experimental unit that is 

being measured repeatedly over generations. 

Usually, only the F1 and F2 generations are analyzed, as both of these generations were exposed to 

the chemical throughout their entire lives, whereas the F0 generation was first exposed in the egg 

state or later.

Tests for differences across generations and differences across weeks within each generation, as 

well as treatment effects within and across generations are done using contrasts. The analysis begins 

with evaluations of the requirements for ANOVA, namely normality (Shapiro-Wilk and AndersonDarling tests) and variance homogeneity (Levene test). Transformations of variables are applied to 

achieve these requirements where the original data do not. Where no other transformation is found, 

analysis is based on a normalized rank-order transform.

The analysis with all generations included tests for differences (1) between generations averaged 

across weeks and groups, (2) between groups averaged across generations and weeks, (3) between 

weeks averaged across generations and groups, (4) between groups within the same generation, (5) 

between groups within the same generation and week, (6) between weeks within the same group and 

generation, and (7) between generations within the same group and week. If every such comparison 

is made with a 5% false positive rate, there is a very high probability of some false positives 

occurring. To control the false positive rate, some adjustment is needed for the number of 

comparisons. However, it is not appropriate to use a crude Bonferroni or Bonferroni-Holm type 

adjustment for all comparisons simultaneously, for this would grossly inflate the false negative rate.

The adjustments are primarily based on the ANOVA F-tests, except main effects of treatment are 

tested using the Dunnett test, which adjusts for the number of comparisons independent of any Ftest. For the main effect of generation or week, there is no “control” level and every pair of levels is 

a comparison of possible interest. For these two main effects, if the F-test for the main effect is 

significant at the 0.05 level, then the pairwise comparisons across levels of that factor can then be 

tested at the 0.05 level without further adjustment.

However, the model includes two- and three-factor interactions, so that a main effect for, say, 

generation, may not be significant even though generation has a significant impact on results. Thus, 

if a two- or three-factor interaction involving generation is significant at the 0.05 level, then 

comparisons of levels of generation at the 0.05 significance level are done without further 

adjustment. Similar statements can be made for week.

Next are F-tests for significance of treatment within weeks and generations, the so-called ‘slices’ in 

the ANOVA table. If, for example, the slice for treatment within generation F1 and week 12 is 

significant at the 0.05 level, then the pairwise comparisons for treatment within that generation and 

week are made at the 0.05 level without further adjustment. Similar statements apply to tests for 

week within a generation and treatment and for generation within a week and treatment.
Finally, for comparisons not covered by a significant slice F-test, comparisons are adjusted using the 

Bonferroni-Holm adjustment to p-values. Separate adjustments are made for tests of each factor.

The model includes all main effects, two-factor interactions, and the three-factor interaction. It is 

quite likely that some of these interactions and main effects will not be significant. It is possible to 

implement a scheme that would first eliminate the three-factor interaction if it is not significant, then 

eliminate the least significant two-factor interaction (if not significant at the .05 level) and continue 

in sequential fashion until only significant factors and interactions remain in the model. Only if no 

interaction involving a factor is significant, would a non-significant main effect be eliminated.

There are several problems with the above procedure. First, eliminating a term at step 3, for 

example, might make a term eliminated at step 2 now significant. Thus a stepwise procedure might 

be adopted, such as used in stepwise regression. This can be done if the model is formulated 

carefully, though it can be tedious and can produce misleading results. There is another problem that 

arises from the need to make multiple comparisons beyond the ANOVA F-tests. It can be quite 

challenging to determine how to test a comparison of interest when some interactions are eliminated 

from the model. The most straightforward procedure is to leave all terms in the model so as to 

accommodate the various comparisons of interest. There is nothing wrong with retaining a nonsignificant term in the final model. This could be a problem with a very complex model with a large 

number of potential explanatory variables that should be reduced to a manageable number. In the 

present case, there are only three basic model terms, generation, week, and treatment, all of which 

have very clear meaning and do not overlap. Moreover, it is entirely plausible for all factors to be 

important, and for egg production to vary across weeks within the same treatment group and for 

different generations to show different responses to the treatments. It thus is justifiable to retain all 

model terms. This will also allow easier comparisons of chemicals, as all are modeled in the same 

way.

The statistics flow-chart for multi-generation egg production studies are captured in Figures 1a-1c.

Analysis of egg production in one generation

The same general procedure can be followed if a single generation is analyzed. In this case, there are 

two main effects, treatment and week, and a single two-factor interaction. Dunnett’s test still 

controls the false positive rate for comparisons of treatment main effects, i.e., treatments averaged 

across weeks. For main effects of weeks, i.e., comparisons of weeks averaged across treatments, if 

either the week main effect or the week-by-treatment interaction is significant at the 0.05 level, then 

the comparisons of weeks averaged across treatments or within a treatment are done at the 0.05 level 

with no further adjustment. Similarly, if the two-factor interaction is significant at the 0.05 level, 

then treatments within the same week are compared at the 0.05 level without further adjustment to 

the p-values. If the two-factor interaction is not significant, then comparisons of weeks within a 

treatment or treatments within a week are compared using Bonferroni-Holm adjusted p-values.



Appendix , Section 4: Analysis of Histopathology Data via RSCABS

The following is a detailed description of the RSCABS procedure and its rationale including 

example data and analysis provided by John Green. In addition but not included in this ISR, John 

Green (DuPont), Timothy Springer (Wildlife International) and Amy Saulnier (The Franklin 

Company) are preparing a publication detailing the statistical analysis of histopathology endpoints. 

However at this time, it is not ready for distribution.

Histopathology data require statistical methods different from those used for continuous 

responses, such as growth or VTG, and from those used for quantal data, such as 

mortality or sex reversal, since for a histopathology response, an animal is graded on an 

ordered but non-numeric scale, usually 0-5, with 0 corresponding to no finding, 1 for

minimal, 5 for very severe and 2, 3, and 4 increasing degrees of severity between 1 and 5. 

The scores 0-5 carry no numerical implications other than order.

Histopathology responses can come from a single generation or from a multigeneration 

study. The Cochran-Mantel-Haenszel and Chi-Square tests can be done to test for 

generational differences. Cochran-Mantel-Haenszel (CMH) tests can be done for 

generational differences across the study and within treatment and for treatment effects 

across generations. For a single generation or for treatment effects within a generation, a 

Chi-Square test can be done. An exact permutation version of the Chi-Square test with a 

Monte Carlo simulation to estimate variance is preferred due to low and uneven 

frequency of observations. If there are multiple fish per replicate (much the preferred 

study design), then a CMH test can be done for between-rep heterogeneity within 
generations. To illustrate this approach, an experiment with medaka exposed to 

trenbolone from the USEPA Duluth multi-generation research work will be used.
Table 1: Experimental Design for 8-Week Study

As is evident from Table 1, the experimental setup is highly unequally replicated. While 

there are, with only a few exceptions, six replicates per treatment per generation, the total 

number of fish and the numbers of males and females per replicate are highly variable. 

That has implications for how the data should be analyzed.

Some CMH results are given in Table 2. The first row, for female Asynchronous 

Development/Malformation, Gonad or Gon_Asynch_Dev_Mal, gives the test for 

“General Association” after adjustments are made for concentration differences. This test 

indicates that there are no differences between the generations except those that are

treatment related. This can be interpreted as a check against non-treatment related effects. 

The second row shows that there were no significant treatment effects within generation 

F2. Since nothing is given for the F1 generation, there were evidently no data or the 

severity was constant across all treatment groups and control (and the latter was in fact

the case). The third row shows there was no significant difference between the 13 ug/L 

group and the control in the F2 generation and the fourth row shows there was no 

significant difference between the generations for females at the 13 ug/L exposure group. 

The remaining table entries are of one of these types. To explore this a bit more, consider 

gonadal Increased Oocyte Atresia or Gon_Incr_Oocyte_Atresia. There are significant 

differences between each of the treatment groups and control within each generation, 

except for the two highest test concentrations (32 and 84 ug/L) in the F1 generation.

What the CMH test does not indicate is whether the severity scores in the treatment 

groups tend to be higher or lower than those in the control. So the CMH results are 

somewhat analogous to ANOVA F-tests: They indicate that differences exist but not in 

which direction or by how much. A visual inspection of summary data, such as given in 

Table 3, would make clear, at least in the simplest cases, what the direction of change is.
Where the distribution of scores is less transparent, visual inspection may be an 

unsatisfactory way to understand the implication of a CMH test.

Screening tests are performed to determine whether a chemical is an endocrine disruptor, 

and in principle, a NOEC is not needed. So one may inquire why not perform a simple Ftest for a continuous endpoint or Chi-square test for incidence or score data? Such tests 

detect differences between any of the treatment groups, ignoring direction. Only 

comparisons of treatment groups to control are of interest. Tests for significant trend are 

consistent with the expectation of a monotonic dose response. Improved power from 

trend tests, with no power penalty for identifying the NOEC.

This can be explored further by using the Mann-Whitney (or, equivalently, the Wilcoxon) 

test. This test requires only that the responses be ordered, which is true for histopathology 

scores. It does not require that the treatments be numbers in any meaningful way other 

than being ordered (e.g., score 3 indicates greater severity than scores 0, 1, or 2). 

Technically, the responses must be measured on an ordinal scale but need not be

measured on a ratio or even an interval scale.

Table 3 gives Mann-Whitney test results for gonadal Increased Oocyte Atresia.

The Mann-Whitney test results themselves still do not provide the direction of change 

and the tables of incidences must be consulted for that. It is interesting that the MannWhitney test is more sensitive than the CMH in that is declares significant the difference 

between the high test concentration and the control in the F1 generation. However, the 

frequency table shows that the high test concentration has less severe scores than the 

control, whereas all the other statistically significant treatment effects show more severe 

scores in the treatment groups relative to the control. Clearly, some caution is required to 

interpret these statistical findings. It is possible to present the Mann-Whitney results 

differently so as make clear the direction of effect.

There are issues with the CMH, Chi-Square, and Mann-Whitney tests that make them 

less than ideal.
Table 2: Cochran-Mantel-Heanszel Test Results, Part 1

If fish are grouped more than one to a tank in multiple tanks per test concentration and 

control, as is the case with the trenbolone example data, then the CMH and chi-Square 

tests ignore the replicate nature of the experiment. This may also be true of the MannWhitney, depending on whether individual fish are counted or replicate medians are used. 

That is, there is no allowance for replicate-to-replicate variability in addition to fish-tofish within-replicate variability. This is the same issue as arises with probit analysis (and
some other methods) for analyzing quantal responses. It is an issue with the standard 

Cochran-Armitage test as well. One could base the Mann-Whitney test on replicate 

median score, but this would ignore variability within replicate and also ignore 

differences in replicate size (number of fish per replicate). Where there is little variation 

in replicate sizes, this latter point is not serious. The replicate is the proper unit of 

analysis, so loosing the between-rep variation, as with CMH and Chi-Square and one 

version of Mann-Whitney, is problematic.

A 1-generational Kruskal-Wallis test for treatment effects can also be done for each 

generation. The Kruskal-Wallis test is another omnibus test for whether there are 

differences among the treatment groups and control within a generation. If significant, it 

does not indicate which differences are significant, only that there are significant 

differences. Similar to the ANOVA F-test, the Kruskal-Wallis test is not a good indicator 

of whether toxicity effects exist. A significant K-W may mean some two treatment

groups differ from each other without any treatment group differing significantly from

the control. On the other hand, a significant difference between a treatment group and the 

control can exist without the K-W test being significant because that test guards against 

comparisons of no interest to toxicologists and thereby looses power to detect the specific 

differences that are of interest. So, regardless of whether the K-W test is significant,

Mann-Whitney tests should be done to determine which, if any, treatment groups differ 

significantly from the control. Either an adjustment to the p-values for the number of 

comparisons made per generation is done or no adjustment of p-values is made for the 

number of comparisons made of treatments to controls. Adjusted p-values may cause 

some differences of interest to be missed, which unadjusted p-values would cause an 

elevated false positive rate. The recommendation is to use Bonferroni-Holm adjusted pvalues, as a reasonable compromise between the extremes of no adjustement and a very 

crude adjustment such as Bonferroni (without the Holm modification).

Table 3: Mann-Whitney Test Results for Female Gonadal Increased Oocytes Atresia

Table of Conc by Gon_Incr_Oocyte_Atresia - Generation=F1
Table 4: Conc by Gon_Incr_Oocyte_Atresia - Generation=F2

Table 5: Summary Statistics for Gon_Incr_Oocyte_Atresia from

TREN03MEDAKA_8_FEMALES

1-Generation Kruskal-Wallis Tests for Treatment Effects on Gon_Incr_Oocyte_Atresia

Generation response p_KWTest Signif

F1 Gon_Incr_Oocyte_Atresia 0.000101 *

F2 Gon_Incr_Oocyte_Atresia 0.017904 *

Table 6: 1-Gen Mann-Whitney Tests for Treatment Effects on Gon_Incr_Oocyte_Atresia

One proposal being investigated by USEPA Duluth is to rank-order animals for each 

histopathology response, that is score the fish 1-N with N the total number of fish in the 

study and a score of 1 corresponds to the least severe and a score on N corresponds to the 

most severe finding of that particular histopathology endpoint. If this procedure is 

followed, the analysis is by the ANOVA based on the indicated rank-order. A concern 

with this approach is that a statistically significant effect might be found that corresponds
X

(X − X )

to a very mild increase in severity of no biological importance. The likelihood of this is 

still under investigation. Further detail and examples will be presented to the OECD 

VMG-eco Fish Drafting Group at the June, 2010 meeting.

There are concerns with all the methods discussed up to this point. As pointed out above, 

one is ignoring either the replicate tank design of the experiment or the unequal sample 

sizes. Furthermore, what none of these tests does is make use of any expected 

monotonicity or trend in the concentration-response. This is a fundamental biological 

issue and ignoring it is not sound science. An alternative procedure is discussed next to 

handle these concerns and also to quantify the severity of effect in a clear manner. The 

procedure to be described does that and, as a result, has greater power to detect true 

treatment effects while at the same time reducing the chance of a declaring significant a 

spurious effect at a lower concentration that is not seen at higher test concentrations. This 

is analogous to the improvements in analyzing continuous responses by the Williams or

Jonckheere tests compared to Dunnett or another pairwise method and is derived from the

Cochran-Armitage test for quantal data.

Histopath Scores Compared to Incidence Data

Score data can be converted to incidence data by recording just presence or absence. 

However, important information may be lost in the process. The basic concepts of 

incidence data are shown in the following table.

Table 7A: General Form of Incidence Table

A simple chi-square statistic tests for independence of the cell counts and dose by 

standardizing the comparison of the predicted cell count under independence to what is 

observed. The predicted value and test statistic are given by the

 Xij = Ri

*Cj N χ 2 = ∑ ij

i, j

ˆ 2

ij

ˆ

ij

It is helpful to express the test statistic in terms of the predicted proportion of responders. 

This allows the expression of the model for this proportion, here shown as a constant.
j 1

(p

j j

j j

Table 7B: General Form of Incidence Table Expressed as Proportions

The predicted value and test statistic, with k-1 degrees of freedom, are given by

p

 = R N , pij = Xij /Cj

χ 2 = ∑ ij

j

− p

 )

2

Vj

, where Vj = p



j (1− p



)

Cj

The simple chi-square statistic can be significant because of change in within-column 

variance, or a single unusual value. It takes no account of any concentration-response 

relationship. The Cochran-Armitage test is built on a presumed linear relationship 

between dose and row proportions. Theory indicates linearity is not important. Instead of 

modeling the proportion in each test concentration affected as constant, the CochranArmitage test uses

p

 = a + b* D ,

where Dj is some measure of concentration, and a and b are estimated from the data.

Dj can be actual conc, log(conc), or simple equal spacing (0, 1, 2, 3, ...). This last option 

is considered best but differs little from using log(conc). The Chi-Square statistics is then 

partitioned into a 1 degree of freedom test for trend and a k-2 degree of freedom for lack 

of fit to this trend.

Standard tests for incidence data include (1) step-down Cochran-Armitage test, w/ or w/o 

the Rao-Scott adjustment for extra-between-rep variance (heterogeneity) and (2) FisherExact test.

Example 1: Gonadal Increased Oocyte Atresia in F1 Females

Consider the standard Cochran-Armitage test for gonadal Increased Oocyte Atresia that 

treats any severity score greater than 0 as an incidence. Thus, the analysis compares 

incidences of any degree of severity against complete absence (score 0) of gonadal 

Increased Oocyte Atresia.
Heterogeneity Check of Between-Replicate Variances - Doses=6

For Response=Gon_Incr_Oocyte_Atresia with Severity Score >=1

Female data for generation F1

STATISTIC VALUE Conc DF PROB DOSES SIGNIF

Chi-Square 11.2 0 5 0.047556 6 *

Chi-Square 7.366667 32 5 0.194767 6

Table of Gon_Incr_Oocyte_Atresia1P by Conc

Gon_Incr_Oocyte_Atresia1P 

Conc

Frequency| 0| 2| 5| 13| 32| 84| Total

---------+------+------+------+------+------+------+

0 | 15 | 25 | 25 | 27 | 15 | 16 | 123

---------+------+------+------+------+------+------+

1 | 6 | 0 | 0 | 0 | 2 | 0 | 8

---------+------+------+------+------+------+------+

Total 21 25 25 27 17 16 131

STANDARD COCHRAN-ARMITAGE TEST FOR Gon_Incr_Oocyte_Atresia in F1

Generation RSCORE DOSES T PROBT SIGNIF

F1 1 6 -2.41223 .007927702 *

F1 1 5 -2.08832 0.018384 *

F1 1 4 -3.64173 .000135408 *

F1 1 3 -3.36797 .000378625 *

F1 1 2 -2.86606 .002078094 *

So, by the step-down Cochran-Armitage test, there is a significant reduction in the 

proportion of female fish with severity score 1 or greater of gonadal Increased Oocyte 

Atresia in every test concentration compared to the control. Note that the Mann-Whitney 

test did not find a significant reduction in the 32 ug/L concentration. However, the ChiSquare test for between-replicate heterogeneity was mildly significant in the control and 

the Cochran-Armitage test ignores that. Table 4 shows the control replicate information. 

The table makes clear that the distribution of scores in reps E and F are different from 

that in reps A-D.

Table 8: F1 Controls by Replicate and Gon_Incr_Oocyte_Atresia Score

The Rao-Scott modification of the Cochran-Armitage test is designed to take account of 

heterogeneous between-rep variance as well as different replicate sizes, as is also evident 

in Table 4. The analysis is repeated using the Rao-Scott Cochran-Armitage test.
RAO-SCOTT COCHRAN-ARMITAGE TEST for F1 Gon_Incr_Oocyte_Atresia SEVERITY 

SCORE >= 1 FROM DATA TREN03MEDAKA_8_FEMALES

Generation RSCORE DOSES T PROBT SIGNIF

F1 1 6 -2.38372 .008569268 *

F1 1 5 -2.07268 0.019101 *

F1 1 4 -3.60662 .000155103 *

F1 1 3 -3.34664 .000408987 *

F1 1 2 -2.86039 .002115616 *

The differences with the standard Cochran-Armitage test in this example are minor. 

There is still a problem, however. Both the standard and Rao-Scott adjusted CochranArmitage test ignore important information, namely that the severity of the 

histopathology finding. These tests treat a severity score of 1 the same as a score of 5,

which makes the analysis incomplete, at best. Histopathology responses have the 

following structure.

Table 9: General Form of Table of Severity Scores

The proportion of responders in each severity level and dose are to be analyzed. Many 

approaches are possible. Some, such as linear-by-linear association depend on rather 

complex models and are rather rigid in terms of the relationship between exposure 

concentration and score. Others ignore reps or rep sizes. The recommendation put 

forward here is to use as much important information from the experiment as possible.

The Rao-Scott Cochran-Armitage by Slices (RSCABS) test is a serious attempt to do this. 

The test can be described simply as follows:

Rao-Scott Cochran-Armitage by Slices (RSCABS) test

• Step 1: For each rep, count the number of fish in rep with severity 1 or greater

– Apply stepdown Rao-Scott Cochran-Armitage test to these counts

• Step 2: For each rep, count the number of fish in rep with severity 2 or greater

– Apply stepdown test Rao-Scott Cochran-Armitage to these counts

• . . .

–

• Step K: For each rep, count the number of fish in rep with severity K or greater

– Apply stepdown Rao-Scott Cochran-Armitage test to these counts
Step 1 has already been demonstrated above. It found every treatment group had 

significantly reduced incidence of severity score 1 or greater gonadal Increased Oocyte 

Atresia compared to the control. Below are the remaining steps.

Step 2

RAO-SCOTT COCHRAN-ARMITAGE TEST FOR F1 Gon_Incr_Oocyte_Atresia SEVERITY 

SCORE >= 2 FROM DATA TREN03MEDAKA_8_FEMALES

Generation RSCORE DOSES T PROBT SIGNIF

F1 2 6 -3.26758 .000542349 *

F1 2 5 -3.30818 .000469527 *

F1 2 4 -3.27534 .000527673 *

F1 2 3 -3.03267 .001212007 *

F1 2 2 -2.58008 .004938894 *

Conclusions for Example 1 for Gonadal Increased Oocyte Atresia

Thus, at step 2, there is a significant reduction in the proportion of female fish with 

severity score 2 or greater of gonadal Increased Oocyte Atresia in every test 

concentration compared to the control. There were no severity score 3 or greater in any 

test concentration in the F1 generation, so the test stops here. There are two conclusions. 

First, there is a significantly reduced incidence of positive severity scores for gonadal 

Increased Oocyte Atresia in every test concentration compared to the control. Second, 

there is a significantly reduced incidence of severity score 2 or greater for gonadal

Increased Oocyte Atresia in every test concentration compared to the control. Since there 

is no severity score of 3 or greater, the statistical significance indicates a minimal to mild 

treatment associated change in gonadal Increased Oocyte Atresia, but one which appears 

in every test concentration. This significance arises from two control replicates, E and F, 

and may not be of real biological importance.
Example 2: Gonad Stage Male F1

Table 10: Data for Gonad Stage Male F1

1-Generation Kruskal-Wallis Tests for Treatment Effects on Gon_Stage

Generation response p_KWTest Signif

F1 Gon_Stage 0.00672 *

The Kruskal-Wallis test indicates there are significant differences among the control and 

treatment groups.

1-Generation Mann-Whitney Tests for Treatment Effects on Gon_Stage

Generation Test p2_Wil Signif Response 

F1 2 vs 0 0.30043 Gon_Stage 

F1 5 vs 0 0.00852 * Gon_Stage 

F1 13 vs 0 0.96477 Gon_Stage 

F1 32 vs 0 0.26381 Gon_Stage 

F1 84 vs 0 0.32873 Gon_Stage

The Mann-Whitney tests indicate the 5 ug/L concentration group tends to have a different 

gonad stage than the controls. An inspection of the data indicates the fish exposed to 5 

ug/L trenbolone tend to have a later gonad stage than the controls. Since the higher 

concentrations are not significantly different from the control, the result at 5 ug/L is 

possibly spurious.

Next, consider the RSCABS analysis.

Heterogeneity Check of Between-Replicate Variances - Doses=6

For Response=Gon_Stage with Severity Score >=1

Male data for generation F1

STATISTIC VALUE Conc DF PROB DOSES SIGNIF

Chi-Square 2.236667 0 5 0.815522 6

Chi-Square 4.210526 5 5 0.519521 6

Chi-Square 3.958333 32 5 0.55543 6

There is no significant evidence of heterogeneous between-rep variance. There are 

differences in replicate sizes. RSCABS will be done.

Percent Gon_Stage with Severity >=1 is constant. (The lowest stage is 1.) No test can be 

done.
Heterogeneity Check of Between-Replicate Variances - Doses=6

For Response=Gon_Stage with Severity Score >=2

Male data for generation F1

STATISTIC VALUE Conc DF PROB DOSES SIGNIF

Chi-Square 6.341176 0 5 0.274422 6

Chi-Square 4.095076 2 5 0.53581 6

Chi-Square 5.884615 13 5 0.317609 6

Chi-Square 5.62963 32 5 0.343941 6

There is no significant evidence of heterogeneous between-rep variance. There are 

differences in replicate sizes.

MALE Generation F1 with Scores>=2

Table of Gon_Stage2P by Conc

Gon_Stage2P 

Conc

Frequency| 0| 2| 5| 13| 32| 84| Total

---------+------+------+------+------+------+------+

0 | 5 | 8 | 0 | 4 | 1 | 0 | 18

---------+------+------+------+------+------+------+

1 | 17 | 11 | 20 | 13 | 18 | 16 | 95

---------+------+------+------+------+------+------+

Total 22 19 20 17 19 16 113

RAO-SCOTT COCHRAN-ARMITAGE TEST FOR Doses=6

Generation RSCORE DOSES T PROBT SIGNIF

F1 2 6 2.73001 .003166604 *

F1 2 5 1.87718 0.030246 *

F1 2 4 0.99012 0.16106

The 84 and 32 ug/L groups have significantly greater proportion of gonad stage 2 and 

higher than the controls. The 5 ug/L group is not found to have a significantly greater 

proportion of gonad stage 2 and higher than the controls. (Note: In the Table of 

Gon_Stage2P by Conc, the Row labeled 0 is those fish with stage less than 2 and the row 

labeled 1 is for those fish with stage 2 or higher.) It might seem strange that the 

proportion of stage 2 or higher fish in the 5 ug/L group is higher than that in the 32 and

84 ug/L groups but is not significant, while the rates in 32 and 84 ug/L groups are 

significant. This is the result of applying a trend-based test such as Rao-Scott CochranArmitage which takes all the data up to the highest included concentration into account. 

The incidence rate at 13 ug/L is relatively low, so the trend through that concentration is 

not significant and testing stops. The high incidence at 5 ug/L is not followed by a high 

incidence at the next tested concentration and is thus considered insufficient evidence of 

a treatment-related effect.
Heterogeneity Check of Between-Replicate Variances - Doses=6

For Response=Gon_Stage with Severity Score >=3

Male data for generation F1

STATISTIC VALUE Conc DF PROB DOSES SIGNIF

Chi-Square 6.337222 0 5 0.274774 6

Chi-Square 2.454167 2 5 0.783381 6

Chi-Square 6.27451 5 5 0.280417 6

Chi-Square 6.296296 13 5 0.278446 6

Chi-Square 3.80406 32 5 0.577957 6

Chi-Square 1.733333 84 4 0.784654 6

Again, there is no significant evidence of between-rep heterogeneity. There are still 

differences in replicate sizes.

MALE Generation F1 with Scores>=3

Table of Gon_Stage3P by Conc

Gon_Stage3P 

Conc

Frequency| 0| 2| 5| 13| 32| 84| Total

---------+------+------+------+------+------+-----+

0 | 12 | 11 | 3 | 8 | 6 | 8 | 48

---------+------+------+------+------+------+-----+

1 | 10 | 8 | 17 | 9 | 13 | 8 | 65

---------+------+------+------+------+------+-----+

Total 22 19 20 17 19 16 113

RAO-SCOTT COCHRAN-ARMITAGE TEST FOR F1 Gon_Stage SEVERITY SCORE >= 3

FROM DATA TREN03MEDAKA_8_MALES

Generation RSCORE DOSES T PROBT SIGNIF

F1 3 6 0.87533 0.19070

There is no significant concentration-response trend in the incidence of gonad stages 3 

and higher.

Heterogeneity Check of Between-Replicate Variances - Doses=6

For Response=Gon_Stage with Severity Score >=4

Male data for generation F1

STATISTIC VALUE Conc DF PROB DOSES SIGNIF

Chi-Square 3.289815 0 5 0.655401 6

Chi-Square 2.955556 2 5 0.706838 6

Chi-Square 7.986111 5 5 0.157003 6

Chi-Square 4.476667 13 5 0.483011 6

Chi-Square 8.382353 32 5 0.136384 6

Chi-Square 5.511111 84 4 0.238755 6

Again, there is no significant evidence of between-rep heterogeneity. There are still

differences in replicate sizes.
MALE Generation F1 with Scores>=4

Table of Gon_Stage4P by Conc

Gon_Stage4P 

Conc

Frequency| 0| 2| 5| 13| 32| 84| Total

---------+------+------+------+------+------+------+

0 | 18 | 18 | 12 | 15 | 17 | 12 | 92

---------+------+------+------+------+------+------+

1 | 4 | 1 | 8 | 2 | 2 | 4 | 21

---------+------+------+------+------+------+------+

Total 22 19 20 17 19 16 113

RAO-SCOTT COCHRAN-ARMITAGE TEST FOR F1 Gon_Stage SEVERITY SCORE >= 4

FROM DATA TREN03MEDAKA_8_MALES

Generation RSCORE DOSES T PROBT SIGNIF

F1 4 6 0.21230 0.41594

There is no significant concentration-response trend in the incidence of gonad stages 4

and higher.

Conclusions for Example 2 for Gonad Stage in Male F1 Medaka

There was a significant tendency for an increase in gonad stage 2 fish at 32 ug/L and 

above, but no indication of an increase in stages 3 or 4 fish at these exposure levels. This 

is quite different from what is obtained from the Mann-Whitney test which indicated a 

significant increase in gonad stage in the 5 ug/L group but not in any higher 

concentration. Also, the Mann-Whitney test gave no indication of how severe the 

increase was, merely that it was significant. The percentages of stage 1 fish were 23, 42,

0, 24, 5, and 0 at 0, 2, 5, 13, 32, and 84 ug/L, respectively. No trend is evident in these 

percentages below 32 ug/L.

Example 3 from Trenbolone Exposures for 16 Weeks

The results and data for this example came from a different experiment with trenbolone 

on 16 week old animals.

Table 11: RSCABS for Female F1 Kidney Tubules, Epithelium, Hypereosinophilia
Table 12: MW for Female F1 Kidney Tubules, Epithelium, Hypereosinophilia

Table 13: Data for Female F1 Kidney Tubules, Epithelium, Hypereosinophilia

So MW finds significantly increased Female F1 Kidney Tubules, Epithelium, 

Hypereosinophilia only at 84 ug/L exposure. RSCABS finds significant increases at 84,

32, and 13 ug/L. RSCABS is picking up on the trend towards affects in higher exposure 

levels. MW considers evidence only from the control and a single exposure group and 

thus loses power. RSCABS does not find the five score 2 or 3 fish at 13 ug/L significant

at the slice Score ≥ 2 because the next higher concentration has no fish with scores higher 

than 1.

Summary of All Results for Medaka Exposed to Trenbolone for 8 Weeks

In the tables below, summaries of the results of the Mann-Whitney and RSCABS 

analyses are given, so that direct comparisons can be made to the relative performance of 

these two tests. Only the statistically significant findings are shown.
Table 14: F1 Female Mann-Whitney Test Results

Table 15: F1 Female RSCABS Test Results

Discussion

The KW test found significant differences among the groups for

Gon_Decr_Yolk_Formation, but the MW test failed to find any treatment groups
different from the control. RSCABS found the 32 and 84 ug/L groups to differ 

significantly from the control. The RSCABS results are given below.

Heterogeneity Check of Between-Replicate Variances - Doses=6

For Response=Gon_Decr_Yolk_Formation with Severity Score >=1

Female data for generation F1

STATISTIC VALUE Conc DF PROB DOSES SIGNIF

Chi-Square 3.811508 32 5 0.576861 6

No variance heterogeneity found.

Table of Gon_Decr_Yolk_Formation1P by Conc

Gon_Decr_Yolk_Formation1P 

Conc

Frequency| 0| 2| 5| 13| 32| 84| Total

---------+--------+--------+--------+--------+--------+--------+

0 | 21 | 25 | 25 | 27 | 14 | 16 | 128

---------+--------+--------+--------+--------+--------+--------+

1 | 0 | 0 | 0 | 0 | 3 | 0 | 3

---------+--------+--------+--------+--------+--------+--------+

Total 21 25 25 27 17 16 131

F1 Gon_Decr_Yolk_Formation SEVERITY SCORE >= 1 FROM DATA 

TREN03MEDAKA_8_FEMALES

RAO-SCOTT COCHRAN-ARMITAGE TEST FOR Doses=6

Generation RSCORE DOSES T PROBT SIGNIF

F1 1 6 1.79990 0.035938 *

F1 1 5 2.66316 .003870540 *

RAO-SCOTT COCHRAN-ARMITAGE TEST FOR Doses=4

No Gon_Decr_Yolk_Formation with Score>=1

No test can be done.

It is difficult to accept the significant effect attributed to the high test concentration. What 

has happened is that the increase in severity 1 or greater at 32 ug/L has made the trend 

through 84 ug/L significant. This is not typical of step-down trend tests, but clearly this 

example shows it can happen. This is the flip side of the earlier example where the MannWhitney test found an intermediate test concentration significant but not the two higher 

test concentrations and RSCABS found significant the two higher test concentrations but 

not the intermediate. A reasonable interpretation of the data after this first step in 

RSCABS is that for this endpoint would be a possible treatment effect at 32 ug/L, but 

questionable since it is not observed at a higher concentration. As indicated below, there 

was one fish in the 32 ug/L group with severity score 3, so an effect at this exposure 

concentration cannot be dismissed without further scientific judgment being brought to 

bear.
Heterogeneity Check of Between-Replicate Variances - Doses=6

For Response=Gon_Decr_Yolk_Formation with Severity Score >=2

Female data for generation F1

STATISTIC VALUE Conc DF PROB DOSES SIGNIF

Chi-Square 7.96875 32 5 0.157966 6

No variance heterogeneity found.

Table of Gon_Decr_Yolk_Formation2P by Conc

Gon_Decr_Yolk_Formation2P 

Conc

Frequency| 0| 2| 5| 13| 32| 84|Total

---------+------+--------+--------+--------+--------+--------+

0 | 21 | 25 | 25 | 27 | 16 | 16 | 130

---------+------+--------+--------+--------+--------+--------+

1 | 0 | 0 | 0 | 0 | 1 | 0 | 1

---------+------+--------+--------+--------+--------+--------+

Total 21 25 25 27 17 16 131

F1 Gon_Decr_Yolk_Formation SEVERITY SCORE >= 2 FROM DATA 

TREN03MEDAKA_8_FEMALES

RAO-SCOTT COCHRAN-ARMITAGE TEST FOR Doses=6

Generation RSCORE DOSES T PROBT SIGNIF

F1 2 6 1.03157 0.15114

Heterogeneity Check of Between-Replicate Variances - Doses=6

For Response=Gon_Decr_Yolk_Formation with Severity Score >=3

Female data for generation F1

STATISTIC VALUE Conc DF PROB DOSES SIGNIF

Chi-Square 7.96875 32 5 0.157966 6

No variance heterogeneity found.

Table of Gon_Decr_Yolk_Formation3P by Conc

Gon_Decr_Yolk_Formation3P 

Conc

Frequency| 0| 2| 5| 13| 32| 84|Total

---------+------+--------+--------+--------+--------+--------+

0 | 21 | 25 | 25 | 27 | 16 | 16 | 130

---------+------+--------+--------+--------+--------+--------+

1 | 0 | 0 | 0 | 0 | 1 | 0 | 1

---------+------+--------+--------+--------+--------+--------+

Total 21 25 25 27 17 16 131

F1 Gon_Decr_Yolk_Formation SEVERITY SCORE >= 3 FROM DATA 

TREN03MEDAKA_8_FEMALES

RAO-SCOTT COCHRAN-ARMITAGE TEST FOR Doses=6

Generation RSCORE DOSES T PROBT SIGNIF

F1 3 6 1.03157 0.15114
Heterogeneity Check of Between-Replicate Variances - Doses=4

For Response=Gon_Decr_Yolk_Formation with Severity Score >=1

Female data for generation F2

STATISTIC VALUE Conc DF PROB DOSES SIGNIF

Chi-Square 5.971154 13 5 0.309036 4

Both MW and RSCABS found significant treatment related results for 

Gon_Incr_Oocyte_Atresia. The only difference in conclusions was that the latter found 

the 32 ug/L group significant but the MW did not. All other conclusions were the same. 

This was discussed in detail in Example 1 and will not be repeated here.

KW found significant differences among the groups for Gon_Perifollicular_Cell_HH 

but the MW and RSCABS tests found no treatment significantly different from the 

control.

MW found significant differences in Gonad Phenotype in the two high test 

concentrations compared to the control. RSCABS provides much more detailed 

information. From Table 15, it is evident that there are significantly reduced incidences 

of gonad phenotypes 2 and greater in these two high test concentration compared to the 

control. RSCABS also indicates increased incidence of gonad phenotypes 4 and 5 at 13 

and 5 ug/L, though the detailed output provided below shows that these latter two results 

are driven by 2 fish in the control. That and the change in direction suggest the 5 and 13 

ug/L results are very likely spurious.

Gon_Phenotype4P 

Conc

FEMALE Generation F1 with Scores>=4

Table of Gon_Phenotype4P by Conc

Frequency| 0| 2| 5| 13| 32| 84|Total

---------+------+--------+--------+--------+--------+--------+

0 | 2 | 0 | 0 | 0 | 7 | 16 | 25

---------+------+--------+--------+--------+--------+--------+

1 | 19 | 25 | 25 | 27 | 10 | 0 | 106

---------+------+--------+--------+--------+--------+--------+

Total 21 25 25 27 17 16 131

F1 Gon_Phenotype SEVERITY SCORE >= 4 FROM DATA 

TREN03MEDAKA_8_FEMALES

RAO-SCOTT COCHRAN-ARMITAGE TEST FOR Doses=6

Generation RSCORE DOSES T PROBT SIGNIF

F1 4 6 -6.97158 1.567E-12 *

F1 4 5 -2.66207 .003883107 *

F1 4 4 2.04015 0.020668 *

F1 4 3 1.87736 0.030234 *
MW reports no significant effect on gonad stage whereas RSCABS finds a significant in 

stage 4 in the high test concentration. The data below show a 12.5 % increase in stage 4 

fish in the high test concentration compared to the control.

Table of Gon_Stage4P by Conc

Gon_Stage4P 

Conc

Frequency| 0| 2| 5| 13| 32| 84|Total

---------+------+--------+------+--------+--------+--------+

0 | 21 | 25 | 25 | 27 | 16 | 14 | 128

---------+------+--------+------+--------+--------+--------+

1 | 0 | 0 | 0 | 0 | 1 | 2 | 3

---------+------+--------+------+--------+--------+--------+

Total 21 25 25 27 17 16 131

F1 Gon_Stage SEVERITY SCORE >= 4 FROM DATA TREN03MEDAKA_8_FEMALES 

RAO-SCOTT COCHRAN-ARMITAGE TEST FOR Doses=6

Generation RSCORE DOSES T PROBT SIGNIF

F1 4 6 2.54551 .005455849 *

F1 4 5 1.52472 0.063664

Both MW and RSCABS report significant increase in testicular degeneration in the high 

test concentration. RSCABS makes clear that this is an increase from total absence to 

minimal.

MW and RSCABS report significant effects in Tubules, Epithelium, Hypereosinophilia 

in the 32 and 84 ug/L test concentrations. RSCABS shows that these are due to increases 

in severity scores 1, 2, and 3, so the effects are mild to moderate.

MW and RSCABS report significant effects in Tubules, Epithelium, Hypetrophy in the

32 and 84 ug/L test concentrations. RSCABS shows that these are due to increases in 

severity scores 1, 2, and 3, so the effects are mild to moderate.

MW and RSCABS report significant effects in Tubules, Epithelium, Vacuolization in 

the 84 ug/L test concentrations. RSCABS shows that these are due to increases in 

severity scores 1, so the effects are minimal.

RSCABS reports a significant effect in Tubules, Protein at the 82 ug/L test 

concentration. MW does not. RSCABS makes clear that this is a minimal (severity score

1) effect.

MW and RSCABS report significant effects in liver Eosinophilia in the 32 and 84 ug/L 

test concentrations. RSCABS shows that these are due to increases in severity scores 1, 

so the effects are minimal.
Table 16: F2 Female Mann-Whitney Test Results

Table 17: F2 Female RSCABS Test Results

Discussion

MW and RSCABS report significant effects in Increased Oocyte Atresia in the 13, 5, and

2 ug/L test concentrations. RSCABS makes clear that these are all due to increases in 

severity score 1, so the effects are minimal.

The Kruskal-Wallis test found differences among the groups in Gonad stage but neither

MW nor RSCABS found any treated effects.

MW found significant effects in kidney Glomeruli, Mineralization at 2 and 5 ug/L but 

not at higher test concentration. RSCABS found no significant effects. The tables below 

shows almost no difference in the incidence of score 1 or greater in these two test 

concentrations. It is difficult to understand why MW finds significance.

FEMALE Generation F1 with Scores>=1

Table of Kid_Tub_Mineralization1P by Conc

Kid_Tub_Mineralization1P 

Conc

Frequency| 0| 2| 5| 13| 32| 84|Total

---------+------+------+--------+--------+--------+--------+

0 | 16 | 19 | 19 | 22 | 12 | 14 | 102

---------+------+------+--------+--------+--------+--------+

1 | 5 | 6 | 6 | 5 | 5 | 2 | 29

---------+------+------+--------+--------+--------+--------+

Total 21 25 25 27 17 16 131
FEMALE Generation F1 with Scores>=2

Table of Kid_Tub_Mineralization2P by Conc

Kid_Tub_Mineralization2P 

Conc

Frequency| 0| 2| 5| 13| 32| 84| Total

---------+------+--------+--------+------+--------+--------+

0 | 20 | 25 | 25 | 27 | 17 | 16 | 130

---------+------+--------+--------+------+--------+--------+

1 | 1 | 0 | 0 | 0 | 0 | 0 | 1

---------+------+--------+--------+------+--------+--------+

Total 21 25 25 27 17 16 131

MW finds a significant effect in Tubules, Cellular Debris/ Casts in the 2 ug/L test 

concentration but not at any higher test concentration. While there is an increase of 21% 

in the severeity score 1 fish at the 2 ug/L exposure, the fact that this is not observed at 

higher test concentrations suggests it is a spurious finding. There is clearly no 

concentration-response trend in the data. With one exception in the 2 ug/L test 

concentration, all findings are minimal (have severity score 1).

FEMALE Generation F2 with Scores>=1

Table of Kid_Tub_Cellulardebris_casts1P by Conc

Kid_Tub_Cellulardebris_casts1P 

Conc

Frequency| 0| 2| 5| 13| Total

---------+--------+--------+--------+--------+

0 | 23 | 11 | 22 | 26 | 82

---------+--------+--------+--------+--------+

1 | 0 | 3 | 2 | 1 | 6

---------+--------+--------+--------+--------+

Total 23 14 24 27 88

F2 Kid_Tub_Cellulardebris_casts SEVERITY SCORE >= 1 FROM DATA 

TREN03MEDAKA_8_FEM

RAO-SCOTT COCHRAN-ARMITAGE TEST FOR Doses=4

Generation RSCORE DOSES T PROBT SIGNIF

F2 1 4 0.13894 0.44475

FEMALE Generation F1 with Scores>=2

Table of Kid_Tub_Cellulardebris_casts2P by Conc

Kid_Tub_Cellulardebris_casts2P 

Conc

Frequency| 0| 2| 5| 13| 32| 84|Total

---------+------+--------+------+--------+--------+--------+

0 | 20 | 25 | 25 | 27 | 17 | 16 | 130

---------+------+--------+------+--------+--------+--------+

1 | 1 | 0 | 0 | 0 | 0 | 0 | 1

---------+------+--------+------+--------+--------+--------+

Total 21 25 25 27 17 16 131
F1 Kid_Tub_Cellulardebris_casts SEVERITY SCORE >= 2 FROM DATA 

TREN03MEDAKA_8_FEM

RAO-SCOTT COCHRAN-ARMITAGE TEST FOR Doses=6

Generation RSCORE DOSES T PROBT SIGNIF

F1 2 6 -1.43958 0.074994

MW found a significant effect in Tubules, Epithelium, Hyperplasia in the 5 ug/L 

exposure group but not at any higher exposure level, whereas RSCABS found nothing 

significant. As shown below, there is evidence of heterogeneity in the 5 ug/L exposure 

group, and this may affect the MW test.

Heterogeneity Check of Between-Replicate Variances - Doses=4

For Response=Kid_Tub_Epithe_Hyperplasia with Severity Score >=1

Female data for generation F2

STATISTIC VALUE Conc DF PROB DOSES SIGNIF

Chi-Square 5.833333 2 4 0.211946 4

Chi-Square 13.44 5 5 0.019587 4 *

There is significant among-rep heterogeneity in the 5 ug/L group, as evident from the 

following data table, where Rep E has a different distribution of severity scores from the 

other reps. The MW test may be overly sensitive to the single severity score 2 fish in rep 

E.

Table 18: Severity Scores for Kid_Tub_Epithe_Hyperplasia in F2 Females at 5 ug/L

FEMALE Generation F2 with Scores>=1

Table of Kid_Tub_Epithe_Hyperplasia1P by Conc

Kid_Tub_Epithe_Hyperplasia1P 

Conc

Frequency| 0| 2| 5| 13| Total

---------+--------+--------+--------+--------+

0 | 23 | 12 | 20 | 27 | 82

---------+--------+--------+--------+--------+

1 | 0 | 2 | 4 | 0 | 6

---------+--------+--------+--------+--------+

Total 23 14 24 27 88
F2 Kid_Tub_Epithe_Hyperplasia SEVERITY SCORE >= 1 FROM DATA 

TREN03MEDAKA_8_FEMAL

RAO-SCOTT COCHRAN-ARMITAGE TEST FOR Doses=4

Generation RSCORE DOSES T PROBT SIGNIF

F2 1 4 0.095535 0.46195

The relatively high incidence of severity scores of 1 or greater at 5 ug/L is evidence of an 

effect at this one test concentration. The fact that there are no fish with adverse findings

at the higher 13 ug/L test concentration suggests a possibly spurious effect at 5 ug/L and 

accounts for the RSCABS approach not finding this significant.

RSCABS found a significant increase in Gonad Proteinaceous Fluid severity score 1 fish 

at 13 ug/L, while MW found nothing significant. So, because the 7% increase in minimal 

effects occured in the high test concentration, RSCABS found it significant. Had this 

occured in an intermediate test concentration, it would not have been significant. The 

effect, if real, is minimal.

FEMALE Generation F2 with Scores>=1

Table of Gon_Proteinaceous_fluid1P by Conc

Gon_Proteinaceous_fluid1P 

Conc

Frequency| 0| 2| 5| 13| Total

---------+--------+--------+--------+--------+

0 | 23 | 14 | 24 | 25 | 86

---------+--------+--------+--------+--------+

1 | 0 | 0 | 0 | 2 | 2

---------+--------+--------+--------+--------+

Total 23 14 24 27 88

F2 Gon_Proteinaceous_fluid SEVERITY SCORE >= 1 FROM DATA 

TREN03MEDAKA_8_FEMALES

RAO-SCOTT COCHRAN-ARMITAGE TEST FOR Doses=4

Generation RSCORE DOSES T PROBT SIGNIF

F2 1 4 1.67093 0.047368 *
Table 19: F1 Male Mann-Whitney Test Results

Table 20: F1 Male RSCABS Test Results

Discussion

The discussion of Gonad stage was given in Example 2 above and will not be repeated 

here.

MW found a significant effect in Tubules, Dilatation in the 5 ug/L exposure group but 

not at any higher test concentration. Since there was no apparent concentration-response 

trend in the data, RSCABS did not find this significant.

KW found significant differences among groups in both Tubules, Epithelium, 

Hypereosinophilia and Tubules, Epithelium, Hypetrophy, but neither MW nor RSCABS 

found any significant treatment effect compared to the control.

MW found a significant effect in Kidney Tubules, Mineralization at the 2 ug/L exposure 

group but not at any higher test concentration. RSCABS found significant, but minimal, 

decreases in this histopathology finding at the two high test concentrations but not at 2 

ug/L. Examination of the incidence of severity score 1 below shows an increase in fish 

with this score in the two lowest test concentrations but no such fish in the three highest 

test concentration. For this reason, RSCABS finds no significant upward trend in the

data. On the other hand, RSCABS does find evidence of a decrease in score 1 or higher 

fish in the highest two test concentrations. Taken together, it would appear that there is 

no treatment related effect on Kidney Tubules, Mineralization.

MALE Generation F1 with Scores>=1

Table of Kid_Tub_Mineralization1P by Conc

Kid_Tub_Mineralization1P 

Conc

Frequency| 0| 2| 5| 13| 32| 84|Total

---------+------+------+--------+--------+--------+--------+

0 | 19 | 11 | 16 | 17 | 19 | 16 | 98

---------+------+------+--------+--------+--------+--------+

1 | 1 | 7 | 4 | 0 | 0 | 0 | 12

---------+------+------+--------+--------+--------+--------+

Total 20 18 20 17 19 16 110
F1 Kid_Tub_Mineralization SEVERITY SCORE >= 1 FROM DATA 

TREN03MEDAKA_8_MALES

RAO-SCOTT COCHRAN-ARMITAGE TEST FOR Doses=6

Generation RSCORE DOSES T PROBT SIGNIF

F1 1 6 -2.51499 .005951835 *

F1 1 5 -1.88798 0.029514 *

F1 1 4 -0.72743 0.23348

MALE Generation F1 with Scores>=2

Table of Kid_Tub_Mineralization2P by Conc

Kid_Tub_Mineralization2P 

Conc

Frequency| 0| 2| 5| 13| 32| 84| Total

---------+------+------+--------+--------+--------+--------+

0 | 19 | 18 | 20 | 17 | 19 | 16 | 109

---------+------+------+--------+--------+--------+--------+

1 | 1 | 0 | 0 | 0 | 0 | 0 | 1

---------+------+------+--------+--------+--------+--------+

Total 20 18 20 17 19 16 110

F1 Kid_Tub_Mineralization SEVERITY SCORE >= 2 FROM DATA 

TREN03MEDAKA_8_MALES

RAO-SCOTT COCHRAN-ARMITAGE TEST FOR Doses=6

Generation RSCORE DOSES T PROBT SIGNIF

F1 2 6 -1.40962 0.079326

Table 21: F2 Male Mann-Whitney Test Results

Table 22: F2 Male RSCABS Test Results

MW and RSCABS find significant effects at 13 ug/L. RSCABS makes clear that this arises 

from an increase in fish with severity scores up to 4 and so is likely a real effect of interest. 

An inspection of the data shows that there are 4 fish out of 20 in the 13 ug/L concentration 

with severity score 4 and 1 with severity score 1.