tttjjj/elt_bench huggingface dataset:
Henrik, a comment on the plot. How many subjects do you have? I would strongly recommend plotting the data individually and use line segments to link individuals. (Line segments linking means is deceptive.) There is no need to plot SEs. The idea is to visually support your statistical analysis. Provided the plot does not become too cluttered, a reader should see (for example) that the clear majority of scores go up from MP-valid-implaus to AC-inval-plaus for the Inductive group & down for the Deductive group. See:
http://www.jstor.org/stable/2685323?seq=1
Especially Figs 1 & 9 bottom panels.
I don't think this answers the OP. I'm assuming @rolando2 reports other stats that are more central to his discussions (e.g., effect sizes), and mostly reports _p_ values as one way of accommodating conventional expectations, even though they don't apply strictly. As such, we should be off-put to whatever extent we're reading too much into _p_ values; we should consider his motivation for the disclaimer. Readers don't know what they should; the OP mentions this. The disclaimer promotes doubt, not trust. It's not that odd to object to a standard while conforming to it; it's not a bold stand.
Welcome to Cross Validated! The answer seems to be unequivocally "Yes" - perhaps you could explain what you understand about moderator, interaction, & main effects that makes you uncertain.
I assume it means thinking about how big the interaction is and whether it matters.
I remain unenlightened. How does it relate to the model?
Why do you want the p-value? Significance tests for the coefficients of an AR model are not particularly helpful as significance is not a good way to select the model order. Use the AIC instead.
Did you have a look at "the run test" ? http://en.wikipedia.org/wiki/Wald%E2%80%93Wolfowitz_runs_test
This seems to be the slightly more general answer.  The more quantities that are marginalised rather than optimised the more 'fully Bayesian' the solution is.  Empirical Bayes is a special case.
@ConjugatePrior I didn't get notification of it when you posted it, so didn't see it until you posted the above comment, and haven't had a chance to check it thoroughly as of yet.
I'd like to see a reference for this assertion: "Mathematica is often faster than R for statistical data crunching."
I meant the interaction effect in the conventional ANOVA sense. (Can it be estimated in MANOVA?) 'Group-group multiple comparisons' are kinda post hoc multiple comparison, control-thyroxine, control-thiouracil, and thyroxine-thiouracil comparisons.
Oh, yeah, that's interesting. You could also control for order of observations within levels of $X$ (and within subjects) then. Maybe more trouble than it's worth to you though. I'm not sure how your simpler alternative would compare. It might work, but it doesn't strike me as appropriate, so proceed with it at your own risk if you wish. HLM might give you richer and clearer info, but I'll admit I haven't even performed it yet myself – I've only studied it. It is a little tricky.
This is too strong a claim. In addition, note that essentially no scientific studies actually use random samples. The closest is polling studies (who are you going to vote for, etc.), & even those aren't really random.
Hm, but why not test it? By using adjusting standard errors you lose out in efficiency, if you really do not have problems with heteroscedasticity.
Hi, thanks for reply. There were two different groups, with different participants but with gain frame and loss frame messages and two levels of motivation, same as in group 1. only difference between group 1 and 2 is the order of presenting framed messages.
Fully agree ! the questions that are asked are different. Registration, landmarking, estimation of derivatives can arise from the functional view. This convince me ! so the big deal with functional data (as it stands in statistical literature) would not be that it is defined on a continuous set but more that it is indexed on an ordered set?
This Pearson's $\\chi^2$-test is related to a test of independence between rows and columns of your `dput` object (43 rows x 2 columns, hence 42 df), which doesn't resemble any of the raw or counts data supplied above. This certainly does not test whether "there is a relationship between the dataset type and the category frequency counts". A correct $\\chi^2$ would have (# items - 1) x (# categories - 1) df, provided it makes sense to use such a test. We need additional information to help you more.
Once you start an analysis based on an observation such as the one you report, all assumptions about probability distributions of test stastistics are off. You would have to conditionalize the test to classes where you stop your search for an interesting relationship by using the criterion you implemented... If there is no a priori hypothesis as to which genes are rlevant, you will have to take the search process into account...
In SAS or R you need a few lines of code to remove empty columns, but how come it did not work in Excel? Have you tried right-clicking the header of the empty column and selecting delete?
@GaetanLion thanks for responding; at least I understand why there's suddenly a downvote, so that improves your chances of a relevant response. I'll try to clarify further shortly.
So then, if I understand you right: technically, formally, a frequentist may regularize as much as he likes but (s)he'll have problems justifying it. A Bayesian might still have trouble quantifying his regularization, but qualitatively (s)he's got a consistent way of incorporating it.
@Michelle: This issue is exactely the one I am interested in. I guess I am just not good enough with the statistical terms. So I am treating within-subject differences of the two conditions as between-subject differences. Would this somehow make my results wrong? I just tried to read more about this and similar designs, but all I can find is about mixed-designs where there is an actual within-subject effect as well as an between-subject effect (and the repetitions are used to measure the within part). However I have repetition to achieve higher data quality only and no between-subject effect.
Thanks - I've worked with the package before. The problem is that there isn't really much difference between t2 and t4, seeing that they are really close together, and very much closer than t1 and t2. So it does make sense trying to merge t2-t4 somehow and use only 2 measurement points instead of 4 (it's a reanalysis of data, so i cannot really tell the reason why the data were assessed in this fairly untypical way). That's where my question comes from.
@StephanKolassa is right about the scaling issue, but if the variance really is very low in sensible terms, then I think you should delete it from the model because it can't make a difference. The ultimate would be a variance of 0 (that is, all subjects have the same value) and then the coefficient is really meaningless.
It seems like the bigger issue here is clearly defining what the intervention you are trying to assess is. There are conceivably a large number of ways to change the average educational level of a population - increase years in school from childhood, or increase immigration of highly educated individuals, but also there is presumably some role of the actual type of education/teaching styles/curriculum that may change the effect that education has on GDP. Without clarity on the intervention, your causal effect may not be identifiable, regardless of analytic approach.
A is the mean for control values and B is the mean for the treated for a given variable. There are 3 repetitions of the experiment thus there are 3x A values and 3x B values. within each repetition another variable which is A/B is calculated, thus having 3 A/B values. i repeated this for 2 different individuals and i want to know if there is a difference in the response to the treatment, thus i want to compare the mean (or whatever is correct) between A/B between each individual. the original A and B had samplings smaller than 25.
Do you understand the concepts of standard-error, confidence interval, statistical population, sample, parameter vs. statistic?  I'd look all those up on wikipedia.
If we define a family of prior distributions $P$ to be conjugate to a likelihood if the posterior also lies in $P$, then the family of all distributions is trivially conjugate to any distribution (i.e. a conjugate prior always exists). And when a simple conjugate family exists, mixtures of this family are also conjugate (i.e. it is not unique unless it's trivial).
Thanks. I hadn't thought of looking in the meta-analytic R packages.
@ Fred : ADF assumes the error term of AR(p) process to be white noise which is a less strong assumption than Gaussian noise. I therefore think that normality is not a requirement. KPSS doesn't assumes the error term to be white noise.
I fixed it, thank you!
For lots of information about this topic, please use our [search](http://stats.stackexchange.com/search?q=%2Blogarithm+%2Binterpretation).
Tim, I don't think you understand the concept of probability sampling, and what weighting is used for. The reason government studies use the probability sampling methods is that they give a picture generalizable to the population, even despite the falling response rates (http://www.people-press.org/2012/05/15/assessing-the-representativeness-of-public-opinion-surveys/). Online panels may produce errors of about 10% on some items, no matter whether they have 1000 participants or 20000 participants -- there were plenty of talks about online panels at the recent AAPOR conference showing this.
Here is a free version http://mathworld.wolfram.com/CentralLimitTheorem.html

The links to the textbooks in the article are also very good at further explaining it. 

The Normal distribution is present just about everywhere, not just in biostatistics.
There is no reason to expect the smoothed estimates of slope and intercept to be close to the  fixed betas in the linear regression.  In particular, the slope should fluctuate wildly.
Intuitely: If your X variables can explain the residuals, then you have omitted variables.
See great pictures of this at http://stats.stackexchange.com/questions/30159/is-it-possible-to-have-a-pair-of-gaussian-random-variables-for-which-the-joint-d
If you have done random sampling it should be possible to compute the inclusion probabilities for units in sample. If you have the inclusion probabilities you can compute design weights and construct estimators for your population parameters of interest.
Eye is a shaky, multi-objective clustering criterion, different for different people. Silhouette is a single-objective one. You certainly have clusters perceived by eye, these are not necessarily "good" from the Silhouette's poit of view.
hello, I'm still struggling with this question and I'm not sure if I spelled it out clearly enough - I'd assume, that a lot of statistics-gurus would know an answer from the top of their head - it really boils down to the question whether or not the coefficients $\\phi_{ij}$ of the \\Phi-matrices in a VAR-model are (partial) correlation-coefficients or not. They clearly have to be related to (estimated) correlation-coefficients, but I can't find a clear reference to what kind of relationship exists?
But what question are you trying to answer with these data? Also, what is the unit of observation (a person, a business, etc), and do you have repeat measures, i.e. does each unit of observation have it's own "response rate"?
Hi @Glen, thanks for your answer. I'll have a detained look at this.
My impression is that it's analogous to the "orthogonal errors" assumption in cross-sectional regression (i.e. it biases the standard errors but not the coefficients), but I'm really interested in hearing the actual answer.
It is a problem of loading correctly the MathJax libraries on blogspot. It seems that I managed to solve the Latex rendering issue using the advice on this page [link](https://groups.google.com/forum/#!searchin/mathjax-users/blogspot/mathjax-users/Jh_4kWotsS8/Jq5fD0eci48J), hope it works for you.
Please see http://stats.stackexchange.com/questions/16921/how-to-understand-degrees-of-freedom. The answer which most directly addresses your question is http://stats.stackexchange.com/a/16931; the other answers provide various refinements and additional ways to understand degrees of freedom. Elsewhere on the Web, the best account I can find of this family of distributions is at http://rip94550.wordpress.com/2012/07/30/regression-1-normality-and-the-chi-square-t-and-f-distributions/. Better explanations appear in texts; my favorite is JC Kiefer, *Intro. to Stat. Inference*, pp 265 *et seq.*
Ordinal regression is probably a bit more robust than that, and allows for estimation of well-defined quantities: means, quantiles, and probabilities.  In addition you have all the power of likelihood ratio, Wald, and score tests and confidence intervals.  Estimates of median $Y$ and mean $Y$ in ordinal regression are not redundant, i.e., they are not trivially connected but are allowed to "float" because of fewer distributional assumptions.
@Andre Because "$\\varepsilon$ is a random variable with zero expectation," $\\text{Var}(\\varepsilon)=\\mathbb{E}(\\varepsilon^2)-\\mathbb{E}(\\varepsilon)^2$ = $\\mathbb{E}(\\varepsilon^2)-0$ = $\\mathbb{E}(\\varepsilon^2)$.  It looks like I omitted to type a "$^2$" in one place--I'll fix that.  Thanks for the catch.
thank you a lot for your detailed answer. I'll keep autocorrelation and seasonal effects in mind.
The problem lies with your assumption that it is possible to gain a "known accurate" sample of 5% of the voters.  That is every bit as hard as gaining a "known accurate" set of ballots from 100% of the voters.  You did not describe how you plan to ensure that your sample is "known [to be] accurate".
@Karen I have updated my answer and added an example from Hox. If my answer is helpful, please consider upvoting it.
I think *True Negative Rate* (also called *specificity* in other settings) is was you are looking for, but see http://en.wikipedia.org/wiki/Precision_and_recall.
It sounds like you don't know many things about ANOVA, either. This is not a problem but you should go the extra mile and get a statistics text book and read it. Especially since it is important to you you probably (hehe) wouldn't want some random internet bozo from a forum mess up your research. Statistics isn't that hard from a user's perspective. And it's cool and interesting. Learning about it is totally worth it and it might even make your research more sound if you know what you're doing.
It is easier to envision what an ROC area does if you *don't* draw the ROC curve but rather think about concordance probability.
@DilipSarwate I really like your derivation of (3), and (for citation purposes) I am wondering whether you obtained that on your own or whether it's in a book...  I also just posted a [related question](http://stats.stackexchange.com/questions/50596/pinskers-inequality-for-baysean-hypothesis-testing)...
@ttnphns: In this quote it *is* a covariance matrix (because $x_i$ are vectors).
(+1) [The Lasso Page](http://www-stat.stanford.edu/~tibs/lasso.html) also contains useful references.
Please supply more details, is this self-study?
@mbq; that is making a strong assumption that the observation is 0. I had been mulling this point and T-Burns is making the same assumption (an unobserved 0). I would prefer perhaps to pad with NA and pass in the `na.rm = TRUE` argument to `mean`. The answer won't be the same as what the OP requested, but it seems more useful. I'll edit my answer to include this.
thanks that was more insightful than my professor's been all year hahaha thank you so much for taking the time to help me!
@chl: although your answer is a little obvious, it IS still an answer, and you should make it so, so it can be accepted.
:Josh he OP was not in my opinion referring to testing hypothesis of model parameter constancy , in your case where or not an AR(3) has constant parameters over time . He O believe is interesting in detecting a heretofore unknown shift in the mean of the residuals.
Since you don't explicitly use label information, except for initial cluster centers, this is just traditional unsupervised clustering. Note that fully supervised clustering does not exist, that's classification.
I already linked that thread in my post! And if you really read my question you will see, that I DO NOT WANT TO use the bootstrap algorithm, but I am asking about the delta-method.
PS: I am starting to think that this wasn't your question...
But if you know that "there is a bomb" (yours) in the plane, which we may call event $A$, and you are willing to accept that the "existence of a second bomb" (event $B$) is independent of $A$, then $P(B\\mid A)=P(B)=1/1000$. Always condition on what you know. And yeah, I deserve a $-1$ for screwing a good joke.
Are your classes well balanced? I.e. the number of instances belonging to class 1 is almost similar to the number of instances of class 2. The reason I'm asking is that If you have a very unbalanced data set and your classifier classifies all (or most) instances as majority class you will still get good results which might or might not indicate overfitting, even with CV in case stratified sampling was used.
We're measuring something on web page views that can be in one of three states -- A, B & C. Let's say (case 1) there are 1 MIL views, and we sample 100K, and find that 20% were A, 30% were B, and 50% were C. Then for a different page (case 2), we have 1.5 MIL views, but can only sample 5K and get a different set of A/B/C percentages (as expected). I want to express confidence in those percentages in some form. This is for a non-stats audience, so we want to keep the language simple. Something like "we're 99% confident that our measurements are accurate in case 1 and 95% confident in case 2".
I've marked this as a possible duplicate (as well as a certain duplicate of another, now closed question).  The thing that might make it different is that you are now asking specifically about medians.  If this is a question about medians I think it is ok to stand; if it is a repeat of the more general question about confidence intervals it is a duplicate.  However, I can't think of any way it would be wrong to calculate confidence intervals for the medians other than because of the missing data problems discussed in the possible duplicate.
So you just to the 0.56 ignoring the constant + 1 there?
Any help would still be very appreciated!
(+1) Regarding your last paragraph: From a mathematical perspective it *does* work "perfectly" in the sense that an MLE will yield a perfect separating hyperplane. Whether your *numerical* algorithm behaves sensibly in that circumstance is a separate matter. Laplace smoothing is often used in such situations.
Exactly, $\\log(price_k)$ is the natural logarithm of the price of product $k$. I should actually have used the notation $\\log(price_n^k)$, because prices are supposed to vary across consumers (if some price has no variation across consumers in your database, you cannot include that price). So for each equation you use the price of all goods.
Could you provide a brief summary of the resources available on this page?
Thank you for the prompt and very useful comment! I will proceed with the Egger's regression method.
The events are not really independent -- does this change anything?
As far as a pure statistical answer goes, I don't think this makes sense.  If your response variable has *any* repeated values, then it must not really be Normally distributed (since the Normal distribution is continuous) ... if the response is a proportion, should you be fitting a binomial GLM instead?  (Or possibly a Beta regression?)
Because the distinction between correlation and lack of dependence is important, equating orthogonality with independence is not a good thing to do.
None of these methods is better "in general", otherwise nobody would be using the other one. You should make your question more concrete with an example of what you want to achieve.
Welcome to our site, Quartz!
It depends on how you identify "background." If it is to be automatically identified from parts of the same image that are believed to be in non-sample areas, then please see http://stats.stackexchange.com/questions/100484/background-subtraction-for-signal-and-error-analysis for a discussion.  If it is identified from a similar image taken with the sample absent, then a different answer might apply.
Observations with outliers in an IV tend to highly influence the parameter estimates of the model. In such a case, transformations might be an option.
@whuber Good point, thanks for pointing that out. I'm not sure whether I should correct that or delete this answer completely as the question has been edited to ask something else.
Unfortunately, that is true and that is also the reason for my post. Random slopes are essential for testing my hypotheses. I have already estimated the model in glmer (assuming discrete data) and it works like a charm. However, the Weibull model would be really my preferred choice. I had a look at Pinheiro/Bates (2000) and wonder if it is possible to estimate the model with nlme? However, I haven't yet found an example which would proof me right.
How many products, I wonder, need to be involved before a simple correlation matrix is insufficient?
+1, this is awesome. (I was going to do +6, but maybe the fact that the question is closed prevents that.) How did you make the top figure?
@Gong-Yi: nice, thanks for updating with the answer!
Okay yes that makes total sense and is similar to what I had in my head. Thanks so much.
How many levels do you have for each of your 2 IVs? In what sense are your data not Gaussian?
I am using ltm.
I don't understand: "All outcomes have the same probability of occuring so the probability of getting an outcome as extreme or more extreme than the observed outcome is unity." What is the ordering on the circle that makes an event more extreme?
What is the question exactly? You want (-0.921,0.389593) as a numeric vector?
In your updated version, are there typos?  For example, is $h$ a function of two variables as in $h(x_4,x_2)$ or one variable as in $h(x_2)$?  Is there a claim that $X_3$ and $X_4$ _are_ (conditionally) independent given the value of $X_2$, but yet $p(x_3,x_4\\mid x_2) \\neq p(x_3\\mid x_2)p(x_4\\mid x_2)$?
@user3378649 The problem here is that you are not putting any of this information of what you have tried, what data you have in your question. We can't help you if you are not *clear* with your question and only provide bits of information. And as a side comment, please note that this is a *community*, not Yahoo Answers. That means a certain level of civility, *contributing* to the community as well as asking questions and being more open to what you have done to solve your problem. (That's why your previous question was closed.) Nobody gets paid to be here to answer questions.
But did I understand it correctly that there has to be at least one granger causality flow in a bivariate cointegrated system?
Also, it sounds like the OP is not (quite) describing principal-components regression in his Method 2.
How about multiplying only $X$ by a constant $\\alpha$? And what happens if $\\alpha=0$ ?
You can also do `RSiteSearch("k-means")`
+1, neat trick. Judging by the OP's comment to another answer, I was going to suggest some sort of panel data model, but this is way better.
So why do people say you need to put in the base linear effect when including quadratics. When considering these reasons, why is it now okay not to do so. I am looking for an answer that takes into account arguments that we should include the base linear variable.
If both are mathematically the same shouldn't they have the same expectation and variance?
Although you ask the question differently and circumstances may be a little different, it concerns *identical* behavior by your software.  There's no need to have two threads open for discussing this: that's why we identify duplicates and create links between them (which is what "closing") does.
the link appears to be broken