I have one sample with values of sugar intake pre and post intervention. I transformed the values for t test as the change from pre to post was negatively skewed but now I dont know how to report the results from t test? Can I just square back the mean and CI?
120436
I'm doing a linear regression with a transformed dependent variable. The following transformation was done so that the assumption of normality of residuals would hold. The untransformed dependant variable was negatively skewed, and the following transform made it close to normal:   $$Y=\sqrt{50-Y_{orig}}$$  where $Y_{orig}$ is the dependent variable on the original scale.   I think it makes sense to use some transformation on the $\beta$ coefficients to work our way back to the original scale. Using the following regression equation,   $$Y=\sqrt{50-Y_{orig}}=\alpha+\beta \cdot X$$  and by fixing $X=0$, we have   $$\alpha=\sqrt{50-Y_{orig}}=\sqrt{50-\alpha_{orig}}$$  And finally,  $$\alpha_{orig}=50-\alpha^2$$  Using the same logic, I found  $$\beta_{orig}=\alpha\space(\alpha-2\beta)+\beta^2+\alpha_{orig}-50$$  Now things work very well for a model with 1 or 2 predictors; the back-transformed coefficients resemble the original ones, only now I can trust the standard errors. The problem comes when including an interaction term, such as  $$Y=\alpha+X_1\beta_{X_1}+X_2\beta_{X_2}+X_1X_2\beta_{X_1X_2}$$  Then the back-transformation for the $\beta$s are not so close to the ones from the original scale, and I'm not sure why that happens. I'm also unsure if the formula found for back-transforming a beta coefficient is usable as is for the 3rd $\beta$ (for the interaction term). Before going into crazy algebra, I thought I'd ask for advice...
79869
I have the mean and standard deviation of a large sample (30k obs) and the mean and std of a subsample (2k obs). The means are percentage figures (i.e. between 0 and 100% and hence not a normal variate). Also the means are not independent, since one is based on a subsample from the other.    Despite seemingly a harmless question, I could not find an appropriate testing procedure. Any ideas on how to test whether the mean of the subsample is different to the mean of the entire sample are much appreciated.
88592
As an example I use Pinheiro, J. C. &amp; Bates, D. M. 2000. Mixed-effects models in S and S-PLUS. Springer, New York. page 225. Rats whose body mass has been measured are fed by 3 different diets over time.   Response: Body mass, fixed effects Time*Diet, random effect ~Time|Rat. The main question with this test was if the interaction term is significant (i.e. difference in growth rate between diets). However, my question is could I also look at the p-values of the main effects to say that body mass increased significantly with time for Diet1 (which is the "dummy variable")?   From Pinheiro, J. C. &amp; Bates, D. M. (2000)   Fixed effects: weight ~Time * Diet                   Value        St.error         DF        t-value         p-value   Intercept       251.60         13.068         157         19.254          &lt;.0001  Time              0.36          0.088          13          4.084          0.0001  Diet2           200.78         22.657          13          8.862          &lt;.0001  Diet3           252.17         22.662         157         11.127          &lt;.0001  Time*Diet2        0.60          0.155         157          3.871          0.0002  Time*Diet3        0.30          0.156         157          1.893          0.0602    As stated by Pinheiro &amp; Bates, the growth rate of diet 2 (TimeDiet2) differs significantly from diet 1. Although could I state like this for the effect of time on Diet1: f(x) = 251.60 (+/-13.068) + 0.36 x (+/- 0.088), t = 4.084, p = 0.0001? I have seen that people have claimed that it is wrong to interpret p-values for the main effects when the interaction is significant. And is it more proper to split the data and run the test  (weight ~Time) for each diet separately, when only looking at the effect of  time on body mass?
43225
I assume it is OK to mix different data transformations in the same analysis. I've had to transform some variables to squared and some to cubed in order to meet normal distribution requirements. I'm assuming that it's OK to then use the transformed variables together for regression analysis?
89592
I have run a mixed effects model with a ln transformed continuous response (seconds) and found a significant effect of the categorical predictor (treatment/control, the only fixed effect in the model).   I want to: 1- Report an effect size (cohen's d, etc) 2- Describe the magnitude of the effect in terms of mean number of seconds that the treated individuals differed from the control individuals, after accounting for the random effects.  I am not sure how to achieve either of these goals. Thank you very much in advance for any advice you can offer.  My code and results are below.  mod1 = lmer(data=data, ln_duration ~ treatment + (1 | id/date/size) +   (1 | visitor), na.action=na.exclude)  Linear mixed model fit by REML  t-tests use  Satterthwaite approximations to degrees of freedom ['lmerMod'] Formula: ln_duration ~ treatment + (1 | id/date/size) +   (1 | visitor)  Data: data  REML criterion at convergence: 248  Scaled residuals:    Min      1Q  Median      3Q     Max  -2.7323 -0.4963 -0.0206  0.5600  3.8502   Random effects:  Groups                             Name        Variance Std.Dev.  display_size:(date:id)             (Intercept) 0.00000  0.0000    date:id                            (Intercept) 0.00000  0.0000    visitor                            (Intercept) 0.03574  0.1891    id                                 (Intercept) 0.01164  0.1079    Residual                                       0.20001  0.4472   Number of obs: 170, groups:   size:(date:id), 130; date:id, 128; visitor, 118; id, 58  Fixed effects:                       Estimate     Std. Error  df t value  Pr(&gt;|t|)     (Intercept)               -0.17012    0.06334  41.63000   -2.686 0.010348 *              treatmenttreatment  0.31172    0.08135  40.27000    3.832 0.000436 *** --- Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1  Correlation of Fixed Effects:             (Intr)     trtmnt -0.729
107352
I have one group of respondents which answer on a scale of 1-5 once before and once after an experiment. I want to see if the experiment made a difference to their responses.  I was told not to use a t-test because of the Likert scale (ordinal data does not seem to fit a t-test) and because my data are not nearly normally distributed (answers to the questions lean heavily to the 1 of the scale (which is not a mistake in the design)).  I am not sure if the Wilcoxon signed-rank test works, because it seems to be designed for differences in groups (as in "Do men respond differently from women?").  Any suggestions on what could actually be used here?  (The answer  refers to a "special paired t-test", but does not explain which one)
50402
I've got a study which is kinda messed up by the design...Turns out I ended up with about 50 patients of which 80% have the outcome and 20% don't (binary outcome).  I've been turning in my bed for the last month trying to figure out what to do with this. The only real answer is "don't" but I have to deliver something in the next days as it's part of a master's thesis.  I have about 10 predictors of interest for the outcome (various variable types) and the research question is whether any of these predictors can predict the outcome. Some already have an established correlation in the literature while some are original hypothesis. Several are significant with a univariate logistic regression, but it doesn't look good in any other way than the actual p-value.  Now obviously I'm not going to be able to answer this research question sufficiently but if you were in my shoes, what sort of statistical analysis would you perform to relay to your supervisors?  EDIT: Link to my (anonymized) data (CSV):
121019
I have $k$ pairs of samples from different distributions. For each pair of samples I want to check if the samples are taken from a normal distribution with the same mean and variance. I assume the normal distributions for each pair is different and independent of other pairs. I do not know the mean and variance of any of the distributions.  I am doing a two sample t-test for each of the pairs. I want to combine the $k$ resulting p-values.   I could use Fisher's method but I am wondering about the distribution of the average t-value. If these were z-values rather than t-values I would use Stouffer's z-test. I could also approximate the t-distribution with a z-distribution and than use Stouffer's z-test, but I am not sure if that is a good approximation.  Is there a test like Stouffer's z-test for t-values?  Is there a better way to combine the t-values?
37317
What are the most accepted ways to visualize the results of an independent two sample t-test? Is a numeric table more often used or some sort of plot? The goal is for a casual observer to look at the figure and immediately see that they are probably from two different populations.
24143
An investigator wishes to produce a combined analysis of several datasets.  In some datasets there are paired observations for treatment A and B.  In others there are unpaired A and/or B data.  I am looking for a reference for an adaptation of the t-test, or for a likelihood ratio test, for such partially paired data.  I am willing to (for now) to assume normality with equal variance and that the population means for A are the same for each study (and likewise for B).
111915
What is "Deviance," how is it calculated, and what are its uses in different fields in statistics?  In particular, I'm personally interested in its uses in CART (and its implementation in rpart in R).   I'm asking this since the  seems somewhat lacking and your insights will be most welcomed.
53263
I want to do an AB test to check if one version does significantly increase revenue. Generically speaking I want to test whether the central tendency (mean) of 2 groups are different from each other on the basis of (unpaired) samples of the 2 groups.   My understanding is, that I could use the following approaches:   Student-t test, if the variance of both groups are the same and both are normally distributed Welch-t test (unequal variance t-test), if the variance of both groups might not be the same but both are still normally distributed Mann–Whitney U test (Wilcoxon rank-sum test), if I cannot make any assumptions about the distribution of both groups   But now I read () that I can always use the Welch-t test. The article argues that it is dangerous to make the assumption of equal variance and additionally that     the unequal variance t-test performs as well as, or better than, the Student's t-test in terms of control of both Type I and Type II error rates whenever the underlying distributions are normal.   And if the groups are not normally distributed, than I can just rank the data beforehand:     Thus, Zimmerman and Zumbo (1993) suggest that the unequal variance t-test can effectively replace the Mann–Whitney U test if the data are first ranked before the test is applied.    So the end conclusion is:     If you want to compare the central tendency of 2 populations based on samples of unrelated data, then the unequal variance t-test should always be used in preference to the Student's t-test or Mann–Whitney U test. To use this test, first examine the distributions of the 2 samples graphically. If there is evidence of nonnormality in either or both distributions, then rank the data. Take the ranked or unranked data and perform an unequal variance t-test.   So my question is:  Do you see any drawbacks in always using the Welch-t test instead of the Student-t test or Mann-Whitney test?
87369
It is a general and maybe basic question, but it will help me to avoid a mistake. To test the dependence of continuous variable on nominal with parametric test (t-test, ANOVA), "the data has to be normally distributed" (distribution have to be not much violated from normal).   But I don't clearly understand: I have to test the normality of the continuous data together (whole sample) or the normality of data in every single group?   And if my groups have small sizes (n=4-6), and therefore I fail to reject null, does this indicate a permission to use parametric methods?  Can anyone provide me a link to some good examples of statistical (biomedical) hypothesis testing with R (google did not helped)?
69265
When testing the difference between 2 proportions why do we use a z-test rather than a t-test?    Further, is there a simple way to conduct an omnibus test for significant differences between more than 2 proportions (in the form of percentages). Is there an equivalent to a one-way ANOVA for this?  I imagine that you could use logistic regression (assuming you have the original data for the proportions in the form of 0s and 1s) Are there other options?
16905
I have a fairly simple question regarding the interpretation of the F-test in Microsoft Excel.  Let't say these are the results of my F-test:    I am now wondering how to interpret it in order to choose the correct t-test (assuming equal or unequal variances) for my data-set.  I have found guides telling me if F critical > F, then use unequal variances. However, some of the guides tell you to use only the p value, so I am unsure which parameters to look at when interpreting the results.
50218
My paper is accepted in one of the Taylor and Francis journals and Today I figured out that I made a mistake in one row of one of my tables ( the minimum of one of variables in statistic analysis table is 0 in the paper but the actual value is 1). In fact, it does not affect the other parts of paper and the verification part.   Editor will provide the proofread of my paper in a week.  My question is, Will the editor give me a chance to edit the paper again? or he will change the grammatical problems his self?  And if I ask the editor to correct that row of paper, will he give the paper to reviewers again? I am worried that if I ask him to correct that mistake, he ask the reviewers to review my paper again. I need my paper to be published soon.
87477
Is it possible for one-way (with $N&gt;2$ groups, or "levels") ANOVA to report a significant difference when none of the $N(N-1)/2$ pairwise t-tests does?   In  @whuber wrote:      It is well known that a global ANOVA F test can detect a difference of means even in cases where no individual [unadjusted pairwise] t-test of any of the pairs of means will yield a significant result.   so apparently it is possible, but I do not understand how. When does it happen and what the intuition behind such a case would be? Maybe somebody can provide a simple toy example of such a situation?  Some further remarks:   The opposite is clearly possible: overall ANOVA can be non-significant while some of the pairwise t-tests erroneously report significant differences (i.e. those would be false positives). My question is about standard, non-adjusted for multiple comparisons t-tests. If adjusted tests are used (like e.g. Tukey's HSD procedure), then it is possible that none of them turns out to be significant even though the overall ANOVA is. This is covered here in several questions, e.g.  and . Update. My question originally referred to the usual two-sample pairwise t-tests. However, as @whuber pointed out in the comments, in the ANOVA context, t-tests are usually understood as post hoc contrasts using the ANOVA estimate of the within-group variance, pooled across all groups (which is not what happens in a two-sample t-test). So there are actually two different versions of my question, and the answer to both of them turns out to be positive. See below.