36k views

When to use the Wilcoxon rank-sum test instead of the unpaired t-test?

This is a followup question to what Frank Harrell wrote here: In my experience the required sample size for the t distribution to be accurate is often larger than the sample size at hand. The ...
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5k views

Why is the asymptotic relative efficiency of the Wilcoxon test $3/\pi$ compared to Student's t-test for normally distributed data?

It is well-known that the asymptotic relative efficiency (ARE) of the Wilcoxon signed rank test is $\frac{3}{\pi} \approx 0.955$ compared to Student's t-test, if the data are drawn from a normally ...
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8k views

Is there any statistical test that is parametric and non-parametric?

Is there any statistical test that is parametric and non-parametric? This question was asked by an interview panel. Is it valid question?
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24k views

How can you test homogeneity of variance of two groups with different sample sizes?

I have two groups of data that have different sample sizes and in order to be able to analyze both sets they must have the same variance. I was told I should use Bartlett's to test the homogeneity of ...
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16k views

Bartlett's test vs Levene's test

I am currently trying to address violations to ANOVA assumptions. I have used Shapiro-Wilk to test normality, and have dabbled with both Levene's test and Bartlett's test of variance equality. I have ...
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28k views

How to choose between sign test and Wilcoxon signed-rank test?

I am trying to pick one from these two tests to analyze paired data. Does anyone know any rules of thumb about which one to pick in general?
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34k views

Normality, and when to use t-test vs. Mann-Whitney U-test?

I am looking for a few rules of thumb of when to determine that my data is 'normal enough' to use a t-test vs. a Mann-Whitney U-test. From what I have read, most real world data sets are non-normal, ...
5k views

Both t-test and F-test are significant, do I report both?

I undertook a large study (N about 200 in both control and treatment) in which one of the user ratings is significantly different (p < 0.0001). When I ran the unpaired t-test, the F-test also ...
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5k views

Relative efficiency of Wilcoxon signed rank in small samples

I have seen in published literature (and posted on here) that the asymptotic relative efficiency of the Wilcoxon signed rank test is at least 0.864 when compared to the t test. I have also heard that ...
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1k views

importance of CLT in t-test and z-test

I was going through the assumptions of z-test and t-test, all most all of the references mention that the data should be normally distributed. There is no mention of estimator's distribution. If the ...
21k views

Comparing z-scores from different data sets

Is it possible to use z-score as a number to compare two different data sets (none of them with normal distribution) and identify which one has an average z-score higher than another? Thanks!
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1k views

Does testing for assumptions affect type I error?

I just performed simple simulation. Made two "populations" with different means and the same variance. Since I prepared them I know that they: are normal, differs in location and both have the same ...
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7k views

t test with log transformation

One of my variables to be compared in a t-test is normally distributed, while the other is non-normally distributed. What test should I use? I thought I should do a reflect log10 transformation on the ...
6k views

Q-Q plot and sample size

To study the quantile-quantile plot, I used the following codes (modified from here). The first group of pictures is derived from 100 data points while the second from 10000. ...
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