# Tag Info

Accepted

### Non-parametric test if two samples are drawn from the same distribution

The Kolmogorov-Smirnov test is the most common way to do this, but there are also some other options. The tests are based on the empirical cumulative distribution functions. The basic procedure is: ...
• 1,078
Accepted

### When should I use scipy.stats.wilcoxon instead of scipy.stats.ranksums?

Frank Wilcoxon's 1945 paper [1] described two tests -- for "Unpaired Experiments" and "Paired Comparisons" which have come to be called the (Wilcoxon) rank sum test and the (Wilcoxon) signed rank test ...
• 286k
Accepted

### If the difference of scores is normally distributed, the sample distributions don't matter in a paired t-test, right?

You are correct. A paired t-test is conducted on the differences of the paired scores. It doesn't look at the individual scores in any way. A paired t-test is precisely the same as a one-sample t-test ...
• 11.5k
Accepted

### Paired t-test with multiple observations per pair

Averaging the data will result in a loss information and statistical power, so it is best avoided. Since you have repeated measures for websites, you can account the differences between websites (or ...
• 63.8k

### Wilcoxon signed rank test – critical value for n>50

The Wilcoxon signed rank test has a null distribution that rapidly approaches a normal distribution. The tables tend to stop by n=50 because the normal approximation is excellent well before that ...
• 286k
Accepted

### Wilcoxon Signed Rank Symmetry Assumption

Although on the surface the two statements above may appear contradictory, they aren't. The Wilcoxon Signed Rank test does require that the paired differences come from a continuous symmetric ...
• 40.4k
Accepted

### Wilcoxon signed-rank test null hypothesis statement

This answer has been revised after being accepted, as I did not adequately appreciate Wilcoxon's critique of the sign test to extend the null hypothesis. I address the difference between the revised ...
• 30.3k

### Questions about Wilcoxon signed rank test

An excellent question. As @Glen_b implied, the signed rank test, unlike the Wilcoxon unpaired 2-sample test, is metric-dependent. A better test is the Kornbrot rank difference test discussed here. ...
• 95.6k

### Same p-value. Is it normal?

Wilcoxon signed-rank test just takes in account the signs of the differences of values of every pair of data, and it doesn't take in account how large is such a difference. Therefore, the only thing ...
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• 1,350
Accepted

### Why is the null hypothesis for Wilcoxon test not rejected if the sample size is 5?

I'll write "differences" when describing the observed values (as if it were a paired test), but for a one-sample test just read 'difference' as 'observation' or 'value'. The possible values ...
• 286k
Accepted

### What exactly does the “symmetric distribution” assumption of the Wilcoxon signed-rank test refer to?

What does a symmetric distribution here exactly refer A symmetric distribution has a probability density or mass distribution for which a reflection through a line leaves the distribution unchanged. ...

### what is the meaning of “One-sample test.”？The following is clearly a two-sample test for wilcox.test

I'm not entirely sure what led you to that conclusion. The $x$ and $y$ variables are supposed to represent scores for the same group tested multiple times (admittedly, the label should be something ...
• 15.8k

### Wilcoxon signed-rank test in R

Stumbled upon this and found it incredibly useful as well as the other CrossValidated post mentioned by @jdobres. Just to expand a little on the answer above which is correct but in hopes that it ...
• 206
Accepted

### What differentiates the wilcoxon test from t test regarding ordinal variables?

The short answer is that you can always use either test in place of the other--but typically they will produce different results. That demonstrates the issue is not one of applicability, but ...
• 328k
I'll give an outline of what's involved. Let's look at the original (no ties) case. Note that a specific rank either contributes $R_k$ or $-R_k$ to the sum (with sign chosen randomly under the null). ...