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I am a very young stats learner, and I need help understanding the justification of a test choice. I have a sample of 39 participants (20 females and 19 males) been measured on task performance, and I wanted to run an independent samples t-test, but one of my groups seems to have a skewed distribution with two outliers. I am not sure if I should run a non-parametric test instead. I will appreciate any help.

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    $\begingroup$ The bins in your first histogram are probably too narrow. If you make them the same for both graphs you might be less concerned about 'outliers'. $\endgroup$
    – Michael Lew
    Dec 7, 2021 at 20:18
  • $\begingroup$ Hm. I'm not sure I understand your point. My concern is around normality and outliers. Q-Q plots, box plot, z score, skewness indicate the skewed distribution and my potential outliers are over 10 per cent of the group so I can't just remove them. Am I wrong somewhere? $\endgroup$
    – marth
    Dec 8, 2021 at 8:12
  • $\begingroup$ There is too often a tendency to think that extreme data points are somehow erroneous or problematical. Often they contain useful information. What makes the software think that the points are 'outliers', and what do you interpret the word 'outlier' to represent. $\endgroup$
    – Michael Lew
    Dec 8, 2021 at 20:26
  • $\begingroup$ The histogram for males uses a much smaller bin width than that for females and it is, at leat arguably, too small given the counts of less than 5. If you use a bigger bin size then the males histogram might look much more similar to the females. $\endgroup$
    – Michael Lew
    Dec 8, 2021 at 20:29
  • $\begingroup$ A t-test does not much care about 'normality' so you could use it if you like. You could also use a non-parametric test if you hold concerns about the parametric test's assumptions holding well enough. If you want to know about the 'outliers' then you need a new set of data. $\endgroup$
    – Michael Lew
    Dec 8, 2021 at 20:32

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It seems to me that the main difficulty with a pooled t test on these data is that the variances differ.

The Q-Q plots do not look bad and (if I read your ourput correctly) the S-W test doesn't reject at 5% level. It is always difficult to judge normality with such small samples.

Suggest using a Welch t test, which does not assume equal variances, instead of a pooled t test.

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  • $\begingroup$ Sorry. I should be more specific when adding my first post. I have to use SPSS and I have a choice between Independent Sample T-test or the Mann-Whitney U test. $\endgroup$
    – marth
    Dec 8, 2021 at 8:08
  • $\begingroup$ I would be surprised if SPSS does not do the Welch t tests. Than Mann-Whitney U test uses a different test statistic than the Wilcoxon Rank Sum test, but the two tests have been shown to be equivalent. // Yes, you should be specific if you want only answers using a particular statistical program, but if you will be doing very much statistical analysis you will find it a heavy disadvantage to use only SPSS (or any other single software). You need to focus on which tests are appropriate in each application and on their assumptions and properties. $\endgroup$
    – BruceET
    Dec 8, 2021 at 14:17
  • $\begingroup$ After you have sample sizes, means, and variances, it is not beyond reach to use a hand calculator to do a Welch t test. $\endgroup$
    – BruceET
    Dec 8, 2021 at 14:21

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