24 questions linked to/from T-test for non normal when N>50?
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### T-test or Mann-Whitney U test [duplicate]

Given the central limit theorem, can you always use a t-test to test a difference between two groups even if the data are not normally distributed but the sample size is large enough? Stated in ...
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### Is the t-test really robust to shape of distribution? [duplicate]

Can I use the t-test to compare means between groups (N=300) if data is not normally distributed?
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### Is normality testing 'essentially useless'?

A former colleague once argued to me as follows: We usually apply normality tests to the results of processes that, under the null, generate random variables that are only asymptotically or ...
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### How to choose between t-test or non-parametric test e.g. Wilcoxon in small samples

Certain hypotheses can be tested using Student's t-test (maybe using Welch's correction for unequal variances in the two-sample case), or by a non-parametric test like the Wilcoxon paired signed rank ...
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### Why does basic hypothesis testing focus on the mean and not on the median?

In basic under-grad statistics courses, students are (usually?) taught hypothesis testing for the mean of a population. Why is it that the focus is on the mean and not on the median? My guess is that ...
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### What is the difference between finite and infinite variance

What is the difference between finite and infinite variance ? My stats knowledge is rather basic; Wikipedia / Google wasn't much help here.
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### Robust t-test for mean

I am trying to test the null $E[X] = 0$, against the local alternative $E[X] > 0$, for a random variable $X$, subject to mild to medium skew and kurtosis of the random variable. Following ...
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### When does the amount of skew or prevalence of outliers make the median preferable to the mean?

I know that "deviations in the data are devil", and when the distribution is highly skewed, it is better to consider median as average rather than mean, but how to decide these hard-limits. For ...
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### Have the reports of the death of the t-test been greatly exaggerated?

Reading through CV all-time classics I came across a statement that I would like to clarify. This is the post and my question refers to the closing remarks: "I have to note that all of the knowledge I ...
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### 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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### Kolmogorov Smirnov conflicts with visual data

I recorded the length of 197 nursing care episodes. My normalised data $(x-\mu)/\sigma$ looks like this: Kolmogorov-Smirnov gives me a p-value of 0.14. Can't be right surely?! Am I misinterpreting my ...
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### Is the inference from a parametric test valid when the population distribution is not normal?

This question arose from reading this post: T-test for non normal when N>50? In the response to this post, the author outlines really well that the assumption of normality with regard to the t-...
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### Distribution normality check

I can not solve the problem from my homework. We conducted two experiments. In the first, there were 400 patients, and in the second, 250. In these experiments, the effects of various drugs ...