I am working on a project which includes 5 groups ;10 rats in each, making 50 rats as total and I was wondering if It's right to run non-parametric tests on this sample size even if the data showed normal distribution
Hi Eman,
This depends on the particular test you want to use as each test tends to have its peculiar assumptions. For example, parametric tests such as t-test requires sample size in each group to be >=30; but one-way ANOVA requires the sample size to be either >=30 or, if less than 30, the combined sample is normally distributed.
The non-parametric alternatives to on-way ANOVA is Kruskal Wallis test while Mann-Whitney test is the alternative to independent t test.
For descriptive part, report Mean (SD) if the data is normally distributed, and Median (IQR) if the data is skewed.
Nonparametric tests were originally invented for small samples (in many cases the Central Limit Theorem comes into play for large samples), and they are valid even if the distributions are normal. The only problem is that parametric tests are usually more powerful than nonparametric tests (if the assumptions of normality and homoskedasticity hold), and the software of parametric tests are often more completely developed, for example post hoc tests (multiple comparisons) are ususally not avaliable for nonparametric tests. If you find, for example, that the 5 group means are significantly different, then you would like to do pairwise comparisons for each pair of means, which is more readily available if you do one-way ANOVA than if you do the Kuskal-Wallis test. And, by the way, homoskedasticity is also an underlying assumption of most nonparametric tests.
non-parametric have to be used becouse we only have data's parameters,but not a model. in this case all data could come from normal distribution but the matrix doesn't have a 5-variated normal distribution necessarly . so even size is big the limit central theorem is only applicable for data standarizations.
Non -parametric tests do not make assumption on the data distribution. Therefore yes, if you want you can use them also for normal distributed data too.
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