Seyyed Amir Yasin Ahmadi ,

I fully agree that researchers can have different viewpoints. But these should be about things that cannot be decided based on evidence. It maybe your viewpoint here that "nonparametric tests are better", but this advice is not at all helpful for Menna who very obviousely did a screening-tye of experiments (ok, we still may have different viepoints here, but Menna can easily clarify). In this experiment, where at least 10 (multiple-to-one) or 45 (all-pairwise) tests are to be performed to identify the groups with "significant" differences, the lowest p-value a nonparametric test with n=4 per group can give for a single test is p= 0.02857. Thus, there is no chance to hold any reasonable FWER or FDR for a family of 10 or even 45 tests. You don't even need to perform these tests because it's clear "by design" that it will be impossible to reject any of the tested hypotheses at a somewhat acceptable level of significance.

PS: with n=7 per group it would be possible to reject at least one out of 45 hypotheses with a nonparametric test while keeping a 5% FWER.

Multiple comparison tests reduce your power due to correction of significance level.

Regarding this rationale Mann Whitney test has more power than Kruskal Wallis.

Another way is to change your variables as binary (0 and 1) and do 2 by 2 Fisher exact test.

When you conducted your power analysis, what did you use? Are in interested in all 10 choose 2 (45) paired comparisons, or just that there is variation by group?

Agree with Seyyed Amir sir

Dr Daniel Wright is right

Maybe you have enough power.

However nonparametric tests are better.

Another suggestion is to consider the mean of your control group as the base (H0) and then do a one sample test for each group (one sample t test or sign test).

Hello Menna Shehata Mahmoud. Some respondents have been advocating for rank-based tests. Before you follow their advice, take a look at the article by Bland & Altman (2009), and pay attention to the final two paragraphs, which I quote below.

--- start of excerpt ---

We have often come across the idea that we should not use t distribution methods for small samples but should instead use rank based methods. The statement is sometimes that we should not use t methods at all for samples of fewer than six observations.4 But, as we noted, rank based methods cannot produce anything useful for such small samples.

The aversion to parametric methods for small samples may arise from the inability to assess the distribution shape when there are so few observations. How can we tell whether data follow a normal distribution if we have only a few observations? The answer is that we have not only the data to be analysed, but usually also experience of other sets of measurements of the same thing. In addition, general experience tells us that body size measurements are usually approximately normal, as are the logarithms of many blood concentrations and the square roots of counts.

--- end of excerpt ---

Source: https://www.bmj.com/content/338/bmj.a3166.long

HTH.

Dear Bruce Weaver

Thank you for giving your valuable time like always

Some researchers have different viewpoint.

Their rationale: Statistical tests are done on samples (not population). Therefore, mean distribution is more important than individual data distribution. According to the central tendency, mean distribution is always normal in spite of normality rejection of individual data distribution at n >=30. Therefore, parametric tests can be performed directly with closed eyes (without normality test).

Some of them generalize the above rationale to lower sample sizes. They believe that in the real world it should be normal. Hence, forced use of parametric tests is a kind of researcher-based correction to overcome the limitation of low sample size.

I have seen many animal and cell culture studies with sample size 3-5 that they used t test, because they need confidence interval anyway.

Best regards and thanks again!

Seyyed Amir Yasin Ahmadi ,

I fully agree that researchers can have different viewpoints. But these should be about things that cannot be decided based on evidence. It maybe your viewpoint here that "nonparametric tests are better", but this advice is not at all helpful for Menna who very obviousely did a screening-tye of experiments (ok, we still may have different viepoints here, but Menna can easily clarify). In this experiment, where at least 10 (multiple-to-one) or 45 (all-pairwise) tests are to be performed to identify the groups with "significant" differences, the lowest p-value a nonparametric test with n=4 per group can give for a single test is p= 0.02857. Thus, there is no chance to hold any reasonable FWER or FDR for a family of 10 or even 45 tests. You don't even need to perform these tests because it's clear "by design" that it will be impossible to reject any of the tested hypotheses at a somewhat acceptable level of significance.

PS: with n=7 per group it would be possible to reject at least one out of 45 hypotheses with a nonparametric test while keeping a 5% FWER.

I'm not an expert on the topic but will offer what I have recently learned, when I was in a similar situation and spoke to my statistics professor. You are testing 10 groups, suggesting you need to use ANOVA. You are also testing the groups vs. time if I understood correctly. This then suggest the need for a 2-Way ANOVA. That allows you to test different parameters (such as time, age, sex) vs. your multiple groups/comparisons that you are doing. You can test for normalcy in a small n value using the Shapiro-Wilks test, even though it is not the most recommended test. Using non-parametric test, which are less powerful, are also an option to check the results of the the 2 way ANOVA, to test the same groups where you find statistical significance and see what a nonparametric test tells you. Keeping in mind that the p-value may be higher because it is a less powerful test.

Hello Alia Mallah, and welcome to the discussion. When Menna Shehata Mahmoud said "I need a statistical test for compare this multiple groups and another test to compare two groups per time", I understood "two groups per time" to mean pair-wise comparisons of group means, not that Time was another factor in the design.

Also, I believe that testing for normality prior to doing t-tests, ANOVA, etc. is ill-advised. My reasons for thinking that are summarized in a short conference presentation I gave several years ago. You can see a PDF of the slides here:

https://www.researchgate.net/publication/299497976_Silly_or_Pointless_Things_People_Do_When_Analyzing_Data_1_Testing_for_Normality_as_a_Precursor_to_a_t-test

If your professor advises testing for normality before doing t-tests or ANOVA, you might consider (diplomatically) sharing my slides with him or her, and then having a discussion about them. ;-)

Cheers,

Bruce

Ehm, if this is a time series experiment, one might consider fitting a regression model. This could be a GLM, so one can adress non-normal distributions. One could then most likely test sensible hypotheses, e.g. about differences in half-times or plateau values ;)

For regression, I think that the groups of study can be considered as a factor variable (the control group as base).

Menna Shehata Mahmoud , which software do you want to use? What is your outcome variable? Could you please give us a list of your variables.

Seyyed Amir Yasin Ahmadi "According to the central tendency, mean distribution is always normal in spite of normality rejection of individual data distribution at n >=30. Therefore, parametric tests can be performed directly with closed eyes"

I would not agree with this statement (and I am not sure if you are citing other scientists or if this is your belief). Simulation studies have shown that the sampling distribution does not always magically become normal with n>=30. Sometimes it needs much larger samples. And it is not necessary to automatically switch to non-parametric procedures, there are plenty of robust methods, if you want to compare central tendencies, which have much higher power in cases of violation of normality (or other assumptions), but please have a look at the books and other publications by Rand R. Wilcox on this topic.

Dr. Rainer Duesing

You are right. I mean distribution of mean in repeated sampling rather than distribution of individual amounts (as you have also mentioned).

The problem is that KS test is based on individual amounts (if I say right! please tell me). Is there any normality test based on mean distribution?