Sure. Some people don't understand statistics and get wrong answers. That is one reason some results are not reproducible. Best Wishes, David Booth

Dear Osama

The application of the same treatment on many animals (experimental units) will give you many different responses, these variation in the response came from the differences genotypes ( each animal has unique genotype) and genotype- environment interaction besides mistakes in the application of the treatment on the different animals, in this case the mean ( central tendency measurement) will be not enough to describe the data set and we also need variation measurement ( dispersive measurement) like standard error (S.E.) or standard deviation beside the mean to describe the data set.

For example when you have two data sets : 1 , 4 , 55 ; and 18 , 20 , 22 the mean for each group will be same = 20 but we notice that variation among the observations of each group obviously different , so the mean only will be not enough to describe the data set .

Good Luck

Choosing any statistical tool and test of hypothesis is based on the research question for which we want answer. People who blindly apply theses tools of analysis to their problem, have no knowledge of reason behind its application. For example, if you want to test for difference of means between two independent samples, and your population variance is unknown and sample size is small (below 30), in that case, you should apply two sample t-test for difference of means.

Similarly, other tests have also fulfill some conditions before applications.

Ujjaval Srivastava

Khalid Hassan

Thank you for the answers

But with small sample size n=5 we should present the data with median and IQR and use non-parametric test not mean

what is your opinion

Dear Osama

The below information from the link:

https://www.healthknowledge.org.uk/public-health-textbook/research-methods/1b-statistical-methods/parametric-nonparametric-tests

which depends on the following reference:

Campbell MJ and Swinscow TDV. Statistics at Square One 11th ed. Wiley-Blackwell: BMJ Books 2009.

"Do non-parametric tests compare medians?

It is a commonly held belief that a Mann-Whitney U test is in fact a test for differences in medians. However, two groups could have the same median and yet have a significant Mann-Whitney U test. Consider the following data for two groups, each with 100 observations. Group 1: 98 (0), 1, 2; Group 2: 51 (0), 1, 48 (2). The median in both cases is 0, but from the Mann-Whitney test P

Selecting what test statistics to employ depend on the hypothesis you are testing. However, the type of statistical analysis (parametric or non-parametric) to employ should be based on the sample size and data distribution. Large sample and normality distribution - employ parametric statistics, small sample and non-normal data - employ the non-parametric statistics.

The last responses are oversimplifications because they ignore the research question. In some cases they are correct but in others they are not. That is why it takes years to get a PhD in Statistics and that still leaves plenty of research available. Please remember that tests on means are not all we do. Best, David Booth

Dear Osama, I agree to your opinion that you should go for non-parametric test for n=5, and if your data looks like skewed, median should be prefer over mean as a measure of central tendency.

For more information, you may refer to:

http://blog.minitab.com/blog/adventures-in-statistics-2/choosing-between-a-nonparametric-test-and-a-parametric-test