Dera Yara M.

Both are non-parametric test and easy to interpret if you have the calculated result page. you can find support on the data interpretation online on the pages of the software developers which you using for the analysis of the data. you can see the support page of MINITAB, the link is:

https://support.minitab.com/en-us/minitab-express/1/help-and-how-to/modeling-statistics/anova/how-to/kruskal-wallis-test/interpret-the-results/key-results/

I am trying to give an outlook on the result interpretation. as well some attached files which helps you better to do the discussion with the analysed data.

Because the samples are not independent, therefore the Mann-Whitney U test cannot be used. Instead, the Wilcoxon signed-rank test is used, also called the Wilcoxon T-test, named for Frank Wilcoxon. It is the equivalent of the paired Student T-test, but for ranked data instead of real-valued data with a Gaussian distribution. "The Wilcoxon signed ranks test is a nonparametric statistical procedure for comparing two samples that are paired, or related. The parametric equivalent to the Wilcoxon signed ranks test goes by names such as the Student’s t-test, t-test for matched pairs, t-test for paired samples, or t-test for dependent samples" { see the book: Nonparametric Statistics for Non-Statisticians: A Step-by-Step Approach by Gregory W. Corder & Dale I. Foreman}.

The default assumption for the test, the null hypothesis, is that the two samples have the same distribution.

Fail to Reject H0: Sample distributions are equal.

Reject H0: Sample distributions are not equal

When working with significance tests, such as Mann-Whitney U and the Wilcoxon signed-rank tests, comparisons between data samples must be performed pair-wise. This can be inefficient if you have many data samples and you are only interested in whether two or more samples have a different distribution.

The Kruskal-Wallis test is a nonparametric version of the one-way analysis of variance test or ANOVA for short. It is named for the developers of the method, William Kruskal and Wilson Wallis. This test can be used to determine whether more than two independent samples have a different distribution. It can be thought of as the generalization of the Mann-Whitney U test.

The default assumption or the null hypothesis is that all data samples were drawn from the same distribution. Specifically, the population medians of all groups are equal. A rejection of the null hypothesis indicates that there is enough evidence to suggest that one or more samples dominate another sample, but the test does not indicate which samples or by how much.

" When the Kruskal-Wallis H-test leads to significant results, then at least one of the samples is different from the other samples. However, the test does not identify where the difference(s) occur. Moreover, it does not identify how many differences occur. To identify the particular differences between sample pairs, a researcher might use sample contrasts, or post hoc tests, to analyze the specific sample pairs for significant difference(s). The Mann-Whitney U-test is a useful method for performing sample contrasts between individual sample sets " { see the book: Nonparametric Statistics for Non-Statisticians: A Step-by-Step Approach by Gregory W. Corder & Dale I. Foreman}.

• Fail to Reject H0: All sample distributions are equal.
• Reject H0: One or more sample distributions are not equal.

Each data sample must be independent, have 5 or more observations, and the data samples can differ in size.

EXAMPLE:

The Wilcoxon signed-rank test

The function takes the two samples as arguments and returns the calculated statistic and p-value.

The complete example is below, demonstrating the calculation of the Wilcoxon signed-rank test on the test problem. The two samples are technically not paired, but we can pretend they are for the sake of demonstrating the calculation of this significance test.

Running the example calculates and prints the statistic and prints the result.

The p-value is interpreted strongly suggesting that the samples are drawn from different distributions.

Statistics=1886.000, p=0.028

Different distribution (reject H0)

The Kruskal-Wallis H-test

It takes two or more data samples as arguments and returns the test statistic and p-value as a result.

( calculates the test and prints the results. here the final result is discussed on a hypothetical data)

The p-value is interpreted, correctly rejecting the null hypothesis that all samples have the same distribution.

Statistics=6.051, p=0.049

Different distributions (reject H0)

Hope the attached files will be helpful and the last attached file is of questions to check and practice. you may also find a paper on non-parametric tests on the researchgate the link for that webpage is:

Research Non parametric Tests

Happy researching...

Dear Yara M..

In addition to the rich documentation provided by the colleague who pressed me, i suggest you to see links and attached file on topic.

http://www.biostathandbook.com/kruskalwallis.html

http://sphweb.bumc.bu.edu/otlt/MPH-Modules/BS/BS704_Nonparametric/BS704_Nonparametric_print.html

https://www.nki.nl/media/837516/m343.pdf

Best regards

Following

Hello Yara,

I would like to know if you could find a satisfactory answer to your question and how you finally chose to discuss your results.

Regards!