Spearman's rho and Kendall's W measure something related, but don't measure the same thing, so I wouldn't mix the two like that in the same analysis. It's best to decide which one represents the kind of similarity you wish to report, and stick with that.

Kendall's W itself isn't usually a test of significance. I know some software report a p-value with it. This is usually equivalent to Friedman's test, with or without a correction for ties. If you are using Friedman's test, I think you are better off reporting it as Friedman's test, and reporting the Kendall W statistic along with it as a measure of the degree of concordance.

It's not clear what are you saying about the paired comparisons. I would urge you to use something like a post-hoc test for Friedman's test (maybe the one suggested by Conover), and not just use paired tests.

You should also be aware that Friedman, Jonckheere-Terpstra, and Kruskal Wallis all test different things. You should be choosing the one that matches what hypothesis you are interested in testing.

A couple of helpful discussions:

https://www.researchgate.net/post/How_can_we_measure_similarities_between_two_sets_of_scores_given_by_two_evaluators

https://www.researchgate.net/post/When_to_use_Kendalls_Tau_correlation_against_Kendalls_W_concordance_A_bit_confused_on_both_of_their_distinctiveness_on_usage_and_requirement

Pay attention to one important point. You want to get a relationship between variables or compare their sizes. If you are looking for a measure of correlation, yes, the tests and correlation coefficients (of course, each in the right place) are used. But if you're looking for a comparison between variable should pay attention to the type of data, such as the Kruskal-Wallis nonparametric test parameters or use.

Anyway, everything in the statistics is right in its place.

Hello Khan

1. This assumptions of the sample size, both variables should be normally distributed (normally distributed variables have a bell-shaped curve). Other assumptions include linearity and homoscedasticity. Linearity assumes a straight line relationship between each of the two variables and homoscedasticity assumes that data is equally distributed about the regression line have to be satisfied for all measures of correlation coefficients and hypotheses testing.

2. The Correlation is used to test relationships between quantitative variables or categorical variables. In other words, it’s a measure of how things are related. The study of how variables are correlated is called correlation analysis.

3. A correlation coefficient gives a numerical summary of the degree of association between two variables .

4. Types:

Pearson r correlation: Pearson r correlation is the most widely used correlation statistic to measure the degree of the relationship between linearly related variables. For example, in the stock market, if we want to measure how two stocks are related to each other, Pearson r correlation is used to measure the degree of relationship between the two. The point-biserial correlation is conducted with the Pearson correlation formula except that one of the variables is dichotomous.

Kendall rank correlation: Kendall rank correlation is a non-parametric test that measures the strength of dependence between two variables. If we consider two samples, a and b, where each sample size is n, we know that the total number of pairings with a b is n(n-1)/2.

Spearman rank correlation: Spearman rank correlation is a non-parametric test that is used to measure the degree of association between two variables. The Spearman rank correlation test does not carry any assumptions about the distribution of the data and is the appropriate correlation analysis when the variables are measured on a scale that is at least ordinal.

5. If the assumptions of normality is not assured, or the sample size is not satisfied Kendall rank correlation or Spearman rank correlation could be developed.

6. For testing the significance between different samples non-parametric tests could be developed. If you have two groups you can develop Wilcoxon test for related samples, and Mann-Whitney for unrelated samples.

7. For three samples, Friedman test for related samples, and Kruskal-Wallis for unrelated samples.

Regards,

Zuhair

In addition, and for more information, please refer to:

. Landau, S. and Everitt, B. S.(2004). A Handbook of Statistical analyses using SPSS.

.Howitt, D. and Cramer, D.(2008). Introduction to SPSS.

Regards,

Spearman's rho and Kendall's W could not be used interchangeably. They are different.

Thank you all for your such a valuable and knowledgeable suggestions and comments. I am using Kendall's W only to calculate the effect size, which can, however, be calculated manually using the following formula (see Tomczak & Tomczak, 2014, p. 24): "Also, for the Friedman test, a non-parametric statistical test employed to compare three or more paired measurements (repeated measures), an effect size estimate can be calculated (and is referred to as W):

W = Friedman's Chi-square / N (k-1)

W = the Kendall's W test value

Chi-square = the Friedman test statistic value

N = sample size

k = the number of measurements per subject

The Kendall’s W coefficient assumes the value from 0

(indicating no relationship) to 1 (indicating a perfect

relationship).

Tomczak, M., & Tomczak, E. (2014). The need to report effect size estimates revisited. TRENDS in Sport Sciences, 1(21:19-25. ISSN:2299-9590.

I am using the following test statistics for the purposes stated against each:

1. Spearman's (rho) = Correlation coefficient.

2. Friedman's Chi-square test to test null hypothesis and know if there is a statistical significance.

3. Wilcoxon signed-rank test to compare two sets of scores of three or more variables i.e. post hoc test.

4. Kendall's W to only calculate the effect size.

My data samples are related and ordinal (Likert scale).

Thank you all again.

For the post-hoc test, it is better to use a post-hoc test made for Friedman than to use pairwise Wilcoxon tests. There is one suggested by Conover. In general, there can be problems with pairwise tests that don't account for the overall variation in the whole data set. But also note that Friedman test is not a generalization of the Wilcoxon test, so it doesn't really make sense for a post-hoc test. My understanding is Friedman is a generalization of the sign test and Quade is a generalization of the paired Wilcoxon test.