A) If I want to compare the mean of percentages between 3 groups of patients in a research, which statistical test is correct to be used in this case?
B) Can pearson correlation test be used (r value) to find the correlation between a percentage % and a value (hormone level).
Thanks
A) I would use a Kruskal-Wallis test
B) Yes, but you might consider the Spearman rank correlation. Do a scatter plot of the two variables to help you decide.
Adrian Esterman, KW-test is not about comparing means, and an interpretetion can be difficult when the shapes of the distributions are not similar. Further, KW is an omnibus test and does not compare individual group. The corresponding two-sample test would be the Mann-Withney/Wilcoxon test, but this is still not about comparing means and difficult to interpret when the distributions have different shapes. And the rank correlation does not assess the linear correlation. From the question I would guess that the assessment of a linear correlation was the aim, but I could be wrong here.
Zainab M. Alawad, what test is "correct" depends on what you like to (and reasonably should) assume about your data. If these precentages can be greater than 100% (like from a comparison to a standard or baseline value), and if it meake sense to assume that the distribution is symmetrical, a t-test is a valid procedure to compare means. However, in this case I would prefer to use the data that was used to calculate the percent-values directly and analyze it with a kind of an ancova model. If the precentages are bound in 0%-100%, you should ideally use a beta regression model. As a work-around you may consider a t-test on the logit-transformated percentage values.
If you want to assess the linear correlation, Pearson's r is the only statistic available. I doubt that this is of any practical use, particularily for your data (it's clear from theory that a linear correlation between percentages and a concentration makes no sense). It might make more sense to check the linearity between logit percentages and log concentrations. As Adrian already mentioned, you may use Spearman's rho to assess the monotone correlation, what may not be linear. I personaly don't find correlation measures very useful, in general. I'd always prefer a sensible model that may be phenomenological (to allow predictions that are of practical use, and to given the uncertainty associated with predictions), or causal (to estimate values of coefficients in the model [and the associated uncertainty] that have a particular practical meaning). What of this makes sense (or could make sense) depends on the concrete experimental design.
A) As Kruskal-Wallis test is non-parametric analogous to one-way parametric ANOVA, first you can go for that to check whether at least one group is significantly different from others or not. If found signifiacnt, then go for Mann-Withney U test in order to compare individual groups.
B) The easiest way of getting the direction and magnitude of such kind of relationship is Spearman's rank correlation coefficient as it is appropriate for continuous aand discrete ordinal variables. While Pearson's correlation assesses linear relationships, Spearman's correlation assesses monotonic relationships (whether linear or not).
Hope this will be helpful for you, Zainab M. Alawad .
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