Thread: Wilcoxon test for statistical significance

1. Wilcoxon test for statistical significance

Hi guys, I have a simple question (sry for the probably imprecise formulation, I never went to a statistics class)

Assume we have a population with two characteristics (like female and male) and all individuals in that population are tested for a biomarker (like kidney function). If I calculate the mean kidney function for female and male separately, I see a difference (e.g. female mean is higher than male mean).

Which statistic test is appropriate to conclude, if this difference is statistical significant? Is the Wilcoxon test appropriate for this situation?

Many thanks!

2. Re: Wilcoxon test for statistical significance

Since you are a stats_Newbie we will need a clarification, every person in the population was tested or every person in your sample from a greater omega sample?

3. Re: Wilcoxon test for statistical significance

Every individual in the sample (e.g. n = 200) of a population (~6 billions) was tested for the same biomarker (kidney function was just an example) characterized by a value.

4. Re: Wilcoxon test for statistical significance

I guess you mean the Wilcoxon–Mann–Whitney test? The Wilcoxon signed-rank test is for paired samples.

The Wilcoxon-Mann-Whitney test cannot be interpreted as testing a null hypothesis that the means are equal (or not unless we add the the assumption that the shape and spread of the distribution is the same in both groups). More generally it tests a null hypothesis that the probability that a randomly sampled member of population 1 will have a higher value on the DV than a randomly sampled member of population 2 is exactly 0.5.

An independent samples t-test would be the usual choice to just compare the means.

5. Re: Wilcoxon test for statistical significance

Thx for the suggestions. However, I have two follow up questions:

For the t-test it is assumed that the population is normal distributed, which is very often not true for biological parameters.

1 If my population and my samples are log-normal distributed, is it appropriate to logarithmize the data and to apply the t-test ?

2 If the data is Weibull distributed or even more complex like Gompertz-Makeham or something, is the t-test appropriate?

6. Re: Wilcoxon test for statistical significance

Originally Posted by Stats_Newbie
For the t-test it is assumed that the population is normal distributed, which is very often not true for biological parameters.
An independent samples t-test does assume that the distribution of the DV is normal within each of the two populations, yes. But provided that observations are independent within each group, the sampling distribution of the t-statistic will converge to a normal distribution as the sample size grows larger, almost regardless of the distribution of the original data. With a sample size of 200, the normality assumption isn't very crucial. If you're worried about it you could use a permutation test instead of a t-test, which might be a less complicated way to go than switching to a non-parametric test or using a transformation.

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