# Thread: Nonparametric for paired, but unequal sample size

1. ## Nonparametric for paired, but unequal sample size

Hi,

I'm in the midst of writing my master thesis, but I'm having issues with the statistics. I've measured muscle cells.

In short, I've 4 groups with different sample sizes. Two of the groups are measured two times (pre- and post-intervention), whereas two groups are measured three times (pre-, mid-, post-intervention). However, there are some missing data, i.e. subjects did not complete post-intervention measurement. We can assume that the distribution between the measurement periods are similar.

Group 1: 10 subjects, pre- & post-intervention
Group 2: 6 subjects, pre- & post-intervention
Group 3: 4 subjects, pre-, mid- & post-intervention
Group 4: 5 subjects, pre-, mid- & post-intervention

My first thought was Wilcoxon test, but with the missing data, incomplete pairs were removed.

Hope I was clear enough, thanks in advance!

2. ## Re: Nonparametric for paired, but unequal sample size

Do you want to compare these 4 groups to each other or just examine each versus a null (e.g., zero) value? Comparisons amongst each other appear to be very much under-powered (perhaps).

Missing data is always a threat due to the possibility of a systematic error, biasing results. You may be able to perform a sensitivity analysis, post hoc, where you impute the same value as base line for these patients (carry last value forward). Your rationale would be, given those with missing data had absolutely no change, the results would still hold or perhaps now you would fail to reject the null hypothesis.

3. ## Re: Nonparametric for paired, but unequal sample size

Originally Posted by hlsmith
Do you want to compare these 4 groups to each other or just examine each versus a null (e.g., zero) value? Comparisons amongst each other appear to be very much under-powered (perhaps).

Missing data is always a threat due to the possibility of a systematic error, biasing results. You may be able to perform a sensitivity analysis, post hoc, where you impute the same value as base line for these patients (carry last value forward). Your rationale would be, given those with missing data had absolutely no change, the results would still hold or perhaps now you would fail to reject the null hypothesis.
I mainly want to compare pre- to post-intervention within each group. If possible, then I would like to compare the groups to each other as well. I was told a mixed effects model would be able to handle my data. I'll also look into sensitivity analysis, thank you. Any other suggestions are appreciated.

I should also add that, as I have measured muscle fiber size approximately 20 cells are measured each time point per subject.

4. ## Re: Nonparametric for paired, but unequal sample size

My prior concern was in regards to your false discovery rate. If you compare the groups you would have I think 6 pairwise comparisons, meaning you would need to correct your level of significance appropriately. Though now you are divulging that there is another level of data, which could help your cause but if effect sizes are not large, you could still be under-powered.

5. ## Re: Nonparametric for paired, but unequal sample size

Originally Posted by hlsmith
My prior concern was in regards to your false discovery rate. If you compare the groups you would have I think 6 pairwise comparisons, meaning you would need to correct your level of significance appropriately. Though now you are divulging that there is another level of data, which could help your cause but if effect sizes are not large, you could still be under-powered.
I understand your concern and I am aware of it. I was hoping that there is still something I can do with the data. I'd of course interpret the results with extreme caution. There is a possibility that I could increase sample size, but in case that option dies I'd hope that I might still be able to run a few analyses in any case.

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