# How can I ascertain the relationship between two variables with low sample-sizes?

So I have this issue. I'm working on investigating the changes in the blood as a certain disease affects the organism. I have two different variables measured on control(healthy) and infected model organism: M, E:

measurement of M gives:

measurement of E gives:

How can I show that there is a correlation between the changes in E and M as the healthy organism becomes ill? Or maybe evaluate the statistical significance of supposing that the change in E can explain the change in M?

• What's your sample size? Only these three items? Aug 4, 2020 at 11:04
• Yeap! :( As in my experiments it's very difficult/lengthy to derive even one sample, i have only these three Aug 4, 2020 at 11:06
• Honestly, with three (or 6?) samples, I wouldn't do much statistics. Plot them on a 2-D plot, showing the relationship between E and M. Aug 4, 2020 at 11:09
• Kinda expected it to be meaningless. Just wanted to see if there is anything I can try. Thank you! Aug 4, 2020 at 11:12
• It's not meaningless. Just report the data with a good, clean interpretation and let the readers judge. Not everything needs a p value attached to it. Aug 4, 2020 at 14:55

With this dataset, it will be tricky to get reliable results. But, if you can collect more data, you can try Gaussian GLMM with an interaction term between treatment and your factor.

It should contain the response variable as your measure; two fixed effects (with the interaction between them), namely treatment (Control and Infection) and your factor (M and E); one random effect - ID of the individual.

Jakub

I second collecting more data if possible, or graphing and contextualizing the findings if you can't collect more data (with a strong call that you or someone else will need to replicate findings in a larger sample). P values have their own issues at the best of times and certainly wouldn't be very meaningful with such a small sample. My other concern is that performing tests of association that assume linearity or monotonic relationships may not be warranted with a sample too small to examine whether those assumptions are valid. From a pragmatic standpoint, if you want to publish or report on the results somewhere (or if a company will make some decision based on these), collect more data first. If you are building toward a larger study/finding, and the pattern of results supports your hypotheses, you could graph it, and use it as preliminary data to report in an application for a grant for a larger study.