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I have done a Western blot experiment and I am trying to figure out the best statistical test to perform on my data. I am comparing the differences in the expression levels of a certain protein in the brains of wild-type mice from two different age groups (postnatal day 12 and postnatal day 30). I have 10 samples in the postnatal day 12 group and 9 samples in the postnatal day 30 group.

I have performed an unpaired parametric t-test to see if there is a statistically significant difference in the protein expression levels between the two age groups. I have performed an unpaired t-test because evidently the mice in the two age groups are different from each other.

However, within each age group, there are some technical replicates (e.g. samples from the same mouse that were used in repeats of the experiment to see if the observed effect is reproducible). I was wondering if it is suitable to use an unpaired t-test if there are technical replicates of a sample within an experimental group?

Any insights are appreciated.

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No, you cannot treat two samples from the same mouse as independent and identically distributed - two technical replicates from the same mouse are obviously going to be more similar than two samples from different mice. As a general rule of thumb, you can only assume that samples at the level of your treatment unit (in this case, individual mice) are IID samples. Failure to do so results in a higher false positive rate than you intend.

You have a few options available to you.

A. You can average your technical replicates so that you have a single measurement from each mouse, then perform an unpaired t-test. This errs on the side of being slightly conservative depending on how skewed your data is.

B. Do a randomization test that considers every level of hierarchy in your experimental design, see here. For full disclosure, I wrote this paper.

Basically, when you have a hierarchical (or nested) experiment like this one, it's important to make sure your statistical analysis plan maintains whatever alpha level you choose (typically 5%). Treating technical replicates as independent samples (which many call "pseudoreplication") automatically fails this criterion.

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  • $\begingroup$ Thank you for your reply. The unpaired t-test that I used on my data is parametric. I was wondering if it is possible to use an unpaired non-parametric t-test (e.g. Mann Whitney U test) on data which has technical replicates in each group? $\endgroup$
    – ceno980
    Jul 12, 2021 at 0:23
  • $\begingroup$ I would read the paper I linked if you want to do a nonparametric test that accounts for technical replicates. It describes a Python package that does exactly what you want (a permutation t test, which is not the same thing as the MWU test - MWU tests for stochastic dominance, which is different from a change in means). $\endgroup$
    – rishi-k
    Jul 12, 2021 at 0:29
  • $\begingroup$ Thank you for your reply. The software I have to use does not have the permutation t test as an option which is why I want to do a Mann Whitney U test. Just to clarify, can the Mann Whitney U test be used when there are technical replicates in each group? Any insights are appreciated. $\endgroup$
    – ceno980
    Jul 12, 2021 at 3:36
  • $\begingroup$ No. If you want to use MWU, you'd have to average your technical replicates together so that you only have a single measurement per mouse. Also, do you want to use MWU? The null hypothesis is not the same as the t-test, and you shouldn't be changing your null hypothesis to fit the test you want to do - rather, you should be doing the opposite. $\endgroup$
    – rishi-k
    Jul 12, 2021 at 3:38
  • $\begingroup$ Thank you. Do you know if a one-way ANOVA can be used if there are technical replicates in each group? I am thinking of using this test since this test compares the means between 2 or more groups, which is what I want to do. $\endgroup$
    – ceno980
    Jul 12, 2021 at 6:27

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