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I'm working in a biology lab and I treat some cells with a drug (treatment) or untreated (control), then transplant them into mice. Each experiment starts with the same cells (being exposed to the drugs or not) and then transplanted into a separate mouse. When dealing with transplantation data, because the recipients are different mice, each transplantation counts as a biological replicate. That's why for example, in experiment one, I have 2 biological (not technical) replicates for the treated cells, and one biological replicate for my control. When running stats, we use a ratio paired t-test to determine statistical significance.

In one of my experiments, I had 1 ctrl condition but 2 treatment conditions and now I'm having trouble running the ratio paired t-test. This is the results that I have:

enter image description here

If I want to run a ratio paired t-test, can I use the Ctrl result from experiment 1 twice as in the image below, and then run the paired t-test?

enter image description here

If yes, when I'm plotting the data I should only use 3 datapoints when drawing the control bar plot and calculating the S.D., right?

If no, then what can I do? I don't want to average the treatment results from experiment 1, since I will lose a datapoint.

Thanks!

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  • $\begingroup$ Are the treatments in experiment 1 two different treatments, or two replicates of the same treatment? What about for experiments 2 and 3, are those the same treatments as in experiment 1? What are the differences between the experiments? I'm struggling to understand where the individual experimental units (mice) fit into your tables - can you clarify please? $\endgroup$ – Izy Mar 18 at 16:57
  • $\begingroup$ I edited the post to clarify a bit. I'll explain a bit more here. - The treatments in experiment 1 are the same (same cells exposed to drug). However, the cells were transplanted into 2 different animals which makes them biological replicates, not technical. - The difference between the experiments is different starting cells. - Each result comes from 1 mouse. So in the table, you're seeing the results from 7 mice ( 3 control, 4 drug treated). - The reason we run this as paired t-test is because the starting cells have different potency, and as such the high variability in the controls. $\endgroup$ – Sadegh Davoudi Mar 18 at 17:45
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When plotting the data - yes you should only use the 3 data points when drawing your control data. You only have 3 data points for your control.

I don't think that it would be valid to do what you propose to do to run your paired t-test. One of the assumptions of the paired t-test is that each of your pairs is an independent observation (of the difference between the groups 'control' and 'treatment'). What you propose to do would ignore the link between the observations in experiment 1 (the link is from the cells) - so you would violate that assumption. Also, by using the control value twice, you would artificially inflate the sample size for the control, which would have an effect on the p value that you calculate.

As I understand it, a ratio paired t-test tests for differences between the logarithm-transformed values. There are some useful comments in gung's post here: https://stats.stackexchange.com/a/155184/212689

As you've got two factors here, 'Treatment' (Control vs Trt) and 'Cells' (experiments 1, 2 and 3), and Treatment is nested within 'Cells', you could use a linear mixed model (e.g. see package lme4 in R) of the form: log(response variable)~Treatment+(1|Cells).

Ideally I'd like to see more replicates, but that's the approach I would use to analyse the data.

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