Mouse sample size problem

#1
Say I have ten cages, each with three mice inside.

Five cages have mutant mice. Five cages have normal mice. Each individual mutant cage is paired to one normal cage, because those 6 animals are littermates.

From these mice I take body weights. I then need to test whether significant body weight differences arise due to the mutation with a matched sample t-test.

The question is, does each cage count as an n of 1 or does each animal? TECHNICALLY, I know it is each cage - statistical units need to be independently ramdomised, treated, must not interfere with each other yadda yadda.

But what exactly is it I would need to demonstrate in order to justify using animals as my statistical units? Do I use an ANOVA to show that all the 5 normal cages do not significantly differ, and that all the 5 mutant cages do not significantly differ? Would this show that which cage they were in didn't matter and allow me to use individual animals as my statistical unit? Or do I use an R-squared test to show that the cage that the proportion of variation due to cage is less than some arbitrary amount?

Also, how would I perform matched sample t-test if the analysis was based on individual animals? Just randomly match mutant and normal mice from the paired cages? I guess the mean differences would still be the same regardless of exactly which mice in matched cages were compared eh?
 
#2
Hi Granty,

Yes, in the books it is writen: "independent data" ==> independent t-test, "dependent data" ==> paired t-test

I think the real prerequisite for the t-test: you should check a randomly selected sample from 2 different groups.
I think ... that if the sample you took can count as a "randomly selected" you can use the "independent t-test" in the individual level.

Of course, you can't take strong dependent data like the same mouse in the morning and in the evening as 2 samples ...

When having dependent pairs, the recommendation is to use "paired t-test" since it will reduce the standard deviation, so you will need a smaller sample. again I'm not sure that in your case it is a prerequisite.

For an extreme example, if you compare, people from 5 cities you don't have a problem to run an independent t-test despite the fact that there is some connection between the people in the same city. (yes I know the connection in the same cage may be stronger).
But even if there is a small difference between the cages, I assume it will be ok if it can be count as "randomly selected"

Does anybody have other thoughts?
 
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