# How to perform a t-test to compare treatment and control groups when the experiment has been replicated three times?

I have data from a experiment that has been repeated 3 times under the same condition. Each time, 5 measurements of each of 2 groups (a control and a treatment) were taken. I want to run a t-test on my data, to infer if there's a signification difference between the control and the treated group.

• How should I use the test?
• Should I take the 15 measurements for each group and feed it to the algorithm (I'm using instat graphpad)?
• Should I average the 5 measurements of each repetition and feed the algorithm the mean and SD of each repetition?
• This is by no means a basic question. Assuming that you know that the t-Test only applies if your data is drawn from a normal distribution (and assuming that it is), the problem at hand is: if you perform the t-test many times, how often do you expect to reject the null hypothesis? The answer really depends on your experimental design (i.e., where you measuring the same set of persons?). You can find a discussion of this problem here: jalt.org/test/bro_27.htm. – Néstor Apr 30 '12 at 5:41

## 1 Answer

• I suppose if repetition was irrelevant, you could do a t-test on your $3\times 5=15$ data points. But I imagine repetition is something that you want to explicitly model.
• Thus, one option would be to do a $3 \times 2$ factorial ANOVA where repetition is between subjects and has three levels and group is also between subjects and has two levels. The main effect of group would test whether marginal means significantly differ between treatment and control averaging across repetitions.
• Actually, this is data from a biological experiment. So the samples for the 3 repetitions were prepared on different days. There are no intentional differences, but there are some random effects, for example the buffer batch used is not the same as in the previous repetition. I suppose this would qualify for your first point, is that right? – Federico Apr 30 '12 at 11:41
• @Federico If in doubt, I'd go with the factorial ANOVA. That said, the factorial ANOVA would give you an estimate of any repetition effects. – Jeromy Anglim Apr 30 '12 at 13:16