I have two conditions, Treatment A, and Treatment B. Participants are randomly assigned to a treatment at the outset. Then I run unpaired t-tests on the data to find any differences. BUT I am also interested in whether the treatment has an effect on specific gender (Male, Female) and race (white, African American, Latino/a, etc.). Right now, I've broken down the data into all Male, all Female, all white, etc. Then I run unpaired t-tests again for Treatment A vs Treatment B on the sub-sample of data.

Is this the correct approach? Should I be doing something like looking at interaction effects instead of doing this? Thoughts much appreciated.

  • 2
    $\begingroup$ Analysis of variance indeed seems called for. Just using t-tests is a very limited way of analysing your data. But you don't explain your response (outcome, dependent) variable(s), which is the first thing to explain.... $\endgroup$
    – Nick Cox
    Commented Jun 30, 2015 at 8:25
  • $\begingroup$ I'm actually not interested in comparing genders and races (e.g., Male vs. Female, white vs. African American, etc.). My understanding is that is what a three-way ANOVA would do. What I want to do is compare WITHIN all Male, then within all Female, Treatment A vs Treatment B. Does an ANOVA still make sense? $\endgroup$ Commented Jun 30, 2015 at 18:04
  • $\begingroup$ Regardless of whether they are of interest, other controls are still at work. You can't squeeze out single factor effects by ignoring other factors. So, same advice. $\endgroup$
    – Nick Cox
    Commented Jun 30, 2015 at 18:06
  • $\begingroup$ But isn't the whole point of a between-subjects design, so that you can have a large N in both treatments and that in itself controls for those factors? $\endgroup$ Commented Jun 30, 2015 at 18:30
  • $\begingroup$ I wouldn't summarize experimental design in that way. Even with a good design, just using single t tests will not somehow take into account the variation with other factors. How could it? $\endgroup$
    – Nick Cox
    Commented Jun 30, 2015 at 18:33

1 Answer 1


Nick Cox already gave a good answer in the comments, but let's summarize it in a formal answer.

  1. By analyzing the same dataset with multiple unpaired t-test, you are not exactly respecting the experimental design. I'm not sure what it would do, but I think you are increasing the chances of Type I error. Someone with a stronger statistical background could say if I'm wrong here.

  2. An ANOVA would better fit your needs. You would have the following list of fixed effects :



Treatment* Gender


Treatment* Race

Treatment* Gender* Race

You are interested in the interactions, but you cannot test the interactions without the main effects.

  1. Like Nick Cox, I would suggest reading a basic book about experimental design.
  • $\begingroup$ Thanks, both you and Nick have been helpful. However, I still don't understand one thing. Say I get a significant effect for the fixed effect of "Treatment*Race". This is telling me there is an interaction between the condition and the race of participants. Does this now justify doing post-hoc t-tests on all participants of each individual race across the two treatments? $\endgroup$ Commented Jul 1, 2015 at 19:55
  • $\begingroup$ You should rather look at a posteriori test such as LSmeans (personnal favorite, but there is other). Easily done with R and SAS. $\endgroup$
    – Emilie
    Commented Jul 2, 2015 at 0:31

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