# 2x2 experimental design: t-tests vs. mixed anova analysis

I have conducted an experimental study, with 1 within-variable (time: T1 and T2) and 1 between-variable (group: control and treatment), measuring just one dependent variable.

I understand that this is a design which would require a mixed ANOVA analysis. Of course two distinct t-tests would be much easier: one dependent and one independent two-sample-t-tests.

What is problematic about using two distinct t-tests in comparison to mixed ANOVA (despite ignoring the interaction effect, which I assume to not exist)?

Thanks for advice.

Update: What I've done so far (in R) is:

t.test(Con$DELTA, mu=0, alternative = c("greater")) t.test(Exp$DELTA, mu=0, alternative = c("greater"))


Two single dependent/paired t.tests for each group, one-sided, because I'm just interested in each groups behavior change success. Afterwards I can compare both groups (with independent two-sample-t-test):

t.test(Con$DELTA, Exp$DELTA)


two-sided test, because I'm not sure which group is better than the other. Each t-test represents one stand-alone hypothesis.

• The 2-way between-by-within ANOVA (or mixed effect ANOVA) will allow you to test for an interaction. Further, if there is no significant interaction, then the 2 main effects will have more power than their individual t-test equivalents because you use all of the data to estimate your variance components. Although this assumes you have homogeneity of variance. – Moose Apr 6 '16 at 12:30
• Ok, but despite giving up some power, it's not forbidden to test two hypotheses with seperate t-tests? In my experimental setting there will not be any interaction effect I think, or at least has no meaning. The groups are independent. – Mac Apr 6 '16 at 14:13
• Well, assuming that T1 is before treatment and T2 is after treatment, you should hope for an interaction. The usual interaction in this case is that treatment has no effect at T1 (the group means are equal) because patients were randomised, but then at T2, after treatment, there is a difference between the groups. – Moose Apr 7 '16 at 11:02
• Look into using a repeated 2x2 ANOVA or an ANCOVA. Running different t-tests is not the way to go. – Moose Apr 7 '16 at 11:12

## 1 Answer

Since you are measuring two time points you need a repeated measure ANOVA. A t-test cannot control for time.

• I thought dependent, repeated or within are used synonymous? I don't have a profound proof, but compare e.g. this site: statistics.laerd.com/statistical-guides/… information: A dependent t-test is an example of a "within-subjects" or "repeated-measures" statistical test. regards – Mac Apr 6 '16 at 9:10