# Is this a case where multiple t-tests would work?

I know if I have three group means, and I compare group1-group2, then group2-group3, and group1-group3, this increases the Type1 error and I should use an ANOVA instead.

What I want to compare instead is: mean1-mean2, mean3-mean4, .... mean11-mean12. The situation is: I have a single dependent variable (match proportion, aka how much the participant looks at the answer vs distraction), but I need to make sure other factors like gender, or answer type, or the target side doesn't show a main effect.

Theoretically, there is not much reason to assume interaction between these 6 variables (e.g. no reason to think male participants will like the answer appearing on the right than female participants), so I am tempted to use multiple t-tests. But I know multiple t-tests on the same population can be a problem. (?)

My question is: (1) are multiple t-tests still a problem when different means are being compared each time and (2) if this is, what is my option? A 2x5 anova?

Any help would be greatly appreciated. Thanks.

Edit: To give more information about the structure of the study, let me give an example of what my data looks like.

Subnum  Gender  EventType  Target Side  MatchProportion
1      F         1           L             0.9
2      M         1           R             0.4
3      M         2           L             0.2
4      F         2           R             0.8


I want to compare the average Match proportion of all four subjects against chance (0.5). But I also need to exclude the possibility of there being a main effect of gender, event type, and target side (all of these factors were included for the sake of counterbalancing, and none are of theoretical interest to me).

• You could also do a p-value adjustment for multiplicity. The Bonferroni inequality provides one conservative method but there are many others including adjustments by bootstrap or by permutations. – Michael R. Chernick Aug 21 '19 at 17:40