J.R. S. answered 03/18/17
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Ph.D. in Biochemistry--University Professor--Chemistry Tutor
It is true that multiple t-tests will increase the likelihood of error, however, there is a post hoc test called the Bonferoni test which supposedly corrects (somewhat) for this. You might consider looking into this option. Otherwise, you can still use a two-way ANOVA to do the multiple comparisons you are interested in.