Question

When doing an experiment with many groups, what
is the problem with doing t tests between all possible
groups without any correction? Why does use of the
analysis of variance avoid that problem?

Answer 1

Not sure what kind of correction you mean, but probably refer to the fact that if you have n groups, you have k = n!/2(n-2)! possible pairs to analyze, and with many the problem of spurious "significance" arises,
e.g., (0.95)^k where k is the number of pairings tested.

Answer 2

Thank you. ANOVA does not make these multiple comparisons.