Why ANOVA and not multiple t-tests? Why MANOVA and not multiple ANOVA’s, etc.

ANOVA reigns over the t-test and the MANOVA reigns over the ANOVA. Why?
If we want to compare several predictors with a single outcome variable, we can either do a series of t-tests, or a single factorial ANOVA.
Not only is a factorial ANOVA less work, but conducting several t-tests for each predictor separately will result in a higher probability of making Type I errors. In fact, with every single t-test there is a chance of a Type I error. Conducting several t-tests compounds this probability. In contrast, a single factorial ANOVA controls for this error so that the probability of a Type I error remains fixed at e.g. 5%.
Similarly, if we want to compare one or several predictors with a more than one outcome variable, we can either do a series of ANOVA tests, or a single MANOVA or factorial MANOVA. Here too a Type I error is likely due to unnecessary multiple significance tests with (possibly) correlated outcome variables. A MANOVA takes into account the correlation of multiple outcome variables while separate ANOVA’s can’t detect this correlation.

So, be sure to use the right test so not to compound your Type I error!