As per my understanding here's the what/why/when of the following hypotheses tests in a crude sense:
- t-test: Used when comparing means between two samples
- ANOVA (one way): Used when you have one dependent variable and one independent (i.e., categorical) variable and you wish to analyze the 'means' (i.e., effects) across multiple groups. Simply stated, multi-way t-tests in essence.
- ANOVA (two way): Similar to one-way except you have two independent (i.e., categorical) variables
- MANOVA: ANOVA with multiple dependent variables
- ANCOVA: ??
- MANCOVA: ??
Intuitively, the concepts/intuition behind (M)ANOVA makes sense and I understand when/how to apply it and why is it necessary. I've just overly simplified my understanding about them above. However, I lack the similar intuition behind (M)ANCOVA.