One-Way ANOVA

One-way ANOVA is used when you one have one categorical predictor variable and one continuous outcome variable and you want to look at the differences in the continuous outcome variable between the groups that are formed by the categorical predictor variable. This can be done for

Post-Hoc Analyses

An omnibus F in an ANOVA tells you that you have a difference somewhere, but does not tell you where that difference or differences are located. Post-hoc analyses (i.e., analyses done "after the fact" of a significant omnibus F-test) tells you where those differences occur.

The primarily difference between the different types of post-hoc test are the extent to which they control for "family-wise alpha" and (essentially) adjusts the p-value you use to determine what is a "statistically significant" difference.

Two-Way or Factorial ANOVA

Two-way or factorial ANOVA is used when you more than one categorical predictor variable and one continuous outcome variable and want to look at the joint prediction of those categorical predictors. You can also examine the interaction between those categorical predictors.