Comparisons or What Groups Are Really Different
Here's the deal. A significant F just means that there is at least one different pair of means. Look at our original example. Except for the data in the upper left corner, all the graphs could have generated our significant F. We can't tell which pairs are significant.

DANGER - DANGER - WARNING!! Don't Say All the Means Are Different Because F is Significant. WRONG!

We can determine which pairs of means are significantly different from each other. These methods have corrections in them so you don't increase your Type I error rate as would happen if you did all the t tests.