This image illustrates the expected values of a
*t*-distributed random variable and an *F*-distributed random
variable. Under the null hypothesis, the expected value of *t* is 0,
but the expected value of *F* is 1. This is sometimes confusing for
students given that *F* is *t* squared. Notice that if *t*
is exactly 0, then *F* will also be 0, but if *t* is greater than
or less than zero, *F* will always be greater than 0. In other words,
if the null hypothesis is true and two population means are equal, then we would
expect the sample means to be about equal. If the sample means are off by a little
bit in one direction or the other, *t* might be negative or positive, but
*F* will always be positive.