although the expected value of MSB is the same as the expected value of MSE so that

E[MSB] = E[MSE],

the expected value of F is not 1. This is because

E[MSB/MSE] ≠ E[MSB]/E[MSE].

Instead, the expected value of F is : E[F] = dfd/(dfd-2).

When there is only one degree of freedom in the numerator, the relationship between the F and t distributions is very close. Specifically,

F(1,dfd) = t²(dfd)

which means an F with one degree of freedom numerator and dfd degrees of freedom denominator is equal to a t² with dfd degrees of freedom.