T-stat vs. F-stat

CFA Level II
#1

when do you use which?

#2

The t-stat is used to test the significance of the individual independent variables.

E.g. intercept = 0 v intercept <> 0, or b1 = 1 v b1 <> 1

F-test is used to test if at least one of the independent variablesis significantly different from 0.

The null hypothesis is b1 = b2 = … = bn = 0. The alternative hypothesis is that at least one of them differs from 0.

#3

You use a t-statistic when you’re trying to determine whether a particular regression coefficient – the intercept or a slope coefficient – could equal a particular value; in the case of slope coefficients, the most common value against which you are testing them is zero. If your sample size is large (≥ 30), you can use a z-statistic if you like.

You use an F-statistic when you’re trying to determine whether all of the slope coefficients (taken together, as a group) could be zero.

So:

  • Intercept: use a t-statistic
  • Single slope: use a t-statistic
  • All slopes (together): use an F-statistic
1 Like
#4

You da man!

#5

Thanks.