Normally when conducting an F-Test one is hoping the F-Test of all variables is significant although the single T-Tests yield insignificant results.

But can the reverse also be true? That is a worse F-Test than the single T-Tests?

  • $\begingroup$ Well, it's certainly possible to have, say, five out of 100 t-tests significant at the 95% level of confidence and have the F-test say (in effect) "this is just by chance" and not be significant. Would that count as "worse... than the single T-Tests"? $\endgroup$
    – jbowman
    Aug 30, 2018 at 18:43
  • $\begingroup$ Thanks for your answer. For example: Lag 1 T-Test: 0.03(p-value), Lag 2 T-Test: 0.02(p-value) and F-Test of both Lags: 0.1(p-value) $\endgroup$
    – Ben
    Aug 30, 2018 at 18:44