I am analysing an experiment run with 20 participants using a $2\times 2$ mixed design ANOVA. The experiment has

  • one within subjects variable A with two levels (a1, a2)
  • one between subjects variable B with two levels (b1, b2)

The following are the results of the ANOVA analysis:

B F(1,18) = 5,84 p<0,026493 SS=1,44 MSe=0,25

A F(1,18) = 11,1 p<0,003734 SS=1,25 MSe=0,11

B*A F(1,18) = 7,16 p<0,015412 SS=0,81 MSe=0,11

Is there any reason to run post-hoc test in this context? SPSS complains about variables having less than 3 levels and, for this reason, doesn't allow me to run Post-hoc tests.

Question Is it possible to run bonferroni post-hoc test in this kind of scenario? If not, why? If yes, how to do it in SPSS?


There's no use for a post hoc test here. What could you possibly find in a post hoc that isn't obvious from the ANOVA? There's a main effect of A and a main effect of B and an interaction.

Some people do them to do something like test whether A1B1 - A1B2 is significant while A2B1 - A2B2 is not. They find that result and report it as important but it's meaningless because it tells you less than the interaction already told you. Significant and not-significant is not a test of differences between conditions dependent upon the level of the other condition. The interaction already was that test.


The interaction test can be significant, whereas the post hocs are not, especially if it's a cross-over pattern. That's why they need to be conducted.

  • 7
    $\begingroup$ Which post hoc test would you conduct? There are only two levels. Any statistically significant result would demonstrate difference between the two levels. $\endgroup$ – Behacad Jun 4 '14 at 19:40
  • 1
    $\begingroup$ In the light of the information in the other answer (which you're free to disagree with, if you explain why), can you expand your answer to explain the apparent discrepancy? $\endgroup$ – Glen_b -Reinstate Monica Jun 4 '14 at 22:53
  • $\begingroup$ I don't even see how this answers the question... $\endgroup$ – Nick Stauner Jun 5 '14 at 3:48

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