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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?

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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.

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  • $\begingroup$ I'm in the same situation as posted by the OP, but I am confused as to how I can clearly explain the nature of the 2 by 2 interaction without doing post hoc tests. For example, if the change in group A between time 1 and time 2 is quite different than the change in group B between time 1 and time 2, how can they be statistically shown without post hoc tests? $\endgroup$ – pdhami Jan 1 at 22:03
  • $\begingroup$ @pdhami what you just described is exactly what the interaction test is. You could say, "The change in group A is smaller (or larger, or in the opposite direction or whatever the case may be) than group B as evidenced by the interaction, F(1, 28) = ... " No additional test between any individual pair of means can show that. $\endgroup$ – John Jan 10 at 8:42
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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.

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    $\begingroup$ 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
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    $\begingroup$ 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 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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