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i'm testing the relationship between four age groups of teachers on their perceived level of job security. I've run an omnibus f-test on some data, 240 subjects- no examples of any skewness, and it has come out as significant, F (3, 236)= 3.17, p=.03. But when I move onto planned comparisons (using matlab's XECI program), the largest effect I'm getting between any of the groups is 0.35 (using Bonett's delta, even though homogeneity of group variances holds, just to be safe).. I'm just wondering if anyone could shed some light on what's going on here? Is 0.35 SDs enough of a difference between the two groups to provide evidence of an effect, and therefore make the omnibus f-test significant? Thank you in advance for any help you can provide!

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If you have enough cases, even a very small group difference might be seen as "significant" by the criterion of p < 0.05, as your ability to detect a difference scales about inversely with the square root of the number of cases. Also, your F-test, which only has p = 0.03, simply determines whether there are any differences at all among all the groups, rather than differences among the groups in your planned comparisons. So in principle your findings aren't necessarily that surprising, although it's always good to check that you haven't made some error in setting up your calculations.

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