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When I request post-hoc tests for a one-way ANOVA using ONEWAY, one of the ouput sections is "Homogeneous Groups". The bottom row of these tests is often (e.g., Tukey HSD, REGWF and REGWR, but not for Tukey B) labeled "Sig.", which in SPSS always indicates a "significance level." When this row is displayed, it often has different values for each homogeneous group and the values are generally > 0.05.

What is this "Sig." row and how am I to interpret it?

It may help to see this. Any "homogeneous groups" output will do, like: http://web.pdx.edu/~newsomj/da1/ho_ANOVA%20example.pdf (at the bottom of page 2 you can see these "Sig." values are 1.0, although clearly group 2 differs from groups 1 and 3). Or here's David Howell mentioning that he doesn't know what "Sig" means here: http://www.uvm.edu/~dhowell/gradstat/psych341/lectures/AnovaReviewFolder/class2.html (Howell wrote the statistics book I use with my students).

I have consulted the SPSS manual (BASE and ALGORITHMS) and over a dozen SPSS ONEWAY tutorials but none of them has answered this question. Many skip over homogeneous groups entirely and I take it that some people consider this output less important than the multiple comparisons output, which is a fair point, but I need to find some explanation for this "Sig." row.

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  • $\begingroup$ Sig. is interpretation of probability. Typically, but not necessarily, probabilities > 0.05 are not significant and probabilities <0.05 are significant for the test being performed. This may seem backwards but isn't because we usually assume the opposite of what we are trying to show. So if we assume $A=B$ and obtain $p<0.05$ we have shown it is unlikely that $A=B$ so that (usually 19 times out of 20) $A\neq B$. Question may be too basic to leave open here, don't know. $\endgroup$ – Carl Feb 23 '17 at 3:16
  • $\begingroup$ @Carl - Yes, perhaps I should have been clearer. I'm aware of that, but this use by SPSS must mean something else (or, more likely, it's the probability of something other than the post hoc test). A picture may be worth 1000 words; I'll see if I can add a link to a PDF. $\endgroup$ – Alan Mead Feb 23 '17 at 3:23
  • $\begingroup$ Indeed, your question may been closed if you hadn't cleared up that particular ambiguity. Future reference, be specific. $\endgroup$ – Carl Feb 26 '17 at 2:38
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In my version of SPSS, this section of output is called Homogeneous Subsets rather than Homogeneous Groups. According to the SPSS documentation, available in SPSS from Help > Algorithms, the sig. row should be the p-value of the difference between the category with the highest mean in the group and that with the lowest, where the p-value will be computed based on whatever post hoc test has been selected. I write "should", as I always find myself having to guess a bit when reading SPSS algorithm documentation, and this is no exception.

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