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I ran a 2x2 ANOVA in which I predicted anxiety from two binary predictors (gender and agegroup).

Tests of Between-Subjects

Parameter Estimates

I couldn't understand why the p-values in the Tests of Between-Subjects Effects table did not match those in the Parameter Estimates table. The p-values for agegp and gender don't match, although the one for the interaction does.

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In SPSS General Linear Models procedure (GLM: i.e. ANOVA, MANOVA, etc.) with categorical predictors (factors) specified, the p-values discrepancy observed for the factors between the ANOVA-table and the parameter estimates table has this reason. ANOVA table always corresponds to deviation contrast coding of the factors. Parameters table corresponds to indicator (i.e. dummy variables) contrast coding of the factors.

You may check it yourself. Do some basic ANOVA in GLM. Then recode your factor(s) into deviation variables (codes 1, 0, -1) and perform linear regression with them. Compare the p-values with those from ANOVA table. Likewise, recode your factor(s) into dummy variables (codes 1, 0) and perform linear regression. Compare the p-values with those from parameter estimates table.

Parameters table always correspond to regressional, type III SS, reckoning of sums-of-squares, but ANOVA table could reflect also other reckoning (such as type I or II or IV SS) which will add to the discrepancy of p-values.

Note that using syntax of GLM command, specifically LMATRIX subcommand, you can request different ways to recode factors internally into various types of contrast variables. The p-values for those will be displayed in an additional table of the output.

P.S. In SPSS, there exists, besides GLM, also and older procedure MANOVA - now available only through syntax, not menu. Despite being "old", the command is still very valuable and keeps some options not available in GLM (including allowance of fractional case weights). There, if I remember correctly, no "discrepancy" occurs because by default the procedure uses deviation coding only.

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  • $\begingroup$ +1. Correct me if I am wrong, but it seems that unlike what I saw mentioned in some documents, the discrepancy occurs even in the balanced ANOVA design. Also, I note that if one factor has more than 2 levels, then I guess there will be several corresponding parameters in the parameters table, with separate p-values, whereas the ANOVA table will report only one p-value for the main effect of each factor. $\endgroup$
    – amoeba
    Commented Apr 30, 2016 at 14:16
  • $\begingroup$ @amoeba, yes of course, ANOVA table aggregates levels of factors, as by tradition. One can do the proper aggregation by hand in the parameters table to be able to compare with those ANOVA-table p-values. As for the first part of your comment about a balanced design, I didn't quite understand it, sorry. $\endgroup$
    – ttnphns
    Commented Apr 30, 2016 at 14:39
  • $\begingroup$ In the ANOVA context, "balanced" design means that all "cells" (combinations of each factor level) have the same number of samples. If ANOVA is unbalanced, then various complications arise, such as the difference between Type I/II/III sums of squares, etc. My point here is that the discrepancy between p-values in the ANOVA table and in the Parameter Estimates table arises even in the well-behaved balanced situation. $\endgroup$
    – amoeba
    Commented Apr 30, 2016 at 20:43
  • $\begingroup$ @amoeba, I know things you are saying about the balanced/unbalanced designs. What I did not understand was your apparent concern (surprise?) that those p-value differences are observed under balancedness as well. Were you expecting them to vanish? $\endgroup$
    – ttnphns
    Commented Apr 30, 2016 at 23:48

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