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Hi everyone, I wonder if anyone can shed some light on this issue... For argument's sake, say we have two categorical variables: A (with 2 levels: codes 0 and 1), B (with 2 levels: codes 0 and 1). For each of the 4 A x B combinations we have data collected from 8 different individuals. We construct a regression model of the form: Y = constant1 + beta1*A + beta2*B + E The result is Coefficientsa Model Unstandardized Coefficients Standardized Coefficients t Sig. B Std. Error Beta 1 (Constant) 59.844 3.446 17.368 .000 A 7.813 3.979 .274 1.964 .059 B -17.188 3.979 -.602 -4.320 .000 a. Dependent Variable: Y We also conduct a two-way ANOVA (without interaction). The result is: Tests of Between-Subjects Effects Dependent Variable: Source Type III Sum of Squares df Mean Square F Sig. Corrected Model 2851.563a 2 1425.781 11.258 .000 Intercept 97350.781 1 97350.781 768.700 .000 A 488.281 1 488.281 3.856 .059 B 2363.281 1 2363.281 18.661 .000 Error 3672.656 29 126.643 Total 103875.000 32 Corrected Total 6524.219 31 a. R Squared = .437 (Adjusted R Squared = .398) We can see that the p-values for A and B and the associated test statistics (where F=t^2) are the same for the regression and two-way ANOVA analysis. Now we add the interaction (A*B) term. For the regression we get: Coefficientsa Model Unstandardized Coefficients Standardized Coefficients t Sig. B Std. Error Beta 1 (Constant) 66.875 3.055 21.890 .000 A -6.250 4.320 -.219 -1.447 .159 B -31.250 4.320 -1.094 -7.233 .000 A*B 28.125 6.110 .853 4.603 .000 a. Dependent Variable: Y For the two-way ANOVA we get: Tests of Between-Subjects Effects Dependent Variable: Source Type III Sum of Squares df Mean Square F Sig. Corrected Model 4433.594a 3 1477.865 19.793 .000 Intercept 97350.781 1 97350.781 1303.831 .000 A 488.281 1 488.281 6.540 .016 B 2363.281 1 2363.281 31.652 .000 A * B 1582.031 1 1582.031 21.188 .000 Error 2090.625 28 74.665 Total 103875.000 32 Corrected Total 6524.219 31 a. R Squared = .680 (Adjusted R Squared = .645) We have that, although that the p-value for the interaction and the associated test statistic (where F=t^2) is the same for the regression and two-way ANOVA analysis, the p-values for A and B differ. What is the reason for this? I assume that it is related to how we are interpreting the statistics? For regression, Montgomery and Peck (1992) say that the test statistic for each regressor in the model is a "partial test" that is the "test of xi given the other regressors in the model" i.e. in our case, t=-1.447 (p=0.159) is the test for A given B and the interaction are in the model, t=-7.233 (p<0.001) is the test for B given A and the interaction are in the model and t=4.603 is the test for the interaction given A and B are in the model. However, I am confused as to how the interpretation of the two-way ANOVA differs from that of the regression model. I hope that someone can throw some light on this. Many thanks in advance. Kim Dr Kim Pearce PhD, CStat, Fellow HEA Senior Statistician Haematological Sciences Room MG261 Institute of Cellular Medicine William Leech Building Medical School Newcastle University Framlington Place Newcastle upon Tyne NE2 4HH Tel: (0044) (0)191 208 8142 You may leave the list at any time by sending the command SIGNOFF allstat to [log in to unmask], leaving the subject line blank.