“Kinds” By-the-Numbers # pops # crits # preds # controls # controlled Which is better? Model or Model Comparison to Use 1 1 1 0 0 no Simple correlation (direct p-value) 2 1 1 0 0 yes Comparing a correlation across populations (ZF) 1 1 2 0 0 yes Comparing correlated correlations (ZS) 1 2 1 0 0 yes Comparing correlated correlations (ZS) 1 1 1 1 2 no Partial correlation(direct p-value) 1 1 1 2+ 2 no Multiple partial correlation (direct p-value) 1 1 1 1 1 no Semi-partial correlation (direct p-value) 1 1 1 2+ 1 no Multiple semi-partial correlation (direct p-value) 1 1 2+ 0 0 no Multiple regression model (R² F-test and/or t-test of b/Beta) 1 1 3+ 0 0 yes Are the preds in one model a subset of the preds in the other model? Comparing nested multiple regression model (R²∆ F-test) 1 1 2+ 0 0 yes Comparing non-nested multiple regression model (ZS) 2 1 2+ 0 0 yes Comparing a multiple regression model across populations (ZF & ZS ) 1 2 2+ 0 0 yes Comparing a multiple regression model across criteria (ZS )Different Questions & Details (Some of the models have multiple characterizations) The Major Question or Hypothesis The details Model or Model Comparison to Use Are two variables correlated? Simple correlation (direct p-value) Are two variables correlated? Is the correlation difference for 2 populations? Comparing a correlation across populations (ZF) Are two variables correlated? Are the correlations different if we change predictors? Comparing correlated correlations (ZS) Are two variables correlated? Are the correlations different if we change criterion? Comparing correlated correlations (ZS) Is a criterion better correlated with one predictor than with another predictor? Comparing correlated correlations (ZS) Is a predictor better correlated with one criterion than with another criterion? Comparing correlated correlations (ZS) Are two variables correlated? Control both variables for 1 control variable. Partial correlation (direct p-value) Are two variables correlated? Control both variables for 2+ control variables Multiple partial correlation (direct p-value) Are two variables correlated? Control one of the variables for 1 control variable Semi-partial correlation (direct p-value) Are two variables correlated? Control one of the variables for 2+ control variable Multiple semi-partial correlation(direct p-value) Does a regression model work? Multiple regression model (R² F-test &/or t-test of b/Beta) Does a particular predictor contribute to the model? b t-test & Comparing nested multiple regression models (R²∆ F-test) Does a subset of predictors work as well as “all” the predictors? Comparing nested multiple regression models (R²∆ F-test) Does one subset of predictors work as well as another subset of predictors? Comparing non-nested multiple regression models (ZS) Does a regression model work? Is the model different for 2 populations? Comparing a multiple regression model across populations (ZF & ZS ) Does a regression model work? Is the model different for 2 criteria? Comparing a multiple regression model across criteria (ZS )Are 2 variables correlated? ry,x Does a model work? R²y.x1,x2,x3 using R² F-test or r²y.y’ where y’ = bx1 + bx2 + bx3 + a Relationships between Bivariate & Control, Multivariate Models & Comparisons Based on the idea that a multivariate model is represented by its predictions (y’) Are two variables correlated after ry,x.v controlling both for a 3rd variable or ryr,xr where yr = y – (bv + a) & xr = x – )bv + a) Are two variables correlated after ry,x.v.w controlling both for 2+ variables or ryr,xr where yr = y – (bv + bw + a) & xr = x – (bv + bw + a) Are two variables correlated after ry(x.v) controlling one of them for a 3rd variable or ry,xr where xr = x – )bv + a) Are two variables correlated after controlling ry(x.v.w) controlling one of them for 2+ variables or ry,xr where xr = x – (bv + bw + a)Are 2 variables correlated differently in two populations? ry,x in Pop1 vs. ry,x in Pop2 using ZF Does a model work differently in two populations? using ZF ZS R²y.x1,x2,x3 in Pop1 vs. R²y.x1,x2,x3 in Pop2 or r²y.y’ in Pop1 vs. r²y.y’ in Pop2 where y’ = bx1 + bx2 + bx3 + a & y’ = bx1 + bx2 + bx3 + a Are 2 predictors correlate differently with a criterion? (correlated correlations) ry,x1 vs. ry,x2 using ZS Does a model work differently well for 2 criteria? R²y.x1,x2,x3 vs. R²z.x1,x2,x3 using ZS or r²y.y’ vs. r²z.z’ where y’ = bx1 + bx2 + bx3 + a & z’ = bx1 + bx2 + bx3 + a Do two non-nested models work differently well? R²y.x1,x2,x3 vs. R²y.x1,x4,x5 using ZS or r²y.y’1 vs. r²y.y’2 where y1’ = bx1 + bx2 + bx3 + a & y2’ = bx1 + bx4 + bx5 + a Is a predictor correlated differently with 2 criteria? (correlated correlations) ry,x1 vs. rz,x1 using ZS Do two nested models work differently well? R²y.x1,x2,x3,x4 vs. R²z.x1,x2 using R²∆