Statistics for the Social Sciences Psychology 340 Fall 2006 Putting it all together

Statistics for the Social Sciences The Relationship Among Major Statistical Methods The general linear model General Specialized Multiple regression/correlation Bivariate correlation ANOVA t-test

Statistics for the Social Sciences The Relationship Among Major Statistical Methods The general linear model General Specialized Multiple regression/correlation Bivariate correlation ANOVA t-test

Statistics for the Social Sciences The General Linear Model Multiple correlation (R) Proportionate reduction in error (R 2 ) Bivariate regression & Bivariate correlation –Special case of multiple regression

Statistics for the Social Sciences The Relationship Among Major Statistical Methods The general linear model General Specialized Multiple regression/correlation Bivariate correlation ANOVA t-test

Statistics for the Social Sciences The t Test as a Special Case of ANOVA t test –Two groups ANOVA (F ratio) –More than two groups Parallels in their basic logic Numeric relationship of the procedures

Statistics for the Social Sciences Links Between the t Test for Independent Means and ANOVA

Statistics for the Social Sciences The Relationship Among Major Statistical Methods The general linear model General Specialized Multiple regression/correlation Bivariate correlation ANOVA t-test

Statistics for the Social Sciences ANOVA as a Special Case of the Significance Test of Multiple Regression ANOVA Correlation/Regression SS Within = SS Error SS Total = SS Total SS Between = SS Total – SS Error R 2 =r 2 ANOVA Correlation/Regression SS Within = SS Error SS Total = SS Total SS Between = SS Total – SS Error R 2 =r 2 Exp.Control corresponds to the main effect X has two values Exp & Control X has two values Exp & Control ANOVA for two groups as a special case of the significance of a bivariate correlation

Statistics for the Social Sciences ANOVA as a Special Case of the Significance Test of Multiple Regression ANOVA for more than two groups as a special case of the significance of a multiple correlation Nominal coding

Statistics for the Social Sciences ANOVA as a Special Case of the Significance Test of Multiple Regression –Factorial ANOVA: Each main effect will have have a  associated with it. Each interaction term will also have a  associated with it. ANOVA for more than two groups as a special case of the significance of a multiple correlation

Statistics for the Social Sciences The Relationship Among Major Statistical Methods The general linear model General Specialized Multiple regression/correlation Bivariate correlation ANOVA t-test

Statistics for the Social Sciences The t Test as a Special Case of the Significance Test for the Correlation Coefficient Correlation coefficient –Degree of association between two variables t test –Significance of the difference between the two population means Both use the t distribution to determine significance –Recall: test statistic to test significance of Pearson’s r

Statistics for the Social Sciences Relation Between Correlation and t Test for Independent Means

Statistics for the Social Sciences Choice of Statistical Tests General Specialized Multiple regression/correlation Bivariate correlation ANOVA t-test t test, ANOVA, and correlation can all be done as multiple regression –However, each usually used in specific research contexts –Correlation and regression automatically give estimates of effect size and not just significance