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Statistics for the Social Sciences

Statistics for the Social Sciences. Psychology 340 Fall 2006. Putting it all together. General. Specialized. The Relationship Among Major Statistical Methods. The general linear model. Multiple regression/correlation. Bivariate correlation. ANOVA. t-test. General. Specialized.

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Statistics for the Social Sciences

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

  2. General Specialized The Relationship Among Major Statistical Methods • The general linear model Multiple regression/correlation Bivariate correlation ANOVA t-test

  3. General Specialized The Relationship Among Major Statistical Methods • The general linear model Multiple regression/correlation Bivariate correlation ANOVA t-test

  4. The General Linear Model • Bivariate regression & Bivariate correlation • Special case of multiple regression • Multiple correlation (R) • Proportionate reduction in error (R2)

  5. General Specialized The Relationship Among Major Statistical Methods • The general linear model Multiple regression/correlation Bivariate correlation ANOVA t-test

  6. 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

  7. Links Between the t Test for Independent Means and ANOVA

  8. General Specialized The Relationship Among Major Statistical Methods • The general linear model Multiple regression/correlation Bivariate correlation ANOVA t-test

  9. corresponds to the main effect X has two values Exp & Control Exp. Control ANOVA as a Special Case of the Significance Test of Multiple Regression ANOVACorrelation/Regression SSWithin = SSError SSTotal = SSTotal SSBetween = SSTotal – SSError R2 = r2 • ANOVA for two groups as a special case of the significance of a bivariate correlation

  10. Nominal coding 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

  11. 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

  12. General Specialized The Relationship Among Major Statistical Methods • The general linear model Multiple regression/correlation Bivariate correlation ANOVA t-test

  13. 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

  14. Relation Between Correlation and tTest for Independent Means

  15. Multiple regression/correlation General Bivariate correlation ANOVA Specialized t-test Choice of Statistical Tests • 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

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