1. Wrap-up and Review Wrap-up and Review PSY440 July 8, 2008

2. Repeated Measures & Mixed Factorial ANOVA Basics of repeated measures factorial ANOVA –Using SPSS Basics of mixed factorial ANOVA –Using SPSS Similar to the between groups factorial ANOVA –Main effects and interactions –Multiple sources for the error terms (different denominators for each main effect)

3. Example Suppose that you are interested in how sleep deprivation impacts performance. You test 5 people on two tasks (motor and math) over the course of time without sleep (24 hrs, 36 hrs, and 48 hrs). Dependent variable is number of errors in the tasks. –Both factors are manipulated as within subject variables –Need to conduct a within groups factorial ANOVA

4. Example Factor B: Hours awake 24 B 1 36 B 2 48 B 3 Factor A: Task A 1 Motor 0104001040 0315103151 6559565595 A 2 Math 1103111031 1212312123 4664446644

5. Example SourceSSdfMSF A Error (A) 1.20 13.13 1414 1.20 3.28 0.37 B Error (B) AB Error (AB) 104.60 6.10 2.60 8.10 28282828 52.30 0.76 1.30 1.01 69.00 1.29

6. Example It has been suggested that pupil size increases during emotional arousal. A researcher presents people with different types of stimuli (designed to elicit different emotions). The researcher examines whether similar effects are demonstrated by men and women. –Type of stimuli was manipulated within subjects –Sex is a between subjects variable –Need to conduct a mixed factorial ANOVA

7. Example Factor B: Stimulus Neutral B 1 Pleasant B 2 Aversive B 3 FactorA: Sex A 1 Men 4323343233 8653886538 3326133261 A 2 Women 3241332413 6467564675 2163221632

8. Example SourceSSdfMSF Between A Error (A) 0.83 20.00 1818 0.83 2.50 0.33 Within B AB Error (B) 58.10 0.07 39.20 2 16 29.00 0.03 2.45 11.85 0.01

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

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

11. The General Linear Model Multiple correlation (R) Proportionate reduction in error (R 2 ) Bivariate regression & Bivariate correlation –Special case of multiple regression

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

13. 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

14. Links Between t Test for Independent Means & ANOVA

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

16. 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

17. 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

18. 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

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

20. 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

21. Relation Between Correlation and t Test for Independent Means

22. 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

23. Final Exam –Basic Probability –Descriptive statistics Means Standard deviation –Normal Distribution –Distribution of sample means (Central Limit Theorem) –Error types Type 1 (  ) Type 2 (  ) Statistical power –Hypothesis testing 1-sample z test T-tests –1-sample –Related samples –Independent samples ANOVA –1 factor –Repeated Measures –Factorial Correlation & regression –Experimental Design Topics

24. Final Exam Make sure you know which test to use to answer different questions about a data set: One or two categorical variables? Two or more continuous variables? One or more categorical variable and one continuous variable? Also, refer to flow chart from lecture. When to use repeated measures vs. between groups ANOVA? When to use one, two, or paired samples t-tests?