1. Univariate Statistics PSYC*6060 Class 11 Peter Hausdorf University of Guelph

2. Agenda Final Exam Details Howell Chapter 16 Group exercise Thesis Examples Cohen Article

3. Final Exam 3 hours Questions –10 multiple choice –10 short answer –3 multiple answer 50/50:conceptual/practical

4. Howell Chapter 16 Design matrices Integrating ANOVA and regression ANOVA with unequal Ns One way ANCOVA Factorial ANCOVA Alternative experimental designs

5. Design matrices Allows us to look at ANOVA in a multiple regression framework 1 1 0 0 1 0 1 0 0 1 123456123456 X =  A1A1 A2A2 A3A3 y = Xb + e Y ij =  +  j + e ij Y 11 =  +  1 + e 11 Y 21 =  +  1 + e 21 Y 12 =  +  2 + e 12 Y 22 =  +  2 + e 22 Y 13 =  +  3 + e 13 Y 23 =  +  3 + e 23

6. ANOVA – Unequal ns Non-Drinking Drinking Row Means Michigan 13 15 14 16 12 18 20 22 19 21 23 17 18 22 20 X 11 = 14 X 12 = 20 X 1. = 18 Arizona 13 15 18 14 10 24 25 17 16 18 12 16 17 51 10 14 X 21 = 14 X 22 = 20 X 2. = 15.9 Column X. 1 = 14 X.2 = 20 Means

7. ANOVA – Unequal ns Method I – each effect is adjusted for all other effects Method II – defines interaction first and then main effects Method III – assigns SS based on order in which you select the variables

8. Linear Regression Skin fold (cm) Blood sugar Sum of squares - regression Sum of squares - error

9. One Way ANCOVA Depression Score Weeks in Therapy Psychotherapy Positive Thinking

10. Assumptions for ANCOVA Linear relationship between Y and covariate Homogeneity of regression

11. Calculations Calculating SS Treat(adj) –Run regression with covariate only –Run regression with treatments only –SS Treat(adj) = SS reg  c – SS regc Calculating Adjusted means –Use regression equation and mean value of covariate and dummy codes for treatments

12. Adjusted Means Use regression equation with mean value of covariate

13. Factorial ANCOVA IV - 3X3 design with 1 covariate –Task Pattern recognition Cognitive Driving Simulation –Smoking Active Delayed Non –Distraction DV - Number of errors

14. Factorial ANCOVA Pattern Recognition NS: Errors 9 8 12 10 …….. Distract 107 133 123 94 ……. …… Driving Simulation AS: Errors 3 2 0 0 …… Distract 130 83 91 92 …… C T1 T2 G1 G2 TG11 TG12 TG21 TG22 CTG11 CTG12 CTG21 CTG22 1071 0 1 0 1 0 0 0 107 0 0 0 9 130 -1 -1 -1 -1 1 1 1 1 130 130 130 130 3

15. Alternative Experimental Designs Matched Samples Difference Scores