Univariate Statistics PSYC*6060 Class 11 Peter Hausdorf University of Guelph
Agenda Final Exam Details Howell Chapter 16 Group exercise Thesis Examples Cohen Article
Final Exam 3 hours Questions –10 multiple choice –10 short answer –3 multiple answer 50/50:conceptual/practical
Howell Chapter 16 Design matrices Integrating ANOVA and regression ANOVA with unequal Ns One way ANCOVA Factorial ANCOVA Alternative experimental designs
Design matrices Allows us to look at ANOVA in a multiple regression framework 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
ANOVA – Unequal ns Non-Drinking Drinking Row Means Michigan X 11 = 14 X 12 = 20 X 1. = 18 Arizona X 21 = 14 X 22 = 20 X 2. = 15.9 Column X. 1 = 14 X.2 = 20 Means
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
Linear Regression Skin fold (cm) Blood sugar Sum of squares - regression Sum of squares - error
One Way ANCOVA Depression Score Weeks in Therapy Psychotherapy Positive Thinking
Assumptions for ANCOVA Linear relationship between Y and covariate Homogeneity of regression
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
Adjusted Means Use regression equation with mean value of covariate
Factorial ANCOVA IV - 3X3 design with 1 covariate –Task Pattern recognition Cognitive Driving Simulation –Smoking Active Delayed Non –Distraction DV - Number of errors
Factorial ANCOVA Pattern Recognition NS: Errors …….. Distract ……. …… Driving Simulation AS: Errors …… Distract …… C T1 T2 G1 G2 TG11 TG12 TG21 TG22 CTG11 CTG12 CTG21 CTG
Alternative Experimental Designs Matched Samples Difference Scores