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Univariate Statistics PSYC*6060

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.

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Univariate Statistics PSYC*6060

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  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. m A1 A2 A3 1 2 3 4 5 6 1 1 0 0 1 1 0 0 1 0 1 0 1 0 1 0 1 0 0 1 1 0 0 1 X = Design matrices Allows us to look at ANOVA in a multiple regression framework Y ij = m + tj + e ij y = Xb + e Y 11= m + t1 + e 11 Y21 = m + t1 + e 21 Y12 = m + t2 + e12 Y22 = m + t2 + e22 Y13 = m + t3 + e13 Y23 = m + t3 + e23

  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 X11 = 14 X12 = 20 X1. = 18 Arizona 13 15 18 14 10 24 25 17 16 18 12 16 17 51 10 14 X21 = 14 X22 = 20 X2. = 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 Blood sugar Sum of squares - regression Sum of squares - error Skin fold (cm)

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

  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 regt,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 • 1 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

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