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Lecture slides stats1.13.l17.air
- 1. Statistics One Lecture 17 Factorial ANOVA 1
- 2. Two segments ≒ Factorial ANOVA ≒ Example 2
- 3. Lecture 17 ~ Segment 1 Factorial ANOVA 3
- 4. Factorial ANOVA ≒ Two Independent Variables (IVs) ≒ One Dependent Variable (DV) 4
- 5. Example ≒ Suppose an experiment is conducted to examine the effect of talking on a mobile phone while driving IV1: Driving difficulty IV2: Conversation demand DV: Driving errors 5
- 6. Example 6
- 7. Factorial ANOVA ≒ Three hypotheses can be tested: More errors in the difficult simulator? More errors with more demanding conversation? More errors due to the interaction of driving difficulty and conversation demand? 7
- 8. Factorial ANOVA ≒ Three F ratios FA FB FAxB 8
- 9. Factorial ANOVA ≒ Main effect: the effect of one IV averaged across the levels of the other IV 9
- 10. Example 10
- 11. Factorial ANOVA ≒ Interaction effect: the effect of one IV depends on the other IV (the simple effects of one IV change across the levels of the other IV) 11
- 12. Example 12
- 13. Factorial ANOVA ≒ Simple effect: the effect of one IV at a particular level of the other IV 13
- 14. Example 14
- 15. Factorial ANOVA ≒ Main effects and interaction effect are independent from one another 15
- 16. Factorial ANOVA ≒ Remember, factorial ANOVA is just a special case of multiple regression It is a multiple regression with perfectly independent predictors (IVs) 16
- 17. Partition SS in the DV SSB SSAxB SSA SSS/AB 17
- 19. Remember, GLM ≒ General Linear Model (GLM) ≒ Y = B0 + B1X1 + B2X2 + B3X3 + e ≒ Y = DV ≒ X1 = A ≒ X2 = B ≒ X3 = (A*B) 19
- 20. F ratios ≒ FA = MSA / MSS/AB ≒ FB = MSB / MSS/AB ≒ FAxB = MSAxB / MSS/AB 20
- 21. MS ≒ ≒ ≒ ≒ MSA = SSA / dfA MSB = SSB / dfB MSAxB = SSAxB / dfAxB MSS/AB = SSS/AB / dfS/AB 21
- 22. df ≒ ≒ ≒ ≒ ≒ dfA = a - 1 dfB = b - 1 dfAxB = (a -1)(b - 1) dfS/AB = ab(n - 1) dfTotal = abn - 1 = N - 1 22
- 23. Follow-up tests ≒ Main effects Post-hoc tests ≒ Interaction Analysis of simple effects ≒ Conduct a series of one-way ANOVAs (or t-tests) 23
- 24. Effect size ≒ Complete 2 侶 ≒ 侶2 = SSeffect / SStotal ≒ Partial 2 侶 ≒ 侶2 = SSeffect / (SSeffect + SSS/AB) 24
- 25. Effect size (complete) 侶2 for the interaction = SSAxB / SSTotal SSB SSA SSAxB SSS/AB 25
- 26. Effect size (partial) 侶2 for the interaction = SSAxB / (SSAxB + SSS/AB) SSB SSA SSAxB SSS/AB 26
- 27. Assumptions ≒ Assumptions underlying factorial ANOVA DV is continuous (interval or ratio variable) DV is normally distributed Homogeneity of variance 27
- 28. Segment summary ≒ Factorial ANOVA Three F-tests (FA ,FB ,FAxB) Main effects Interaction effect Simple effects 28
- 29. Segment summary ≒ Factorial ANOVA Effect size (complete and partial eta-squared) Post-hoc tests (follow main effects) Simple effects analyses (follow interaction) Homogeneity of variance assumption ≒ Levenes test 29
- 30. END SEGMENT 30
- 31. Lecture 17 ~ Segment 2 Factorial ANOVA Example 31
- 32. Example ≒ Strayer and Johnson (2001) conducted an experiment to examine the effect of talking on a mobile phone while driving ≒ They tested subjects in a driving simulator . 32
- 33. Example ≒ To manipulate driving difficulty, they simply made the driving course in the simulator more or less difficult 33
- 34. Example ≒ To manipulate conversation demand, they included two talking conditions: In one condition the subject simply had to repeat what they heard on the other line of the phone 34
- 35. Example ≒ To manipulate conversation demand, they included two talking conditions: In the other condition the subject had to think of and then say a word beginning with the last letter of the last word spoken on the phone For example, if you hear ship, say a word that begins with the letter p, such as peach 35
- 36. Example ≒ IV1 = driving difficulty (easy, difficult) ≒ IV2 = conversation demand (none, low, high) ≒ DV = errors in driving simulator 36
- 37. Example 37
- 40. Results: Simple effects ≒ Simple effect of A at each level of B Effect of driving difficulty at each level of conversation demand ≒ Simple effect of B at each level of A Effect of conversation demand at each level of driving difficulty 40
- 41. Example 41
- 46. END SEGMENT 46