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Lecture slides stats1.13.l17.air

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This lecture discusses factorial ANOVA: - Factorial ANOVA examines the effects of two or more independent variables on a dependent variable. It tests for main effects of each independent variable and interaction effects between the variables. - An example experiment examines the effects of driving difficulty and conversation demand on driving errors in a simulator. Results show significant main effects and interactions. - Follow-up tests include analyzing simple effects to further examine significant interactions. Assumptions include normality and homogeneity of variance. Effect sizes can be calculated using complete or partial eta-squared.

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Statistics One Lecture 17 Factorial ANOVA 1
Two segments ?? Factorial ANOVA ?? Example 2
Lecture 17 ~ Segment 1 Factorial ANOVA 3
Factorial ANOVA ?? Two Independent Variables (IVs) ?? One Dependent Variable (DV) 4
Example ?? Suppose an experiment is conducted to examine the effect of talking on a mobile phone while driving ¨C? IV1: Driving difficulty ¨C? IV2: Conversation demand ¨C? DV: Driving errors 5
Example 6
Factorial ANOVA ?? Three hypotheses can be tested: ¨C? More errors in the difficult simulator? ¨C? More errors with more demanding conversation? ¨C? More errors due to the interaction of driving difficulty and conversation demand? 7
Factorial ANOVA ?? Three F ratios ¨C? FA ¨C? FB ¨C? FAxB 8
Factorial ANOVA ?? Main effect: the effect of one IV averaged across the levels of the other IV 9
Example 10
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
Example 12
Factorial ANOVA ?? Simple effect: the effect of one IV at a particular level of the other IV 13
Example 14
Factorial ANOVA ?? Main effects and interaction effect are independent from one another 15
Factorial ANOVA ?? Remember, factorial ANOVA is just a special case of multiple regression ¨C? It is a multiple regression with perfectly independent predictors (IVs) 16
Partition SS in the DV SSB SSAxB SSA SSS/AB 17
Independent predictor variables X1 Y X2 X3 18
Remember, GLM ?? General Linear Model (GLM) ?? Y = B0 + B1X1 + B2X2 + B3X3 + e ?? Y = DV ?? X1 = A ?? X2 = B ?? X3 = (A*B) 19
F ratios ?? FA = MSA / MSS/AB ?? FB = MSB / MSS/AB ?? FAxB = MSAxB / MSS/AB 20
MS ?? ?? ?? ?? MSA = SSA / dfA MSB = SSB / dfB MSAxB = SSAxB / dfAxB MSS/AB = SSS/AB / dfS/AB 21
df ?? ?? ?? ?? ?? dfA = a - 1 dfB = b - 1 dfAxB = (a -1)(b - 1) dfS/AB = ab(n - 1) dfTotal = abn - 1 = N - 1 22
Follow-up tests ?? Main effects ¨C? Post-hoc tests ?? Interaction ¨C? Analysis of simple effects ?? Conduct a series of one-way ANOVAs (or t-tests) 23
Effect size ?? Complete 2 ¦Ç ?? ¦Ç2 = SSeffect / SStotal ?? Partial 2 ¦Ç ?? ¦Ç2 = SSeffect / (SSeffect + SSS/AB) 24
Effect size (complete) ¦Ç2 for the interaction = SSAxB / SSTotal SSB SSA SSAxB SSS/AB 25
Effect size (partial) ¦Ç2 for the interaction = SSAxB / (SSAxB + SSS/AB) SSB SSA SSAxB SSS/AB 26
Assumptions ?? Assumptions underlying factorial ANOVA ¨C? DV is continuous (interval or ratio variable) ¨C? DV is normally distributed ¨C? Homogeneity of variance 27
Segment summary ?? Factorial ANOVA ¨C? Three F-tests (FA ,FB ,FAxB) ¨C? Main effects ¨C? Interaction effect ¨C? Simple effects 28
Segment summary ?? Factorial ANOVA ¨C? Effect size (complete and partial eta-squared) ¨C? Post-hoc tests (follow main effects) ¨C? Simple effects analyses (follow interaction) ¨C? Homogeneity of variance assumption ?? Levene¡¯s test 29
END SEGMENT 30
Lecture 17 ~ Segment 2 Factorial ANOVA Example 31
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
Example ?? To manipulate driving difficulty, they simply made the driving course in the simulator more or less difficult 33
Example ?? To manipulate conversation demand, they included two ¡°talking¡± conditions: ¨C? In one condition the subject simply had to repeat what they heard on the other line of the phone 34
Example ?? To manipulate conversation demand, they included two ¡°talking¡± conditions: ¨C? 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 ¨C? For example, if you hear ¡°ship¡±, say a word that begins with the letter ¡°p¡±, such as ¡°peach¡± 35
Example ?? IV1 = driving difficulty (easy, difficult) ?? IV2 = conversation demand (none, low, high) ?? DV = errors in driving simulator 36
Example 37
Results: Levene¡¯s test 38
Results: Factorial ANOVA 39
Results: Simple effects ?? Simple effect of A at each level of B ¨C? Effect of driving difficulty at each level of conversation demand ?? Simple effect of B at each level of A ¨C? Effect of conversation demand at each level of driving difficulty 40
Example 41
Results: Simple effects 42
Results: Simple effects 43
Results: Simple effects 44
Segment summary 45
END SEGMENT 46
END LECTURE 17 47

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