双因素方差分析.ppt

1、Two-way ANOVA,Two-way between-subjects ANOVA,Example: Beer-goggles effect,After alcohol had been consumed, subjective perceptions of physical attractiveness would become more inaccurate 2 between-subjects IVs: Gender: male and female Amount of alcohol consumed: 0, 2 pints, and 4 pints,How to enter d

2、ata in SPSS?,Gender: F (1, 42) = 2.03, p.05 Alcohol consumption: F (2, 42) = 20.07, p.001 Gender X Alcohol consumption: F (2, 42) = 11.91, p.001,Corrected Model = Gender + Alcohol + Gender * Alcohol Corrected Model + Error = Corrected Total Corrected Total + Intercept = Total Corrected Model / Corre

3、cted Total = R Squared,Interaction and main effects,Gender, p.05 Alcohol, p.05 Gender X Alcohol, p.001 Main effect is justified by interaction!,Estimated marginal means,Simple main effect of Alcohol,Syntax 1: GLM Attractiveness by alcohol gender /EMMEANS = tables(alcohol*gender)compare(alcohol),Cant

4、 see how the three levels of alcohol differed within each gender group.,Simple main effect of Alcohol,Syntax 2: manova attractiveness by Alcohol(1 3) Gender (0 1) /error = within /design = alcohol within gender(1) alcohol within gender(2).,Simple main effect of Alcohol,2 one-way ANOVA for alcohol on

5、 each level of gender with paired comparisons with correction,When Gender is Male,Participant numbers were different from those used in MANOVA, so MSs of Alcohol were identical, but F values were different.,When Gender is Female,Output report,ANOVA results show that the main effect of Gender is not

6、significant, F (1, 42) = 2.03, p.05, but the main effect of Alcohol consumption is significant, F (2, 42) = 20.07, p.05 (p=.546).,Graph for interaction,Use estimated marginal means,Use excel !,Graph with error bars!,For another example: Instructions and scores,Q: Do exam instruction affect scores of

7、 students with varying abilities? Two IVs: Instruction: neutral, encourage Ability of student: low, medium, high DV: scores,Output,Method: F (1, 54) = 27.19, p.05,No significant interaction, no simple effects Report contrast or paired comparisons for significant main effects,Two-way repeated ANOVA,E

8、xample: wine attitude,Attitudes towards stimuli can be changed using positive or negative imagery (Field, 2005; Stuart, Shimp, & Engle, 1987) Q: does imagery change attitudes towards wine? IV: drink (beer, wine, water) imagery (positive, negative, neutral) DV: attitudes (-100 100),Example: wine atti

9、tude,IV: drink (beer, wine, water) imagery (positive-happy, negative-corpse, neutralperson in an armchair) DV: attitudes (-100 100),Result from ANOVA,Drink: F(1.15, 21.93)=5.11, p=.03 Imagery: F(1.50, 28.40)=122.57, p.001 Drink X Imagery: F(4, 76)=17.16, p.001,Interaction between Drink and Imagery,S

10、imple main effect of Drink,manova beerpos beerneg beerneut winepos wineneg wineneut waterpos waterneg waterneut /wsfactors = drink(3) imagery(3) /wsdesign = drink within imagery(1) drink within imagery(2) drink within imagery(3).,Output of simple main effect of Drink (MANOVA),Simple main effect of D

11、rink (one-way repeated ANOVA)-imagery 1(positive),F(1.55, 29.53)=3.06, p=.074,Simple main effect of Drink (one-way repeated ANOVA)-imagery 2 (negative),F (1.22, 23.26)=14.08, p=.001,Simple main effect of Drink (one-way repeated ANOVA)-imagery 2 (negative),Simple main effect of Drink (one-way repeate

12、d ANOVA)-imagery 3 (neutral),F(1.33, 25.21) = 7.27, p=.008,Simple main effect of Drink (one-way repeated ANOVA)-imagery 3 (neutral),Two-way mixed design ANOVA,IVA: between-subjects IVB: Within-subject,Example: two-way mixed design,Q: How do age and task difficulty affect task performance? IVs: A: Ag

13、e (between-subject) B: Task difficulty (within-subject) DV: task performance AnalyzeGLM-Repeated measures,Output for within-subject effect,Difficulty: F(2, 66)=152.27, p.001, Difficulty X Age: F (4, 66)=36.60, p.001,Output for between-subject effect,Age: F (2, 33)=62.82, p.001,Interaction between Di

14、fficulty X Age,Difficulty X Age: F (4, 66)=36.60, p.001,Simple main effect of Task Difficulty (MANOVA),manova a1 a2 a3 by age (1,3) /wsfactors = a (3) /wsdesign = a /design = mwithin age(1) mwithin age(2) mwithin age(3).,Output of simple main effect of Task Difficulty (MANOVA),Age (1), Difficulty: F

15、 (2,66)=82.72, p.001 Age (2), Difficulty: F (2,66)=141.92, p.001 Age (3), Difficulty: F (2,66)=0.83, p=.442,* * * * * * * * * * * * * * * * * A n a l y s i s o f V a r i a n c e - Design 1 * * * * * * * * * * * * * * * * * Tests involving A Within-Subject Effect. AVERAGED Tests of Significance for a

16、 using UNIQUE sums of squares Source of Variation SS DF MS F Sig of F WITHIN+RESIDUAL 95.50 66 1.45 MWITHIN AGE(1) BY A 239.39 2 119.69 82.72 .000 MWITHIN AGE(2) BY A 410.72 2 205.36 141.92 .000 MWITHIN AGE(3) BY A 2.39 2 1.19 .83 .442,Simple main effect of Task Difficulty (one-way repeated ANOVAs)1

17、,When Age=1, Difficulty: F(1.38, 15.14)=84.19, p.001,Simple main effect of Task Difficulty (one-way repeated ANOVAs)1,Simple main effect of Task Difficulty (one-way repeated ANOVAs)2,When Age=2, F (2,22)=119.07, p.001,Simple main effect of Task Difficulty (one-way repeated ANOVAs)2,Simple main effec

18、t of Task Difficulty (one-way repeated ANOVAs)3,When Age=3, F(2,22)=1.00, p=.384,Simple main effect of Age (MANOVA) 1,manova a1 a2 a3 by age (1,3) /wsfactors = a (3) /wsdesign = mwithin a(1) mwithin a(2) mwithin a(3) /design = age.,Tests involving MWITHIN A(1) Within-Subject Effect. Tests of Signifi

19、cance for T1 using UNIQUE sums of squares Source of Variation SS DF MS F Sig of F WITHIN+RESIDUAL 88.83 33 2.69 MWITHIN A(1) 4624.00 1 4624.00 1717.73 .000 AGE BY MWITHIN A(1) 547.17 2 273.58 101.63 .000,Difficulty (1): Age, F(2, 33) = 101.63, p.001,Simple main effect of Age (MANOVA) 2,Difficulty (2

20、): Age, F (2, 33)=53.78, p.001 Difficulty (3): Age, F (2, 33)=11.95, p.001,Tests involving MWITHIN A(2) Within-Subject Effect. Tests of Significance for T2 using UNIQUE sums of squares Source of Variation SS DF MS F Sig of F WITHIN+RESIDUAL 87.33 33 2.65 MWITHIN A(2) 2304.00 1 2304.00 870.60 .000 AGE BY MWITHIN A(2) 284.67 2 142.33 53.78 .000,Tests involving MWITHIN A(3) Within-Subject Effect. Tests of Significance for T3 usin