国外社会科学统计课件17.ANOVA3.ppt

1、Statistics for the Social Sciences,Psychology 340 Spring 2005,Factorial ANOVA,Outline,Basics of factorial ANOVA Interpretations Main effects Interactions Computations Assumptions, effect sizes, and power Other Factorial Designs More than two factors Within factorial ANOVAs,Statistical analysis follo

2、ws design,The factorial (between groups) ANOVA:,Factorial experiments,Two or more factors Factors - independent variables Levels - the levels of your independent variables 2 x 3 design means two independent variables, one with 2 levels and one with 3 levels “condition” or “groups” is calculated by m

3、ultiplying the levels, so a 2x3 design has 6 different conditions,Factorial experiments,Two or more factors (cont.) Main effects - the effects of your independent variables ignoring (collapsed across) the other independent variables Interaction effects - how your independent variables affect each ot

4、her Example: 2x2 design, factors A and B Interaction: At A1, B1 is bigger than B2 At A2, B1 and B2 dont differ,Results,So there are lots of different potential outcomes: A = main effect of factor A B = main effect of factor B AB = interaction of A and B With 2 factors there are 8 basic possible patt

5、erns of results:,5) A & B 6) A & AB 7) B & AB 8) A & B & AB,1) No effects at all 2) A only 3) B only 4) AB only,2 x 2 factorial design,Condition mean A1B1,Condition mean A2B1,Condition mean A1B2,Condition mean A2B2,Whats the effect of A at B1? Whats the effect of A at B2?,Main effect of A,Main effec

6、t of B,Interaction of A x B,60,45,45,30,X,X,Examples of outcomes,Main effect of A,Main effect of B,Interaction of A x B,45,60,30,45,X,X,Examples of outcomes,Main effect of A,Main effect of B,Interaction of A x B,45,45,45,45,X,X,Examples of outcomes,Main effect of A,Main effect of B,Interaction of A

7、x B,45,45,30,30,Examples of outcomes,Factorial Designs,Benefits of factorial ANOVA (over doing separate 1-way ANOVA experiments) Interaction effects One should always consider the interaction effects before trying to interpret the main effects Adding factors decreases the variability Because youre c

8、ontrolling more of the variables that influence the dependent variable This increases the statistical Power of the statistical tests,Basic Logic of the Two-Way ANOVA,Same basic math as we used before, but now there are additional ways to partition the variance The three F ratios Main effect of Facto

9、r A (rows) Main effect of Factor B (columns) Interaction effect of Factors A and B,Partitioning the variance,Total variance,Stage 1,Between groups variance,Within groups variance,Stage 2,Factor A variance,Factor B variance,Interaction variance,Figuring a Two-Way ANOVA,Sums of squares,Figuring a Two-

10、Way ANOVA,Degrees of freedom,Figuring a Two-Way ANOVA,Means squares (estimated variances),Figuring a Two-Way ANOVA,F-ratios,Example,Example,Example,Example,Example: ANOVA table,Factorial ANOVA in SPSS,What we covered today is a completely between groups Factorial ANOVA Enter your observations in one column, use separate columns to code the levels of each factor Analyze - General Linear Model - Univariate Enter your dependent variable (your observations) Enter each of your factors (IVs) Output Ignore the corrected model, intercept, & total (for now) F for each main effect