Analysis of Experimental Designs II: Factorial ANOVA and Statistical Interpretation

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WattsSEDU7006-8-41Experimental Designs IIExperimental Designs IIAnalysis of Experimental Designs II: Factorial ANOVA and StatisticalInterpretationJackson (2012) Chapter Exercises#2.A 4 x 6 factorial design has two independent variables; the first with four levels andthe second with six. A 4 x 6 factorial design has 24 conditions.#4.A cell mean represents the average score of participants in a condition, where aspecific value of each independent variable interacts. Main effect means represent the averagescore of participants for a single independent variable, where no interaction with otherindependent variables are considered.#6.In a complete factorial design comparison is made between each level of allindependent variables with each level of every other independent variable. An incompletefactorial design is considered incomplete because comparisons are not made between each levelof all independent variables with each level of every other independent variable; somecomparisons are not made (Jackson, 2012).#8.The number associated with the way of the ANOVA identifies the number ofindependent variables. A two-way ANOVA is an analysis of variance with two independentvariables. A three-way ANOVA is an analysis of variance comparing three independentvariables.#10.

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WattsSEDU7006-8-42SOURCEdfSSMSF0.050.01Factor A16060F(1, 30) =9Fcv =4.177.56Factor B24020F(2, 30) =3Fcv =3.325.39A x B29045F(2, 30) =6.75Fcv =3.325.39Error302006.667Total35390SOURCEdfSSMSF0.050.01Factor A24020F(2, 72) =3Fcv =3.154.98Factor B36020F(3, 72) =3Fcv =2.764.13A x B615025F(6, 72) =3.75Fcv =2.253.12Error721502.083Total83400SOURCEdfSSMSF0.050.01Factor A11010F(1, 36) =1.50Fcv =4.177.56Factor B16060F(1, 36) =9.00Fcv =4.177.56A x B12020F(1, 36) =3.00Fcv =4.177.56Error36601.667Total39150#10a.For the first study, Factor A,F(1,30) = 9.00,p< .01; Factor B,F(2,30) = 3.00, notsignificant; Interaction between A x B,F(2,30) = 6.75,p< .01.For the second study, Factor A,F(2,72) = 3.00 not significant; Factor B,F(3, 72) = 3.00,p< .05; Interaction between A x B,F(6.72) = 3.75,p< .01.For the third study, Factor A,F(1, 36) = 1.50 not significant; Factor B,F(1,36) = 9.00,p< .01; Interaction between A x B,F(1,36) = 3.00 not significant.#10b.The first study is a 2 x 3 factorial design and has six conditions. The second studyis a 3 x 4 factorial design and has 12 conditions. The third study is a 2 x 2 factorial design andhas four conditions.#10c.In the first study there were 36 participants in the six conditions. In the secondstudy there were 84 participants in the 12 conditions. In the third study there were 40participants in the four conditions.

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