Ch11_ANOVA2

Ch11_ANOVA2 - Chapter 11 Chapter 11 Two-factor...

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Chapter 11 Two-factor Between-subjects Designs and Analysis of Variance Chapter 11 Two-factor Between-subjects Designs and Analysis of Variance

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Factorial Design Factorial Design involves at least two independent variables and each individual variable has two or more levels. Independent variable is also known as factor. Each distinctive value in the independent variable is known as a level.
Factorial Design Two Factors: A and B A: A1, Drug A; A2, Placebo B: B1, Drug B; B2, Placebo A1 A2 B1 A1B1 (S1) A2B1 (S2) B2 A1B2 (S3) A2B2 (S4)

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Example Research Question: Does “stereotype threat” diminish ability to perform well. Will females who are exposed to the stereotype that “women aren’t good at math” reduce performance in women who “care” about math performance. Procedure: Subjects were identified by “math identification” (importance of math to subject) and “stereotype threat presence” (awareness of the stereotype).
Stereotype threat Dependent variable: Math performance scores. Factor A: Level of math identification (low, high) Factor B: Stereotype threat condition (present, absent)

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Stereotype threat data (p. 285) Math identification Threat A1(low) A2 (high) B1 (yes) 97 90 80 107 80 70 87 81 95 90 B2 (no) 68 87 92 80 84 114 96 127 110 115 1. Separate sample in each cell. 1. Each score in A i B j cell is denoted by ijk X
Means A 1 A 2 B 1 90.8 84.6 X B1 = 87.7 B 2 82.2 112.4 X B2 = 97.3 X A1 = 86.5 X A2 = 98.5 X G =92.5

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How might we test?
Test that any mean is different – H 0 : μ A1B1 = μ A1B2 = μ A2B1 = μ A2B2 H 1 : not all equal

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ANOVA for testing if cell means are the same Source SS Df MS F A,B cells 2837 3 945.7 8.75** Error 1730.0 16 108.1 Total 4567.0 19 Note. Fcrit(3,16)=3.24 at α =.05; Fcrit(3,16)=5.29 at α =.01. *. Significant at p<.05 level; **: Significant at p<.01 level.
Does this answer the question? We know that at least one of the means is different from the others. Can use Tukey HSD to ascertain that differences over 18.8 are statistically significant so that A2B2 (no threat, high math identification) is “different.” But threat “effect” depend on math identification status?

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Main Effects Factor A: If there is a difference in mean math scores with math identification, there is a main effect of math identification. Factor B: If there is difference in mean math scores with stereotype threat, then there is a main effect of stereotype threat status.
Main effects SS • SS A = 10(87.7-92.5) 2 + 10(97.3-92.5) 2 = 720.0 • SS B = 10(86.5-92.5) 2 + 10(98.5-92.5) 2 = 460.8

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Source SS Df MS F A (math ident) 720.0 1 720.0 6.66* B (threat) 460.8 1 460.8 4.26 Error 1730.0 16 108.125 Total 4567.0 19 Note. F crit (1,16)=4.49 at
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Ch11_ANOVA2 - Chapter 11 Chapter 11 Two-factor...

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