Lecture 13 Factorial ANOVA II

# Lecture 13 Factorial ANOVA II - Factorial ANOVA Part 2...

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Factorial ANOVA Part 2 Lecture 13

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Today More on Factorial ANOVA How to do calculations Working with the ANOVA source table Following up on results Tukey’s HSD Graphing mean values
Factorial ANOVA Factorial ANOVA is an experimental design with two or more independent variables Factor = independent variable Each variable can have two or more levels An advantage: we can look at the effect of each variable , AND the interaction between the two variables

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Factorial ANOVA Design Factor A Row Means A1 A2 A3 Factor B B1 Scores on A 1 B 1 1 ) Scores on A 2 B 1 2 ) Scores on A 3 B 1 3 ) µ b1 B2 Scores on A 1 B 2 4 ) Scores on A 2 B 2 5 ) Scores on A 3 B 2 6 ) µ b2 Column Means µ a1 µ a2 µ a3 µ grand
American Idol Example  Factorial ANOVA Research Question: do mean scores for American Idols differ based on attractiveness and gender? Attractive Okay Unattractive Male A 1 B 1 1 ) A 2 B 1 2 ) A 3 B 1 3 ) Female A 1 B 2 4 ) A 2 B 2 5 ) A 3 B 2 6 )

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American Idol Example: Data Attractiveness (A) Attractive Okay Unattractive Gender (B) Male 1 2 1 4 5 6 6 4 4 Female 8 9 10 5 6 6 1 2 3
What questions can we ask? Research Question 1: general Are there any mean differences between each group? Research Question 2: main effect #1 Are there mean differences between levels for IV1? Research Question 3: main effect #2 Are there mean differences between levels for IV2? Research Question 4: interaction Are there mean differences between levels for IV1 depending on levels for IV2?

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Idol example: Research questions Research Question 1: general Are there any mean differences between each group on American idol scores? Research Question 2: main effect #1 Does attractiveness level matter to mean scores? Research Question 3: main effect #2 Does gender matter to mean scores? Research Question 4: interaction Does the score for gender depend on how attractive the person is?
For each research question,  there is… A null hypothesis An alternative hypothesis A calculated test statistic A critical value that must be compared to calculated value A conclusion

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In each case, the null hypothesis (H 0 ) says there is no difference between the groups. The alternative hypothesis (H a ) says that there is a difference.
Hypotheses: Question 1 H 0 : There are no differences in mean rating scores based on attractiveness or gender. H o : µ attractive male = µ attractive female = µ unattractive male = µ unattractive female H a : At least one of the group means differ from the others.

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Hypotheses: Question 2 H 0 : There is no difference in American idol mean scores based on attractiveness. H
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## This note was uploaded on 05/25/2010 for the course PSYC 11 taught by Professor Ryne during the Spring '10 term at UC Riverside.

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Lecture 13 Factorial ANOVA II - Factorial ANOVA Part 2...

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