Lecture 12 Factorial ANOVA I

# Lecture 12 Factorial ANOVA I - Factorial ANOVA Part 1...

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Factorial ANOVA Part 1 Lecture 12

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Today Factorial ANOVA Conceptual background Main effects and interactions The ANOVA source table
ANOVA One way ANOVA- one independent variable with multiple levels Factorial ANOVA- two (or more) independent variables with multiple levels Repeated measures ANOVA- correlated samples within ANOVA

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American Idol Example Two Sample t test Research Question: Do mean votes for American Idols differ based on gender? Males Females 1 ) 2 )
American Idol Example One Way ANOVA Research Question: Do mean votes for American Idols differ based on attractiveness? Attractive Okay Unattractive 1 ) 2 ) 3 )

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American Idol Example Factorial ANOVA Research Question: Do mean votes 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 )
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
Design Notation Identified as R X C Number of rows by the number of columns Example: 2 x 3 ANOVA Row = 1 st independent variable: Gender 2 levels: Male & Female Column = 2 nd independent variable: Attractiveness 3 levels: Very attractive, ok, not attractive These are interchangeable (could be a 3 x 2 – if you flip your table).

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Notation Practice In the following slides, identify the following: Independent variable #1; levels of IV1 Independent variable #2; levels of IV2 R x C notation
Notation Practice Animal Dog Cat Sex Male 1 ) 2 ) Female 3 ) 4 ) IV1 = Sex (Male, Female) IV2 = Animal (Dog, Cat) R x C = 2 x 2 ANOVA

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Notation Practice Year in School Freshman Sophomore Junior Senior Sex Male 1 ) 2 ) 3 ) 4 ) Female 5 ) 6 ) 7 ) 8 ) IV1 = Sex (Male, Female) IV2 = Year in school (freshman, sophomore, junior, senior) R x C = 2 x 4 ANOVA
Notation Practice Major Psych Bus Bio Year in School 1st 1 ) 2 ) 3 ) 2nd 4 ) 5 ) 6 ) 3rd 7 ) 8 ) 9 ) 4th 10 ) 11 ) 12 ) IV1 = Year in school (1 st , 2 nd , 3 rd , 4 th ) IV2 = Major (Psych, Bus, Bio) R x C = 4 x 3 ANOVA

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Factorial Design Starting with a 2 X 2 ANOVA 2 independent variables (Sex, Attractiveness) Each has 2 levels (Male vs. Female; Attractive vs. Unattractive) Very Attractive Unattractive A 1 B 1 A 3 B 1 Female A 1 B 2 3 ) A 3 B 2 4 ) Attractiveness (A) Sex (B)

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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 12 Factorial ANOVA I - Factorial ANOVA Part 1...

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