Lecture 17_two-way ANOVA

Lecture 17_two-way ANOVA - 11/17/2010 1 Two-way ANOVA 1...

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Unformatted text preview: 11/17/2010 1 Two-way ANOVA 1 Review • One-factor ANOVA : – Allowed us to assess the mean differences between several groups • e.g. the effect of therapy on depression in three groups: – Total variation in the dependent variable, depression, was separated into two parts • Between-group variation… i.e., MS B • Within-group variation… i.e., MS W Risk-taking Therapy Counseling Therapy Control Therapy Review • The F-test : The ratio of between group to within group variation W B MS MS F Treatment + Error Error 11/17/2010 2 Factorial ANOVA • More than one factor in a design requires a FACTORIAL ANOVA • Levels of each factor are completely crossed with one another to create several unique treatment conditions in the design – A 2x2 factorial design has 2 factors and four treatment conditions to which subjects can be assigned; a 3x6x2 factorial design has 3 factors and 36 treatment conditions; a 3x6x2x2 factorial design has 4 factors and 72 treatment conditions • Subjects are randomly assigned to only one treatment condition (called a “cell“) (# of levels of Row Factor)x(# of levels of Column Factor) Two-factor ANOVA • Factorial ANOVAs with two factors are known as Two-factor ANOVAs • Although there are more complex ANOVA designs that involve the investigation of more than two factors, we will limit ourselves to the two-factor model in this class • Two-factor ANOVA models are expressed as: Why do a Two-Factor ANOVA? • Economy – Time and resources can be directed into a single research effort (requires smaller samples sizes per condition than a series of one-way designs would) • Control – Can isolate/examine the effect of one factor while controlling for the influence of the other • Generalizability – More than one factor is usually at work in the real world • Interactions – Factorial ANOVAs allow you to consider how the variables work both together and separately 11/17/2010 3 A 2x3 ANOVA Example • A researcher is interested in comparing three types of therapy to treat depression and whether the number of therapy sessions a subject receives affects levels of depression. She is also interested if the therapies differentially perform across number of therapy sessions. • What three research questions does s/he have? Type of Therapy Control Counseling Risk-taking Therapy Duration Three Sessions Six Sessions Research Questions 1. Do mean levels of depression differ across therapy duration (3 vs. 6 sessions)? 2. Do mean levels of depression differ across therapy type (control vs. counseling vs. risk-taking) 3. Do the type of therapy as well as the therapy duration work together to affect mean levels of depression?...
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This note was uploaded on 02/17/2011 for the course PYSC 227 taught by Professor Fairchild during the Spring '10 term at South Carolina.

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Lecture 17_two-way ANOVA - 11/17/2010 1 Two-way ANOVA 1...

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