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Unformatted text preview: 11/17/2010 1 Twoway ANOVA 1 Review • Onefactor 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 • Betweengroup variation… i.e., MS B • Withingroup variation… i.e., MS W Risktaking Therapy Counseling Therapy Control Therapy Review • The Ftest : 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) Twofactor ANOVA • Factorial ANOVAs with two factors are known as Twofactor ANOVAs • Although there are more complex ANOVA designs that involve the investigation of more than two factors, we will limit ourselves to the twofactor model in this class • Twofactor ANOVA models are expressed as: Why do a TwoFactor ANOVA? • Economy – Time and resources can be directed into a single research effort (requires smaller samples sizes per condition than a series of oneway 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 Risktaking 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. risktaking) 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.
 Spring '10
 Fairchild

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