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Unformatted text preview: 1 Analysis of Variance ANOVA Hypothesis Testing Is there a mean difference between 2 populations? Solution: ttest Hypothesis Testing Is there a mean difference between 3 populations? Solution: Analysis of variance (ANOVA) Learning Objectives Know purpose, terminology, and special notation of analysis of variance. Know how to perform an analysis of variance for the data from a singlefactor, independentmeasures experiment. Know what are post hoc tests and when are they used. Know how to report ANOVA results using both a summary table and an Fratio (including df values). Know how to interpret these reports when they appear in scientic literature. Know how to compute percentage of variance accounted for as a measure of e f ect size for an analysis of variance. Introduction to Analysis of Variance Example of a research design with two factors. Factor 1: therapy technique (levels: I versus II) Factor 2: time (levels: before, after, and 6 months after). Factor : variable designating the groups being compared Levels : individual conditions or values that make up a factor Statistical Hypothesis for ANOVA Many different alternatives are possible. For example: Does room temperature affect learning performance? Learning performance under three temperature conditions: 50 , 70 , and 90 (three groups of participants). Problem of multiple comparisons Paired comparisons using ttest: Population 1 and Population 2 Population 1 and Population 3 Population 2 and Population 3 Type I error: rejecting H when there is no effect The Test Statistic for ANOVA Mean difference for more then two means? Standard Error Does room temperature affect learning performance? Goal: measure the amount of variability and explain where it comes from. Total variability: BetweenTreatments variance: how much difference exist between treatment conditions. WithinTreatment variance: how big the differences are when there is no treatment effect. The Fratio No treatment effect, F is near 1 Treatment has a significant effect, F > 1 ANOVA Notation ANOVA Notation Number of treatment conditions (number of levels of a factor) ANOVA Notation Number of treatment conditions (number of levels of a factor) Number of scores in each treatment ANOVA Notation Number of treatment conditions (number of levels of a factor) Number of scores in each treatment Total number of scores in a study = kn ANOVA Notation Number of treatment conditions (number of levels of a factor) Number of scores in each treatment Total number of scores in a study = kn ANOVA Notation Number of treatment conditions (number of levels of a factor) Number of scores in each treatment Total number of scores in a study = kn The structure and sequence of calculations for the analysis of variance. Partitioning the sum of squares ( SS ) for the independentmeasures analysis of variance....
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This note was uploaded on 02/24/2011 for the course PSYC 227 taught by Professor Shinkareva during the Fall '09 term at South Carolina.
 Fall '09
 Shinkareva

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