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PSYC227_fall09_ANOVA

# PSYC227_fall09_ANOVA - Analysis of Variance ANOVA 1...

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1 Analysis of Variance ANOVA

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Hypothesis Testing Is there a mean difference between 2 populations? Solution: t-test
Hypothesis Testing Is there a mean difference between 3 populations? Solution: Analysis of variance (ANOVA)

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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 single-factor, independent-measures 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 F-ratio (including df values). Know how to interpret these reports when they appear in scientific literature. Know how to compute percentage of variance accounted for as a measure of e 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

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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 t-test: Population 1 and Population 2 Population 1 and Population 3 Population 2 and Population 3 Type I error: rejecting H 0 when there is no effect

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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: Between-Treatments variance: how much difference exist between treatment conditions. Within-Treatment variance: how big the differences are when there is no treatment effect.

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The F-ratio No treatment effect, F is near 1 Treatment has a significant effect, F > 1

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ANOVA Notation
ANOVA Notation Number of treatment conditions (number of levels of a factor)

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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

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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

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The structure and sequence of calculations for the analysis of variance.
Partitioning the sum of squares ( SS ) for the independent-measures analysis of variance.

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PSYC227_fall09_ANOVA - Analysis of Variance ANOVA 1...

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