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One-Way Between Subjects ANOVA

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Overview Purpose How is the Variance Analyzed? Assumptions Effect Size

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Purpose of the One-Way ANOVA Compare the means of two or more groups Usually used with three or more groups Independent variable (factor) may or may not be manipulated; affects interpretation but not statistics

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Why Not t-tests? Multiple t-tests inflate the experimentwise alpha level. ANOVA controls the experimentwise alpha level with an omnibus F-test.

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Why is it One Way? Refers to the number of factors How many WAYS are individuals grouped? NOT the number of groups (levels)

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Why is it Called ANOVA? Analysis of Variance Analyze variability of scores to determine whether differences between groups are big enough to reject the Null

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HOW IS THE VARIANCE ANALYZED? Divide the variance into parts Compare the parts of the variance

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Dividing the Variance Total variance: variance of all the scores in the study. Model variance: only differences between groups. Residual variance: only differences within groups.

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Model Variance Also called Between Groups variance Influenced by: – effect of the IV (systematic) – individual differences (non-systematic) – measurement error (non-systematic)

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Residual Variance Also called Within Groups variance Influenced by: – individual differences (non-systematic) – measurement error (non-systematic)

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Sums of Squares Recall that the SS is the sum of squared deviations from the mean Numerator of the variance Variance is analyzed by dividing the SS into parts: Model and Residual

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Sums of Squares SS Model = for each individual, compare the mean of the individual’s group to the overall mean SS Residual = compare each individual’s score to the mean of that individual’s group

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Mean Squares Variance Numerator is SS Denominator is df –Model df = number of groups -1 –Residual df = Total df – Model df

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Comparing the Variance

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ASSUMPTIONS Interval/ratio data Independent observations Normal distribution or large N Homogeneity of variance –Robust with equal n’s

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EFFECT SIZE FOR ANOVA Eta-squared ( 2 )indicates proportion of variance in the dependent variable explained by the independent variable

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Take-Home Points ANOVA allows comparison of three or more conditions without increasing alpha. Any ANOVA divides the variance and then compares the parts of the variance.

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