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One-Way Between Subjects ANOVA

One-Way Between Subjects ANOVA. Overview. Purpose How is the Variance Analyzed? Assumptions Effect Size. Purpose of the One-Way ANOVA. Compare the means of two or more groups Usually used with three or more groups

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One-Way Between Subjects ANOVA

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  1. One-Way Between Subjects ANOVA

  2. Overview • Purpose • How is the Variance Analyzed? • Assumptions • Effect Size

  3. 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

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

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

  6. 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

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

  8. 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.

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

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

  11. 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

  12. 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

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

  14. Comparing the Variance

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

  16. EFFECT SIZE FOR ANOVA • Eta-squared (h2)indicates proportion of variance in the dependent variable explained by the independent variable

  17. Reporting F-test in APA Format A one-way between-subjects ANOVA indicated a significant difference among the three conditions, F(2,57) = 88.55, p < .001, h2 = .76.

  18. Review Question! What does an eta-squared of .76 represent?

  19. Review Question! What are the three things than can cause Model Variance?

  20. Review Question! How is variance related to sum of squares?

  21. Choosing Stats Individuals participating in an alcohol abuse treatment program rate their craving for alcohol at four points in time: immediately after beginning the program and then one, two, and three months after beginning the program. You want to determine whether there is a significant decrease in alcohol craving over time.

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