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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. 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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