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Chapter 6

Chapter 6. Differences Among Group Means: One-Way Analysis of Variance. One-Way Analysis of Variance. ANOVA Comparison of group means. ONEWAY ANOVA. One independent variable Two or more levels. ANOVA. Type of Data Required Nominal-level independent variable/s

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Chapter 6

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  1. Chapter 6 Differences Among Group Means: One-Way Analysis of Variance

  2. One-Way Analysis of Variance • ANOVA • Comparison of group means

  3. ONEWAY ANOVA • One independent variable • Two or more levels

  4. ANOVA • Type of Data Required • Nominal-level independent variable/s • Continuous dependent variable

  5. ANOVA • Assumptions • Mutually exclusive groups • Normally distributed dependent variable • Homogeneity of variance

  6. ANOVA • Source of Variance • Between group variation • Within group variation • Total variation

  7. ANOVADegrees of Freedom • Total = n-1 • Between = k-1 • Within = n-k • (k = # of groups)

  8. POST-HOC TESTS • Scheffe • Bonferroni • Least Significant Difference Test (LSD) • Tukey's Honestly Significant Difference (HSD) • Student Newman-Keuls • Tukey's Wholly Significant Difference (WSD)

  9. SCHEFFE • Critical value changed based on number of comparisons • Formula • Fcv = (k-1) (F alpha) • When df = 2,30, p=.05, Fcv = 3.32 • Fcv = (3-1) (3.32) = 6.64

  10. BONFERRONI • Desired alpha divided by number of comparisons • Example • .05/number of comparisons

  11. LEAST SIGNIFICANT DIFFERENCE (LSD) • Equivalent to multiple t tests • Pooled estimate of variance used rather than specific group variance

  12. TUKEY’S HONESTLY SIGNIFICANT DIFFERENCE (HSD) • Most conservative • Critical values remain same, regardless of total number of means to be compared

  13. STUDENT NEWMAN-KEULS • Similar to Tukey’s HSD • Critical values do not stay same, reflect variables being compared

  14. TUKEY’S WHOLLY SIGNIFICANT DIFFERENCE • Critical values are the average of Tukey’s HSD and Newman-Keuls • Therefore, intermediate in conservatism between those two measures

  15. PLANNED COMPARISONS • A priori contrasts • Orthogonal contrasts • n-1 contrasts • sum of each vector equals zero • sum of cross-products equals zero

  16. Research Question • Do the three smoking groups differ significantly in reported life satisfaction?

  17. SPSS - Oneway • ANALYZE • Compare Means • One-Way ANOVA • Post hoc -select test • Options • Descriptives • Homogeneity of variance test • Brown Forsythe • Welch

  18. Hypotheses for Oneway • The still smoking group will score significantly lower on life satisfaction than the other two groups. • The never smoked and the quit smoking groups will not differ significantly on life satisfaction.

  19. Contrasts for Oneway

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