1. Differences Among Group Means: One-Way Analysis of Variance
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. ANOVA Degrees 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

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