Differences Among Group Means: One-Way Analysis of Variance 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 Continuous dependent variable

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

ANOVA Source of Variance Between group variation Within group variation Total variation

ANOVA Degrees of Freedom Total = n-1 Between = k-1 Within = n-k (k = # of groups)

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)

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

BONFERRONI Desired alpha divided by number of comparisons Example

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

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

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

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

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

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

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

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.

Contrasts for Oneway