Analysis of Variance (ANOVA) Similar to t-test, except can compare 3 or more groups Similar to t-test, except can compare 3 or more groups Compares variability (spread of means) between different groups with variability within each of the groups Compares variability (spread of means) between different groups with variability within each of the groups

ANOVA Significant F test indicates we can reject the null hypothesis (populations means are equal). Significant F test indicates we can reject the null hypothesis (populations means are equal). Significant F-test (p<.05) tells us if there is an general (omnibus) difference between types of subjects (levels) within the group Significant F-test (p<.05) tells us if there is an general (omnibus) difference between types of subjects (levels) within the group Next determine where group differences are: Next determine where group differences are: Planned comparisons (a priori) – want to examine specific comparisons Planned comparisons (a priori) – want to examine specific comparisons Unplanned comparisons (post-hoc) – want to explore where there are differences (more common) Unplanned comparisons (post-hoc) – want to explore where there are differences (more common)

One-way ANOVA Focus on one-way between-groups ANOVA Focus on one-way between-groups ANOVA One independent (grouping) variable with 3 or more levels or groups One independent (grouping) variable with 3 or more levels or groups One dependent continuous variable One dependent continuous variable Research Question: Do low/medium/high performing students differ in their levels of self-efficacy? Research Question: Do low/medium/high performing students differ in their levels of self-efficacy?

Assumptions of ANOVA Normality Normality Use histogram Use histogram Want normal curve (like bell-shape) Want normal curve (like bell-shape) Homogeneity of variances Homogeneity of variances ANOVA presumes variance in scores same for each of the groups ANOVA presumes variance in scores same for each of the groups Use Levene’s test for homogeneity of variances Use Levene’s test for homogeneity of variances Want significance level greater than.05 Want significance level greater than.05 If violated (p<.05), use Welsh and Brown-Forsythe tests If violated (p<.05), use Welsh and Brown-Forsythe tests

Procedures For post-hoc comparisons For post-hoc comparisons Analyze Analyze Compare means One-way ANOVA Dependent (cont.) variable -> “Dependent List” Independent (cat.) variable into “Factor” Missing values – Exclude case by case Click post-hoc (Tukey)

Example - ANOVA Research Question: Is there a difference in optimism scores for young, middle-aged, and old subjects (18-29, 30-44, 45+)? 1. Dataset: Survey3ED.sav (Pallant) 2. Use ANOVA to assess whether there are significant differences between age groups in their levels of optimism 3. Dependent variable is: Total Optimism (Toptim) 4. Independent variable is: Age group (AGEgp3) 5. Check Missing values (exclude case analysis by analysis) 6. Check Options (e.g., Levene’s test for equality of variances) 7. Check Post-hoc (Tukey)

Your turn Based on your research interests, what research questions would require a one-way ANOVA? Based on your research interests, what research questions would require a one-way ANOVA? Use the Omnibus dataset Use the Omnibus dataset Try it out! Try it out!