Analysis of Variance: One-Way and Two-Way ANOVA

1. ANALYSIS OF VARIANCE By ADETORO Gbemisola Wuraola

2. ANOVA is sub-divided into • One- way ANOVA • Two- way ANOVA • “n” – way ANOVA ONE-WAY ANALYSIS It is used to determine possible effect of a single non-metric independent variable (factor) on a metric dependent variable.

3. In one-way ANOVA we seek to determine if three or more categories of an independent variable is significantly different in terms of average values of a continuous dependent variable.

4. ONE-WAY ANOVA • It compares three or more means What you need: • --One categorical variable with three or more categoriesindependent • --One continuous variable--- STEPS • --Analyse • --Compare means

5. --One-way ANOVA --Move dependent variable into Dependent list box --Move independent variable into Factor box --Option (click descriptive & means plot) ---and make sure a dot is the Exclude cases analysis by analysis box --Continue --OK

6. Interpretation When the ANOVA value has a p-value less than or equal to 0.05, it is said that the categories are significantly different; otherwise it is not. POST-HOC TEST • Post hoc test becomes important when p-value indicates that the categories are significantly different. This test enables us to identify which of the group (groups) are significantly different. • This is indicated with placement of star (*) in front of the categories.

7. Two-way ANOVA • Two-way ANOVA is used when the goal is to test the effect of two categorical independent variables on a continuous dependent variable—this is the test for “main effect”. • It also test for “interaction effect”. E.g. Education with 4 categories and Sex (male, female), and income as the dependent variable. • Is educational categories significantly different among males or females.

8. Steps • Analyse • Select general linear model • Select univariate • click on dependent variable & move it to the dependent variable box • click on the independent variable & move it into fixed factor box

9. Click on options , select descriptive, estimate of effect size, homogeneity test. • Click continue • Click post-hoc • Click on independent variables with at least three (3) categories & move into the post-hoc box. • Select the test for it – turkey. • Click continue • Ok

10. INTERPRETATION Descriptive statistics • Check that the statistics are ok Levene's Test of Equality of Error Variance Table • This test an underlying assumption: The sig. value must be greater than 0.05 (or 0.01). Main output—Test of Between-Subject effects Table • Interaction effects(two indep. Variables separated by *): if Sig. less than 0.05 it means there is interaction effect—there is significant difference in first independent variable GIVEN the second one. • Main Effects—check each of the indep. Variables and their Sig. value; if less than 0.05, that variable is having a main effect (i.e. the categories are significantly different in terms of the dep. Variable). Otherwise not sig. different.

11. Post Hoc If your main effects or interaction effects is established through the Sig. value(s) for the independent variables is significant. • Then under the table Multiple Comparisons • check the significant variable and see where you have *. Where this appears indicates the categories are the ones significantly different.