ANALYSIS OF VARIANCE

By

ADETORO Gbemisola Wuraola

ANOVA is sub-divided into One- way ANOVATwo- 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.

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.

ONE-WAY ANOVAIt compares three or more means What you need:--One categorical variable with three or

more categoriesindependent--One continuous variable--- STEPS--Analyse--Compare means

--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

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.

Two-way ANOVATwo-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.

Steps

AnalyseSelect general linear modelSelect univariate click on dependent variable & move

it to the dependent variable box click on the independent variable &

move it into fixed factor box

Click on options , select descriptive, estimate of effect size, homogeneity test.

Click continueClick 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 continueOk

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.

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.