Centre for
Multilevel
Modelling
The development of this E-Book has been
supported by the British Academy.
Analysis of Variance practical
In this practical we will investigate how we model the influence of a categorical predictor on a continuous response.
In this example, we will test formally for an association between a student's test score on the PISA science test, SCISCORE, and their
parents' educational attainment, an indicator often used to capture a family's socio-economic resources. The variable PAREDU classifies
highest parental educational qualification into three categories and, as such, this an appropriate predictor or independent variable to use in
ANOVA (known as a factor with three levels in ANOVA terminology). The statistical test explores whether the mean science test score is
different across the three educational groups. Evidence of achievement gaps of this kind is often used in the discussion and quantification
of inter-generational social mobility.
ANOVA in SPSS (Practical)
In this case we are interested in the effect of PAREDU on our response variable SCISCORE. PAREDU has 3 categories: Low: GCSE or equiv,
Medium: A-level or equiv, High: University degree. We will begin to look at this relationship graphically and look at the distribution of
SCISCORE separately for each category and a good way to do this is via a box plot. To do this in SPSS:
Select Boxplot from the Legacy Dialogs submenu of the Graphs menu.
Select Simple and Summaries for groups of cases and click on the Define button.
Transfer the Science test score[SCISCORE] variable to the Variable box.
Transfer the Highest qualification of parent[PAREDU] variable to the Category Axis box.
Click on the OK button.
This will produce a table detailing the numbers of valid observations which we do not show here and then a plot with a box for each
category as shown below:
A boxplot uses the 1st and 3rd quantiles of the data to form the box with the median presented as a line in the middle of the box. In this
case the medians are for each category as follows: Low: GCSE or equiv = 502.5175, Medium: A-level or equiv = 523.0240 and for High:
University degree = 561.2170 and we see that category High: University degree has the highest median whilst category Low: GCSE or equiv
has the lowest median.
In fact we will be fitting an analysis of variance (ANOVA) model and this is based on group means rather than medians and so an
alternative error bar plot is useful. To get this in SPSS do the following:
Select Error Bar from the Legacy Dialogs submenu of the Graphs menu.
Select Simple and Summaries for groups of cases as for the boxplot and click on the Define button.
Transfer the Science test score[SCISCORE] variable to the Variable box.
Transfer the Highest qualification of parent[PAREDU] variable to the Category Axis box.
Click on the OK button.
The graph will appear as shown below:
