- Number of pupils in sixth form (e.g., 120)
Each of these variables represents a property or characteristic of a school which is likely
to vary from one school to another. Variables may represent characteristics of objects
(such as schools), or attributes of individuals (height, sex and exam score) or other
entities.
Numbers are used to represent properties of variables and impart information about
them. When used in this way the values associated with each variable are called data.
One such piece of information is a datum. Many observations in education involve
categorizing and measuring data. An important first distinction to make when examining
data is to decide whether observed quantities have been obtained by enumeration (which
is categorical or frequency data) or by measurement (which gives quantitative data).
This distinction has important implications for the choice of statistical methods used.
Categorical VariablesWhen observations are categorized, they are not merely placed indiscriminately into
categories; qualitative judgments based on similarities and differences are made.
Numbers which are used in a qualitative way have no more than a labelling role. A
number used in a categorical labelling role carries no implied order, amount or quantity
and is used simply as a description. For example, each school might be categorized by
religious denomination: 1 representing Roman Catholic; 2 representing Jewish; 3
representing Church of England; etc. Numbers are used here to label observations about
the categories of schools. The category variable in this case ‘school denomination’, is
referred to as a nominal variable. This qualitative use of numbers is the most limited
form of data classification. It simply takes advantage of the property of identity, and the
assignment of numbers is arbitrary. The only rule to apply is that objects must be
assigned to categories on a logical basis. For example, Jewish schools do not belong to
the same denominational class of schools as Roman Catholic schools. The fact that
Roman Catholic schools are assigned a value of 1 and Jewish schools a value of 2 is
purely arbitrary and these numbers cannot be used in any meaningful mathematical way.
Whereas ‘sibling attends the school’ and ‘state of buildings’ are also categorical type
variables, the latter variable is different from the other nominal variables because it
implies ordering of qualitative difference. A school may be judged according to how
much (more or less) repair work is required. ‘State of buildings’ is an ordinal variable. If
schools were classified as belonging to one of the three ordered categories of state of
buildings (excellent, average, poor) then this would be an example of an ordered
category type of variable with the number 1 perhaps representing an ‘excellent
condition’ category, 2 representing an ‘average condition’ category and 3 a ‘poor
condition’ category. The assignment of numbers to categories in this instance reflects the
order of the qualitative difference.
The statistical variable ‘position of school in league tables of school examination
results’ is an ordinal variable of individual rank type, rather than of category rank type,
because each school has an individual ranked position (or possibly a joint ranking). A
school’s individual ranked position might, for example, be based on the percentage of 15-
year-old pupils achieving 5 or more GCSEs at grades A to C. Every school could be
listed in order using the percentage of achievers as the criterion. For example, in
Measurement issues 19