November 1994, the School League Table of Examination results was published.
Selecting at random Bolton Education Authority in the NW of England, and excluding
maintained special schools and independent schools, the school in the Authority with the
lowest rank position had a percentage pass rate of 21 per cent and the school which was
ranked the highest had a percentage pass rate of 66 per cent.
In this example, numbers are used to label and to rank in order individual schools.
Ranking of individual schools in this way necessitates the availability of examination
information from each and every school. Similar to ordered categories, the numbers
assigned to individually ranked schools serve as labels and show only differences in
qualitative order.
What do you think the statistical variable ‘position of school in league
table’, based on the percentage of 15-year-olds achieving 5 or more
GCSE passes at grade C or better, is meant to measure? What do you
think about the construct validity of this measure?It is possible that examination passes are thought to be a measure of school performance.
If this is the case one should consider precisely what is being measured or counted and
then ask yourself what other factors might account for the number of examination passes
in a school.
A non-exhaustive list is as follows:
the ability of pupils on entering the school;
the number of pupils entered for exams and the number of exams taken;
the comparability of exams in terms of difficulty;
the effectiveness of teaching;
the school examination policy, for example, a school that only enters pupils
who are thought to have a good chance of obtaining at least a grade C.
As numbers are assigned to individual schools on the basis of ranked position, these
numbers should only be used in certain ways. For example, non-parametric or
distribution free statistics should be used rather than parametric statistics. These terms
will be explained in more detail in later chapters. For the time being, it is sufficient to
consider non-parametric statistics as statistical procedures which do not depend upon
certain distributional and measurement assumptions. Non-parametric statistics are often
used when data are considered to be categorical, that is when statistical variables are at
the nominal or ordinal level of measurement or when a data distribution is not equally
dispersed around its mid-point.
Ranking scores is a simple procedure which sometimes causes confusion. Scores are
ranked in terms of their size, which establishes their relative location. Each score is
assigned a rank of 1, 2, 3, 4, 5, etc, in order of its magnitude. It does not matter whether
the smallest score is given the highest or lowest rank unless the value has some intuitive
meaning. For example, a rank position of 1st in a school league table makes most sense if
it is related to the school which has the best examination pass rate. Sometimes schools
may achieve the same examination pass rate. When this occurs the schools share a ranked
Statistical analysis for education and psychology researchers 20