data include Spearman’s Rho and Wilcoxon Mann-Whitney (see Chapter 7). These tests
are frequently used with higher levels of measurement (interval and ratio) and the data
are then ranked.
Interval ScaleAn interval scale, in addition to labelling and ordering has the essential requirement of
equality of units of measurement. That is, a given numerical distance on an equal interval
scale of measurement, is associated with the same empirical distance on a real
continuum. Interval scales are amenable to certain mathematical manipulations, such as
addition (and subtraction). One limitation of the equal interval scale of measurement is
that it has no absolute zero point. Numbers cannot therefore be multiplied or divided.
Many educational tests and psychological measures such as IQ, provide data that achieve
or approximate to this level of measurement.
Ratio ScaleThe highest type of measurement is a ratio scale. This scale has all the properties of an
interval scale but also has a meaningful absolute zero point where zero means no part at
all of the quantity being measured, for example, a weight of 0 kg means no weight (mass)
at all. Ratio scales of measurement are almost exclusively confined to use in physical
sciences. Most statistical tests that can be used with ratio scales can also be used with
equal interval scales so the distinction in applied statistics is not as important as is often
emphasized.
Example 1It was mentioned earlier in this chapter that a school’s individual rank position in the
national school league tables might, for example, be based on the percentage of 15-year-
old pupils achieving 5 or more GCSEs at grades A to C. To show how conclusions
derived from data are dependent upon measurement assumptions, an example
based on the schools’ league table of examination results is described. For the time being
it can be assumed that league position is meant to reflect the schools’ academic standing
based on examination results. The school which is first in the league would be considered
to be the most academic school and the school which is last would be considered to be
the one demonstrating least academic excellence.
If four schools were selected at random from the national school league table where a
ranking at the top of the league, that is 1st position, indicates the best exam performance
School League Position (Based on GCSE exam performance)
St. James RC (45th)
Gill Road (55th)
Mount Secondary (65th)
St. John Moore (90th)
with which of the following statements would you agree?
Measurement issues 23