ABSTRACT
There is also an additional assumption that we have not previously met, which is that where data are quantities, they must be measured at least on an
interval scale
for the relationship between test statistic and probability to work as advertised. An interval scale is one in which the intervals are meaningful. For example, in the Celsius scale the difference (interval) between 10
°
and 20
°
is the same as that between 20
°
and 30
°
. By contrast, the Beaufort wind scale is not an interval scale. Force 3 (gentle breeze) is more than Force 2 (light breeze), but the difference of one unit between Force 2 and Force 3 cannot be regarded as equivalent to the difference between a Force 9 (severe gale) and a Force 10 (storm). Thus, the Beaufort scale is a
rank scale
but not an interval scale.
