
The Basics of Measurement ◾ 65
By similar argument, we can show that the statement “Program B is faster
than both Programs A and C” is meaningful even though it is false.
However, consider the statement “Program A is more than twice as fast as
Program C.” This statement is not meaningful. To see why, dene acceptable
measures M and M’ as follows:
M(A) = 3; M(B) = 2; M(C) = 1
M(A) = 3; M(B) = 2.5; M(C) = 2
Using scale M the statement is true, since 3 = M(A) > 2M(C) = 2. However,
using M’ the statement is false. Although the statement seems meaningful
given our understanding of speed, the sophistication of the notion twice as
fast was not ...