The need for statistical tests arises when the data are less than
perfectly reliable and are highly variable. As a possibly familar
example, suppose that you had a bathroom scale that was unreli-
able. If you got on and off it a few times in succession, you might find
that sometimes you were a pound above or a pound below the last
reading. If you only got on it once, read the weight, changed your diet
for a week, then got on the scale again and found that you had gained
or lost a pound, you would not know whether the random variations
in the scale's readings were responsible or whether you had actually
changed in weight.

As mentioned in the preceding chapter, most psychological tests
have reliability problems. Assume a person is seen in a psychological
clinic, is given a test, and is diagnosed as depressed. The individual
is treated with a new form of therapy, retested, and is found to be less
depressed. Has the new treatment been effective, or is this a case of
random variation in the scores?

The numbers produced by psychological tests give us a general
idea of people's relative standing, but they do not identify exact true
scores. Random variability in the measurement process adds to or
subtracts from the true score. Random variability is unpredictable
variability caused by chance factors, or caused by such a multiplicity
of varied and changing influences that the precise contribution of
random variability to the scores cannot be determined. This is why

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