In other words, the statisticpð 1 pÞcan be used in place ofs^2 as a measure of
variation; the logic can be seen as follows. First, the quantitypð 1 pÞ, with
0 apa1, attains its maximum value whenp¼ 0 :5. For example,
ð 0 : 1 Þð 0 : 9 Þ¼ 0 : 09
...ð 0 : 4 Þð 0 : 6 Þ¼ 0 : 24
ð 0 : 5 Þð 0 : 5 Þ¼ 0 : 25
ð 0 : 6 Þð 0 : 4 Þ¼ 0 : 24
...ð 0 : 9 Þð 0 : 1 Þ¼ 0 : 09The values ofpð 1 pÞare greatest in the vicinity ofp¼ 0 :5 and decrease as we
go toward both ends (0 and 1) of the range ofp. If we are performing a coin-
tossing experiment or conducting an election; the result would be mostunpre-
dictablewhen the chance to obtain the outcome wanted is in the vicinity of
p¼ 0 :5. In other words, the quantitypð 1 pÞis a suitable statistic to measure
thevolatility, dispersion, andvariation. The corresponding statistic for standard
deviation is
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
pð 1 pÞp
.2.4 COEFFICIENTS OF CORRELATION
Methods discussed in this chapter have been directed to the analyses of data
where a single continuous measurement was made on each element of a sam-
ple. However, in many important investigations we may have two measure-
ments made: where the sample consists of pairs of values and the research
objective is concerned with the association between these variables. For exam-
ple, what is the relationship between a mother’s weight and her baby’s weight?
In Section 1.3 we were concerned with the association between dichotomous
variables. For example, if we want to investigate the relationship between a
disease and a certain risk factor, we could calculate an odds ratio to represent
the strength of the relationship. In this section we deal with continuous mea-
surements, and the method is referred to ascorrelation analysis. Correlation is a
concept that carries the common colloquial implication of association, such as
‘‘height and weight are correlated.’’ The statistical procedure will give the word
a technical meaning; we can actually calculate a number that tells thestrength
of the association.
When dealing with the relationship between two continuous variables, we
first have to distinguish between a deterministic relationship and a statistical
relationship. For adeterministic relationship, values of the two variables are
related through an exact mathematical formula. For example, consider the
COEFFICIENTS OF CORRELATION 83