Introductory Biostatistics

tribution of the dots clusters less closely around the line, and becomes virtually
no correlation when the distribution approximates a circle or oval (the method
is ine¤ective for measuring a relationship that is not linear).

2.4.1 Pearson’s Correlation Coe‰cient

Consider the scatter diagram shown in Figure 2.14, where we have added a
vertical and a horizontal line through the pointðx;yÞand label the four quar-
ters as I, II, III, and IV. It can be seen that

In quartersIandIII,

ðx
xÞðy
yÞ> 0

so that for positive association, we have

X

ðx
xÞðy
yÞ> 0

Furthermore, this sum is large for stronger relationships because most of

the dots, being closely clustered around the line, are in these two quarters.

Similarly, in quarters II and IV,

ðx
xÞðy
yÞ< 0

leading to

Figure 2.14 Scatter diagram divided into quadrants.

COEFFICIENTS OF CORRELATION 85