The Essentials of Biostatistics for Physicians, Nurses, and Clinicians

7.2 Pearson’s Correlation 99

Figure 7.1. Scatter diagram of systolic and diastolic blood pressure (data from Table 7.1 ).

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Systolic BP

Diastolic BP

diastolic pressure to be higher than its average when the systolic
pressure is higher than its average and lower than its average when the
systolic pressure is below its average. Next in Section 7.2 , we will see
how the Pearson correlation describes aspects of the scatter plot, and
in Section 7.3 , how a regression line can be plotted through the data
using the least squares criterion.

7.2 PEARSON ’ S CORRELATION

The Pearson correlation coeffi cient is a parameter that has a natural
place in the bivariate distribution. When we have a sample such as in
the scatter plot for systolic and diastolic blood pressure, we can obtain
a sample estimate. Generally, ρ is used to denote the parameter, and r
to denote the sample estimate of ρ.

rXXYY XXYYiii

n

i

n

iii

n

i

n

=−∑∑== 1 ()ˆˆ∑= 1 ()− ∑=()−ˆ ˆ()−.

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