Introductory Biostatistics

tions often yield similar numerical results. The birth-weight problem of Exam-
ple 2.8 is adapted to illustrate this method with the following steps:

1. Thexandyvalues are presented in two rows; thexvalues in the first row
   are arranged from smallest to largest.


2. For eachyvalue in the second row, we count
   (a) The number of largeryvalues to its right (third row). The sum of
   these is denoted byC.
   (b) The number of smalleryvalues to its right (fourth row). The sum of
   these is denoted byD.
   CandDare the numbers of concordant and discordant pairs.


3. Kendall’s rank correlation is defined by

t¼

C
D

1

2 nðn
^1 Þ

Example 2.11 For the birth-weight problem above, we have the data given in
Table 2.17. The value of Kendall’s tau is

t¼

3
61

1

2 ð^12 Þð^11 Þ

¼
 0 : 88

Note:A SAS program would include these instructions:

PROC CORR PEARSON SPEARMAN KENDALL;
VAR BWEIGHT INCREASE;

If there are more than two variable names listed, the CORR procedure will
compute correlation coe‰cients between all pairs of variables.

2.5 NOTES ON COMPUTATIONS

In Section 1.4 we covered basic techniques for Microsoft’s Excel: how to open/
form a spreadsheet, save, and retrieve it. Topics included data-entry steps such

TABLE 2.17

Total

x 80 81 84 92 94 103 106 107 111 112 118 119
y 118 120 114 75 91 90 72 72 66 63 42 52
C 100200000000 3
D 1010967644320061

90 DESCRIPTIVE METHODS FOR CONTINUOUS DATA