LibraryPirate

EXERCISES 737
Dialog box:
Stat ➤ Basic Statistics ➤ Correlation
Session command:
MTB > CORRELATION C3 C4
Type C3–C4 in Variables. Click OK.
Output:
Correlations (Pearson)
Correlation of (X)Rank and (Y)Rank -0.759
FIGURE 13.10.1 MINITAB procedure and output for computing Spearman rank correlation
coefficient, Example 13.10.1.
Since no ties occurred in the Y rankings, we have gT y = 0
and
a y 2 = 353 - 35
12
- 0 = 3570.0
From Table 13.10.4 we have gd i 2 = 1788.5. From these data we may now
compute by Equation 13.10.4
r s =
3565.5 + 3570.0 - 1788.5
2113565.52135702
= .75
We see that in this case the correction for ties does not make any difference
in the value of r s .
■
Computer Analysis We may use MINITAB, as well as many other statistical
software packages, to compute the Spearman correlation coefficient. To use MINITAB,
we must first have MINITAB rank the observations and store the ranks in separate
columns, one for the X ranks and one for the Y ranks. If we rank the X and Y values of
Example 13.10.1 and store them in Columns 3 and 4, we may obtain the Spearman rank
correlation coefficient with the procedure shown in Figure 13.10.1. Other software packages
such as SAS ® and SPSS, for example, automatically rank the measurements before
computing the coefficient, thereby eliminating an extra step in the procedure.
EXERCISES
For the following exercises perform the test at the indicated level of significance and determine
the p value.
13.10.1 The following table shows 15 randomly selected geographic areas ranked by population density
and age-adjusted death rate. Can we conclude at the .05 level of significance that population density
and age-adjusted death rate are not mutually independent