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616 CHAPTER 12 THE CHI-SQUARE DISTRIBUTION AND THE ANALYSIS OF FREQUENCIES
Computer Analysis The computer may be used to advantage in calculating X 2
for tests of independence and tests of homogeneity. Figure 12.4.1 shows the procedure
and printout for Example 12.4.1 when the MINITAB program for computing X 2 from
contingency tables is used. The data were entered into MINITAB Columns 1 and 2, corresponding
to the columns of Table 12.4.3.
We may use SAS ® to obtain an analysis and printout of contingency table data by
using the PROC FREQ statement. Figure 12.4.2 shows a partial SAS ® printout reflecting
the analysis of the data of Example 12.4.1.
Data:
C1: 260 15 7
C2: 299 41 14
Dialog Box:
Session command:
Stat ➤ Tables ➤ Chi-square Test MTB > CHISQUARE C1-C3
Type C1-C2 in Columns containing the table.
Click OK.
Output:
Chi-Square Test: C1, C2
Expected counts are printed below observed counts
C1 C2 Total
1 260 299 559
247.86 311.14
2 15 41 56
24.83 31.17
3 7 14 21
9.31 11.69
Total 282 354 636
Chi-Sq = 0.595 + 0.474 +
3.892 + 3.100 +
0.574 + 0.457 = 9.091
DF = 2, P-Value = 0.011
FIGURE 12.4.1 MINITAB procedure and output for chi-square analysis of data in Table 12.4.3.