# The FREQ Procedure

### Example 3.6 Output Data Set of Chi-Square Statistics

This example uses the `Color` data from Example 3.1 to output the Pearson chi-square and the likelihood ratio chi-square statistics to a SAS data set. The following PROC FREQ statements create a two-way table of eye color versus hair color.

```proc freq data=Color order=data;
tables Eyes*Hair / expected cellchi2 norow nocol chisq;
output out=ChiSqData n nmiss pchi lrchi;
weight Count;
title 'Chi-Square Tests for 3 by 5 Table of Eye and Hair Color';
run;
```
```proc print data=ChiSqData noobs;
title1 'Chi-Square Statistics for Eye and Hair Color';
title2 'Output Data Set from the FREQ Procedure';
run;
```

The EXPECTED option displays expected cell frequencies in the crosstabulation table, and the CELLCHI2 option displays the cell contribution to the overall chi-square. The NOROW and NOCOL options suppress the display of row and column percents in the crosstabulation table. The CHISQ option produces chi-square tests.

The OUTPUT statement creates the `ChiSqData` output data set and specifies the statistics to include. The N option requests the number of nonmissing observations, the NMISS option stores the number of missing observations, and the PCHI and LRCHI options request Pearson and likelihood ratio chi-square statistics, respectively, together with their degrees of freedom and p-values.

The preceding statements produce Output 3.6.1 and Output 3.6.2. The contingency table in Output 3.6.1 displays eye and hair color in the order in which they appear in the `Color` data set. The Pearson chi-square statistic in Output 3.6.2 provides evidence of an association between eye and hair color (p=0.0073). The cell chi-square values show that most of the association is due to more green-eyed children with fair or red hair and fewer with dark or black hair. The opposite occurs with the brown-eyed children.

Output 3.6.3 displays the output data set created by the OUTPUT statement. It includes one observation that contains the sample size, the number of missing values, and the chi-square statistics and corresponding degrees of freedom and p-values as in Output 3.6.2.

Output 3.6.1: Contingency Table

 Chi-Square Tests for 3 by 5 Table of Eye and Hair Color

The FREQ Procedure

Frequency
Expected
Cell Chi-Square
Percent
Table of Eyes by Hair
Eyes(Eye Color) Hair(Hair Color)
fair red medium dark black Total
blue
 69 66.425 0.0998 9.06
 28 32.921 0.7357 3.67
 68 63.22 0.3613 8.92
 51 53.024 0.0772 6.69
 6 6.4094 0.0262 0.79
 222 29.13
green
 69 59.543 1.5019 9.06
 38 29.51 2.4422 4.99
 55 56.671 0.0492 7.22
 37 47.53 2.3329 4.86
 0 5.7454 5.7454 0
 199 26.12
brown
 90 102.03 1.4187 11.81
 47 50.568 0.2518 6.17
 94 97.109 0.0995 12.34
 94 81.446 1.935 12.34
 16 9.8451 3.8478 2.1
 341 44.75
Total
 228 29.92
 113 14.83
 217 28.48
 182 23.88
 22 2.89
 762 100

Output 3.6.2: Chi-Square Statistics

Statistic DF Value Prob
Chi-Square 8 20.9248 0.0073
Likelihood Ratio Chi-Square 8 25.9733 0.0011
Mantel-Haenszel Chi-Square 1 3.7838 0.0518
Phi Coefficient   0.1657
Contingency Coefficient   0.1635
Cramer's V   0.1172

Output 3.6.3: Output Data Set

 Chi-Square Statistics for Eye and Hair Color Output Data Set from the FREQ Procedure

N NMISS _PCHI_ DF_PCHI P_PCHI _LRCHI_ DF_LRCHI P_LRCHI
762 0 20.9248 8 .007349898 25.9733 8 .001061424