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 The FREQ Procedure

## Example 28.5: Creating an Output Data Set Containing Chi-Square Statistics

This example uses the Color data from Example 28.1 to output the Pearson chi-square and the likelihood-ratio chi-square statistics to a SAS data set. The following statements create a two-way table of eye color versus hair color.

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

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

The OUTPUT statement creates the ChiSqData data set with eight variables: the N option stores the number of nonmissing observations, the NMISS option stores the number of missing observations, and the PCHI and LRCHI options store Pearson and likelihood-ratio chi-square statistics, respectively, together with their degrees of freedom and p-values. The preceding statements produce Output 28.5.1 through Output 28.5.2.

Output 28.5.1: 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) Total fair red medium dark black blue 6966.4250.0998 9.06 2832.9210.7357 3.67 68 63.220.3613 8.92 5153.0240.0772 6.69 66.40940.0262 0.79 222   29.13 green 6959.5431.5019 9.06 38 29.512.4422 4.99 5556.6710.0492 7.22 37 47.532.3329 4.86 05.74545.7454 0.00 199   26.12 brown 90102.031.4187 11.81 4750.5680.2518 6.17 9497.1090.0995 12.34 9481.446 1.935 12.34 169.84513.8478 2.10 341   44.75 Total 228 29.92 113 14.83 217 28.48 182 23.88 22 2.89 762 100.00

Output 28.5.2: Chi-Square Statistics

 Chi-Square Tests for 3 by 5 Table of Eye and Hair Color
 The FREQ Procedure
 Statistics for Table of Eyes by Hair

 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
 Sample Size = 762

The contingency table in Output 28.5.1 displays eye and hair color in the order in which they appear in the Color data set. The Pearson chi-square statistic in Output 28.5.2 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 28.5.3: 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

The OUT= data set is displayed in Output 28.5.3. It contains one observation with the sample size, the number of missing values, and the chi-square statistics and corresponding degrees of freedom and p-values as in Output 28.5.2.

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