The FREQ Procedure

# Overview

The FREQ procedure is a descriptive as well as a statistical procedure that produces one-way to n-way frequency and crosstabulation tables. Frequency tables concisely describe your data by reporting the distribution of variable values.Crosstabulation tables, also known as contingency tables, summarize data for two or more classification variables by showing the number of observations for each combination of variable values.

For one-way frequency tables, PROC FREQ can compute statistics to test for equal proportions, specified proportions, or the binomial proportion. For contingency tables, PROC FREQ can compute various statistics to examine the relationships between two classification variables adjusting for any stratification variables. PROC FREQ automatically displays the output in a report and can also save the output in a SAS data set.

For some pairs of variables, you may want to examine the existence or the strength of any association between the variables. To determine the existence of an association, PROC FREQ computes statistics that test the null hypothesis of no association. To determine the strength of an association, PROC FREQ computes measures of association that tend to be close to zero when there is no association and close to their maximums (or minimums) when there is perfect association. The statistics for contingency tables include

• chi-square tests and measures

• measures of association and tests of these measures

• risks (or binomial proportions) and risk differences for 2×2 tables

• odds ratios and relative risks for 2×2 tables

• tests for trend

• tests and measures of agreement

• Cochran-Mantel-Haenszel statistics.

PROC FREQ computes asymptotic standard errors, confidence limits, and tests for measures of association and measures of agreement. Exact p-values and confidence limits are available for various test statistics and measures. PROC FREQ also performs stratified analyses that compute statistics within, as well as across, strata for n-way tables. The statistics include Cochran-Mantel-Haenszel statistics and measures of agreement.

One-Way Frequency Tables Produced with PROC FREQ is the simplest form of PROC FREQ output. The one-way frequency tables of hair and eye color show the distributions of these variables. PROC FREQ lists each variable value along with the frequencies and percentages. The statements that produce the output follow:

```proc freq data=color;
run;```

In addition to listing the frequency distribution separately for each variable, you can create a crosstabulation table to show the joint frequency distribution for the two variables. Chi-Square Statistics Produced with PROC FREQ shows a two-way crosstabulation table and chi-square statistics that test the association between eye and hair color of children from two regions of Europe. The statements that produce this 3×5 table also

• order the variable values according to their appearance in the data set

• exclude the row and column percentages for each cell

• include the expected frequency for each cell

• include each cell's contribution to the total Pearson chi-square statistic.

In addition to displaying the statistics, the program creates an output data set that contains selected chi-square statistics. For an explanation of the program that produces this output, see Creating an Output Data Set Containing Chi-Square Statistics .

 ``` Chi-Square Statistics for Eye and Hair Color 2 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```

Several SAS procedures produce frequency counts; only PROC FREQ computes chi-square tests, measures of association, and measures of agreement for contingency tables. Other procedures to consider for counting are PROC TABULATE for more general table layouts; PROC REPORT for tables and customized summaries, PROC CHART for bar charts and other graphical representations; and PROC UNIVARIATE with the FREQ option for one-way frequency tables. When you want to fit models to categorical data, use a SAS/STAT procedure such as CATMOD, GENMOD, LOGISTIC, PHREG, or PROBIT. For more information on selecting the appropriate statistical analyses, refer to An Introduction to Categorical Data Analysis (Agresti, 1996) or Categorical Data Analysis Using the SAS System (Stokes, et al. 1995).