Example 3.3 Chi-Square Goodness-of-Fit Tests

This example examines whether the children’s hair color (from Example 3.1) has a specified multinomial distribution for the two geographical regions. The hypothesized distribution of hair color is 30% fair, 12% red, 30% medium, 25% dark, and 3% black.

In order to test the hypothesis for each region, the data are first sorted by Region. Then the FREQ procedure uses a BY statement to produce a separate table for each BY group (Region). The option ORDER=DATA orders the variable values (hair color) in the frequency table by their order in the input data set. The TABLES statement requests a frequency table for hair color, and the option NOCUM suppresses the display of the cumulative frequencies and percentages.

The CHISQ option requests a chi-square goodness-of-fit test for the frequency table of Hair. The TESTP= option specifies the hypothesized (or test) percentages for the chi-square test; the number of percentages listed equals the number of table levels, and the percentages sum to 100%. The TESTP= percentages are listed in the same order as the corresponding variable levels appear in frequency table.

The PLOTS= option requests a deviation plot, which is associated with the CHISQ option and displays the relative deviations from the test frequencies. The TYPE=DOT plot-option requests a dot plot instead of the default type, which is a bar chart. The ONLY global-plot-option requests that PROC FREQ produce only the deviation plot. By default, PROC FREQ produces all plots associated with the requested analyses. A frequency plot is associated with a one-way table request but is not produced in this example because ONLY is specified with the DEVIATIONPLOT request. Note that ODS Graphics must be enabled before requesting plots. These statements produce Output 3.3.1 through Output 3.3.4.

proc sort data=Color;
   by Region;
run;

ods graphics on;
proc freq data=Color order=data;
   tables Hair / nocum chisq testp=(30 12 30 25 3)
                 plots(only)=deviationplot(type=dot);
   weight Count;
   by Region;
   title 'Hair Color of European Children';
run;
ods graphics off;