### Example 119.2 One-Sample Comparison with the FREQ Statement

This example examines children’s reading skills. The data consist of Degree of Reading Power (DRP) test scores from 44 third-grade
children and are taken from Moore (1995, p. 337). Their scores are given in the following DATA step:

data read;
input score count @@;
datalines;
40 2 47 2 52 2 26 1 19 2
25 2 35 4 39 1 26 1 48 1
14 2 22 1 42 1 34 2 33 2
18 1 15 1 29 1 41 2 44 1
51 1 43 1 27 2 46 2 28 1
49 1 31 1 28 1 54 1 45 1
;

The following statements invoke the TTEST procedure to test if the mean test score is equal to 30.

ods graphics on;
proc ttest data=read h0=30;
var score;
freq count;
run;
ods graphics off;

The `count`

variable contains the frequency of occurrence of each test score; this is specified in the FREQ
statement. The output, shown in Output 119.2.1, contains the results.

Output 119.2.1: TTEST Results

The TTEST Procedure

Variable: score

44 |
34.8636 |
11.2303 |
1.6930 |
14.0000 |
54.0000 |

34.8636 |
31.4493 |
38.2780 |
11.2303 |
9.2788 |
14.2291 |

The SAS log states that 30 observations and two variables have been read. However, the sample size given in the TTEST output
is N=44. This is due to specifying the `count`

variable in the FREQ
statement. The test is significant (t = 2.87, p = 0.0063) at the 5% level, so you can conclude that the mean test score is different from 30.

The summary panel in Output 119.2.2 shows a histogram with overlaid normal and kernel densities, a box plot, and the 95% confidence interval for the mean.

Output 119.2.2: Summary Panel

The Q-Q plot in Output 119.2.3 assesses the normality assumption.

The tight clustering of the points around the diagonal line is consistent with the normality assumption. You could use the
UNIVARIATE procedure with the NORMAL option to numerically check the normality assumption.