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 The TTEST Procedure

## Example 67.1: Comparing Group Means Using Input Data Set of Summary Statistics

The following example, taken from Huntsberger and Billingsley (1989), compares two grazing methods using 32 steer. Half of the steer are allowed to graze continuously while the other half are subjected to controlled grazing time. The researchers want to know if these two grazing methods impact weight gain differently. The data are read by the following DATA step.

```   title 'Group Comparison Using Input Data Set of Summary
Statistics';
data graze;
length GrazeType \$ 10;
input GrazeType \$ WtGain @@;
datalines;
controlled  45   controlled  62
controlled  96   controlled 128
controlled 120   controlled  99
controlled  28   controlled  50
controlled 109   controlled 115
controlled  39   controlled  96
controlled  87   controlled 100
controlled  76   controlled  80
continuous  94   continuous  12
continuous  26   continuous  89
continuous  88   continuous  96
continuous  85   continuous 130
continuous  75   continuous  54
continuous 112   continuous  69
continuous 104   continuous  95
continuous  53   continuous  21
;
run;
```

The variable GrazeType denotes the grazing method: `controlled' is controlled grazing and `continuous' is continuous grazing. The dollar sign (\$) following GrazeType makes it a character variable, and the trailing at signs (@@) tell the procedure that there is more than one observation per line. The MEANS procedure is invoked to create a data set of summary statistics with the following statements:

```   proc sort;
by GrazeType;
proc means data=graze noprint;
var WtGain;
by GrazeType;
output out=newgraze;
run;
```

The NOPRINT option eliminates all output from the MEANS procedure. The VAR statement tells PROC MEANS to compute summary statistics for the WtGain variable, and the BY statement requests a separate set of summary statistics for each level of GrazeType. The OUTPUT OUT= statement tells PROC MEANS to put the summary statistics into a data set called newgraze so that it may be used in subsequent procedures. This new data set is displayed in Output 67.1.1 by using PROC PRINT as follows:

```   proc print data=newgraze;
run;
```

The _STAT_ variable contains the names of the statistics, and the GrazeType variable indicates which group the statistic is from.

Output 67.1.1: Output Data Set of Summary Statistics

 Group Comparison Using Input Data Set of Summary Statistics

 Obs GrazeType _TYPE_ _FREQ_ _STAT_ WtGain 1 continuous 0 16 N 16.000 2 continuous 0 16 MIN 12.000 3 continuous 0 16 MAX 130.000 4 continuous 0 16 MEAN 75.188 5 continuous 0 16 STD 33.812 6 controlled 0 16 N 16.000 7 controlled 0 16 MIN 28.000 8 controlled 0 16 MAX 128.000 9 controlled 0 16 MEAN 83.125 10 controlled 0 16 STD 30.535

The following code invokes PROC TTEST using the newgraze data set, as denoted by the DATA= option.

```   proc ttest data=newgraze;
class GrazeType;
var WtGain;
run;
```

The CLASS statement contains the variable that distinguishes between the groups being compared, in this case GrazeType. The summary statistics and confidence intervals are displayed first, as shown in Output 67.1.2.

Output 67.1.2: Summary Statistics

 Group Comparison Using Input Data Set of Summary Statistics

 The TTEST Procedure

 Statistics Variable Class N Lower CLMean Mean Upper CLMean Lower CLStd Dev Std Dev Upper CLStd Dev Std Err Minimum Maximum WtGain continuous 16 57.171 75.188 93.204 . 33.812 . 8.4529 12 130 WtGain controlled 16 66.854 83.125 99.396 . 30.535 . 7.6337 28 128 WtGain Diff (1-2) -31.2 -7.938 15.323 25.743 32.215 43.061 11.39

In Output 67.1.2, the Variable column states the variable used in computations and the Class column specifies the group for which the statistics are computed. For each class, the sample size, mean, standard deviation and standard error, and maximum and minimum values are displayed. The confidence bounds for the mean are also displayed; however, since summary statistics are used as input, the confidence bounds for the standard deviation of the groups are not calculated.

Output 67.1.3: t Tests

 Group Comparison Using Input Data Set of Summary Statistics

 The TTEST Procedure

 T-Tests Variable Method Variances DF t Value Pr > |t| WtGain Pooled Equal 30 -0.70 0.4912 WtGain Satterthwaite Unequal 29.7 -0.70 0.4913

 Equality of Variances Variable Method Num DF Den DF F Value Pr > F WtGain Folded F 15 15 1.23 0.6981

Output 67.1.3 shows the results of tests for equal group means and equal variances. A group test statistic for the equality of means is reported for equal and unequal variances. Before deciding which test is appropriate, you should look at the test for equality of variances; this test does not indicate a significant difference in the two variances (F' = 1.23, p = 0.6981), so the pooled t statistic should be used. Based on the pooled statistic, the two grazing methods are not significantly different (t=0.70, p=0.4912). Note that this test assumes that the observations in both data sets are normally distributed; this assumption can be checked in PROC UNIVARIATE using the raw data.

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