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

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 CL Mean	Mean	Upper CL Mean	Lower CL Std Dev	Std Dev	Upper CL Std 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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