This example, taken from Huntsberger and Billingsley (1989), compares two grazing methods using 32 steers. Half of the steers 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 affect weight gain differently. The data are read by the following DATA step:

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 ;

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.

If you have summary data—that is, just means and standard deviations, as computed by PROC MEANS—then you can still use PROC TTEST to perform a simple t test analysis. This example demonstrates this mode of input for PROC TTEST. Note, however, that graphics are unavailable when summary statistics are used as input.

The MEANS procedure is invoked to create a data set of summary statistics with the following statements:

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

The NOPRINT option eliminates all printed 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 can be used in subsequent procedures. This new data set is displayed in Output 103.1.1 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 103.1.1: Output 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 statements invoke PROC TTEST with 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 103.1.2.

Output 103.1.2: Summary Statistics and Confidence Limits

The TTEST Procedure

Variable: WtGain

GrazeType | N | Mean | Std Dev | Std Err | Minimum | Maximum |
---|---|---|---|---|---|---|

continuous | 16 | 75.1875 | 33.8117 | 8.4529 | 12.0000 | 130.0 |

controlled | 16 | 83.1250 | 30.5350 | 7.6337 | 28.0000 | 128.0 |

Diff (1-2) | -7.9375 | 32.2150 | 11.3897 |

GrazeType | Method | Mean | 95% CL Mean | Std Dev | 95% CL Std Dev | ||
---|---|---|---|---|---|---|---|

continuous | 75.1875 | 57.1705 | 93.2045 | 33.8117 | 24.9768 | 52.3300 | |

controlled | 83.1250 | 66.8541 | 99.3959 | 30.5350 | 22.5563 | 47.2587 | |

Diff (1-2) | Pooled | -7.9375 | -31.1984 | 15.3234 | 32.2150 | 25.7434 | 43.0609 |

Diff (1-2) | Satterthwaite | -7.9375 | -31.2085 | 15.3335 |

In Output 103.1.2, The GrazeType 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 103.1.3 shows the results of tests for equal group means and equal variances.

Output 103.1.3: t Tests

Method | Variances | DF | t Value | Pr > |t| |
---|---|---|---|---|

Pooled | Equal | 30 | -0.70 | 0.4912 |

Satterthwaite | Unequal | 29.694 | -0.70 | 0.4913 |

Equality of Variances | ||||
---|---|---|---|---|

Method | Num DF | Den DF | F Value | Pr > F |

Folded F | 15 | 15 | 1.23 | 0.6981 |

A group test statistic for the equality of means is reported for both equal and unequal variances. Both tests indicate a lack of evidence for a significant difference between grazing methods (t = –0.70 and p = 0.4912 for the pooled test, t = –0.70 and p = 0.4913 for the Satterthwaite test). The equality of variances test does not indicate a significant difference in the two variances . Note that this test assumes that the observations in both data sets are normally distributed; this assumption can be checked in PROC UNIVARIATE by using the NORMAL option with the raw data.

Although the ability to use summary statistics as input is useful if you lack access to the original data, some of the output that would otherwise be produced in an analysis on the original data is unavailable. There are also limitations on the designs and distributional assumptions that can be used with summary statistics as input. For more information, see the section Input Data Set of Statistics.