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 The TTEST Procedure

# Overview

The TTEST procedure performs t tests for one sample, two samples, and paired observations. The one-sample t test compares the mean of the sample to a given number. The two-sample t test compares the mean of the first sample minus the mean of the second sample to a given number. The paired observations t test compares the mean of the differences in the observations to a given number.

For one-sample tests, PROC TTEST computes the sample mean of the variable and compares it with a given number. Paired comparisons use the one sample process on the differences between the observations. Paired comparisons can be made between many pairs of variables with one call to PROC TTEST. For group comparisons, PROC TTEST computes sample means for each of two groups of observations and tests the hypothesis that the population means differ by a given amount. This latter analysis can be considered a special case of a one-way analysis of variance with two levels of classification.

The underlying assumption of the t test in all three cases is that the observations are random samples drawn from normally distributed populations. This assumption can be checked using the UNIVARIATE procedure; if the normality assumptions for the t test are not satisfied, you should analyze your data using the NPAR1WAY procedure. The two populations of a group comparison must also be independent. If they are not independent, you should question the validity of a paired comparison.

PROC TTEST computes the group comparison t statistic based on the assumption that the variances of the two groups are equal. It also computes an approximate t based on the assumption that the variances are unequal (the Behrens-Fisher problem). The degrees of freedom and probability level are given for each; Satterthwaite's (1946) approximation is used to compute the degrees of freedom associated with the approximate t. In addition, you can request the Cochran and Cox (1950) approximation of the probability level for the approximate t. The folded form of the F statistic is computed to test for equality of the two variances (Steel and Torrie 1980).

FREQ and WEIGHT statements are available. Data can be input in the form of observations or summary statistics. Summary statistics and their confidence intervals, and differences of means are output. For two-sample tests, the pooled-variance and a test for equality of variances are also produced.

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