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The TTEST Procedure |

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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