The TTEST Procedure
BOOTSTRAP Statement
BOOTSTRAP </ options>;
The BOOTSTRAP statement requests bootstrap standard error, bias estimates, and confidence intervals.
These bootstrap statistics are currently available only for one-sample, paired, and two-sample designs and only for analyses that assume normal data—although the bootstrap methods themselves do not necessarily assume normality.
Bootstrap results are unavailable if you specify the TEST=RATIO, DIST=LOGNORMAL, or TOST option in the PROC TTEST statement; if you specify the CROSSOVER= option in the VAR statement; or if you specify the WEIGHT statement. They are also unavailable if your input data set contains summary statistics rather than raw observed values.
The sample statistics for which bootstrap standard error, bias estimates, and confidence intervals are provided are as follows:
For a one-sample design: mean and standard deviation of the observations
For a paired design: mean and standard deviation of the paired difference—that is, the difference between the first and second members of an observation pair
For a two-sample design: mean, pooled standard deviation, and unpooled standard deviation of the class difference—that is, the difference between an observation from the first class and an observation from the second class
For more information about how these statistics are computed, see the section Statistics That Are Resampled.
You can specify the BOOTSTRAP plot-request option in the PROC TTEST statement to request plots that are based on bootstrap samples.
Summary of Options
Table 4 summarizes the options available in the BOOTSTRAP statement.
Table 4: Summary of Options in BOOTSTRAP Statement
| Option | Description |
|---|---|
| BOOTCI= | Produces bootstrap confidence intervals for the mean and variability parameter estimates |
| BOOTDATA= | Specifies the bootstrap output data set |
| NSAMPLES= | Specifies the number of bootstrap sample data sets (replicates) |
| SEED= | Provides the seed that initializes the random number stream |
Dictionary of Options
- BOOTCI < = < BC | BOOTT | EXPANDEDPERC | NORMAL | PERCENTILE | TBOOTSE >>
-
produces bootstrap-based confidence intervals. You can request the following types of bootstrap confidence interval:
- BC
produces bias-corrected percentile intervals.
- BOOTT
produces bootstrap t intervals, which use a traditional standard error estimate and quantiles of the bootstrap distribution of the t statistic.
- EXPANDEDPERC
produces percentile-based confidence intervals that include a narrowness bias adjustment.
- NORMAL
produces normal-based confidence intervals that use the bootstrap standard error estimate.
- PERCENTILE
produces percentile-based confidence intervals.
- TBOOTSE
produces t-based confidence intervals that use the bootstrap standard error estimate.
The default option is BOOTCI=BC.
Table 5 shows which analysis parameters are supported for each type of bootstrap confidence interval. A bullet enclosed in parentheses indicates that the confidence limits are the same as for the other method for the same parameter.
Table 5: Parameters That Are Supported for Each Type of Bootstrap Confidence Interval in the BOOTSTRAP Statement
BOOTCI Type Design Parameter Method BC BOOTT EXPERC NORMAL PERC TBOOTSE One-sample Mean 
Std Dev Paired Mean (1–2) Std Dev (1–2) Two-sample Mean (1–2) Pooled Mean (1–2) Satterthwaite ( ) ( ) ( ) Std Dev (1–2) Pooled Std Dev (1–2) Satterthwaite
All six types include confidence intervals for the mean parameter estimate on which the usual hypothesis test is based, for example, the mean for a one-sample design or the mean difference for a paired or two-sample design. For BOOTCI=BC and BOOTCI=PERCENTILE, confidence intervals based on the variability parameter estimate are also produced; these are based on the variability parameter estimate that is used to compute the standard error of the usual hypothesis test for the mean parameter, for example, the standard deviation for a one-sample design or the standard deviation of the difference for a paired or two-sample design.
The ALPHA= and SIDES= options in the PROC TTEST statement set the direction and level of significance that is used in constructing the bootstrap confidence intervals.
For more information about the bootstrap confidence intervals supported by PROC TTEST, see the section Bootstrap Confidence Intervals.
- BOOTDATA=SAS-data-set
specifies the SAS data set that contains the bootstrap sample data when you use a BOOTSTRAP statement. This data set has the number of observations that you specify in the NSAMPLES= option and contains the mean and standard deviation estimates that are calculated for each bootstrap sample.
- NSAMPLES=n
specifies the number of bootstrap sample data sets (replicates). The value must be greater than 1. By default, NSAMPLES=10000.
- SEED=n
provides the seed that initializes the random number stream for generating the bootstrap sample data sets (replicates). If you do not specify the SEED= value, or if you specify a value less than or equal to 0, the seed is generated from reading the time of day from the computer’s clock.