# Paired-Samples T Test

This feature requires the Statistics Base option.

The Paired-Samples T Test procedure compares the means of two variables for a single group. The
procedure computes the differences between values of the two variables for each case and tests
whether the average differs from 0. The procedure also automates the *t*-test effect size
computation.

- Example
- In a study on high blood pressure, all patients are measured at the
beginning of the study, given a treatment, and measured again. Thus, each subject has two measures,
often called
*before*and*after*measures. An alternative design for which this test is used is a matched-pairs or case-control study, in which each record in the data file contains the response for the patient and also for his or her matched control subject. In a blood pressure study, patients and controls might be matched by age (a 75-year-old patient with a 75-year-old control group member). - Statistics
- For each variable: mean, sample size, standard deviation, and standard error
of the mean. For each pair of variables: correlation, average difference in means,
*t*test, confidence interval for mean difference (you can specify the confidence level), and the estimation of the effect size for the*t*-test. Standard deviation and standard error of the mean difference.

## Data considerations

- Data
- For each paired test, specify two quantitative variables (interval level of measurement or ratio level of measurement). For a matched-pairs or case-control study, the response for each test subject and its matched control subject must be in the same case in the data file.
- Assumptions
- Observations for each pair should be made under the same conditions. The mean differences should be normally distributed. Variances of each variable can be equal or unequal.

## Obtaining a Paired-Samples T Test

This feature requires the Statistics Base option.

- From the menus choose:
- Select one or more pairs of variables.
- Optionally, change/select a Estimate effect sizes
option. The settings control how the standardizer is computed in estimating the Cohen's
*d*and Hedges' correction for each variable pair.- Standard deviation of the difference
- The denominator used in estimating the effect size. Cohen's
*d*uses the sample standard deviation of the mean difference. Hedges' correction uses the sample standard deviation of the mean difference adjusted by a correction factor. - Corrected standard deviation of the difference
- The denominator used in estimating the effect size. Cohen's
*d*uses the sample standard deviation of the mean difference adjusted by the correlation between measures. Hedges' correction uses the sample standard deviation of the mean difference adjusted by the correlation between measures, plus a correction factor. - Average of variances
- The denominator used in estimating the effect size. Cohen's
*d*uses the square root of the average variance of measures. Hedges' correction uses the square root of the average variance of measures, plus a correction factor.

- Optionally, you can:
- Select Estimate effect sizes to control the
estimation of the
*t*-test effect size. When the setting is selected, you can further control how the standardizer is computed in estimating the Cohen's*d*and Hedges' correction for each variable pair. - Click Options to control the treatment of missing data and the level of the confidence interval.
- Click Bootstrap for deriving robust estimates of standard errors and confidence intervals for estimates such as the mean, median, proportion, odds ratio, correlation coefficient or regression coefficient.

- Select Estimate effect sizes to control the
estimation of the

This procedure pastes T-TEST command syntax.