# Independent samples t-test

## Description

Use the Independent samples t-test to compare the mean of two independent samples. It tests the null hypothesis that the difference between the means of two samples is equal to 0.

## Required input

- For both Sample 1 and Sample 2 select the variable of interest.
- Optionally select filters to include a subset of cases.

## Options

**Logarithmic transformation**: select this option if the data need Logarithmic transformation.**Correction for unequal variances**: allows to select the t-test (assuming equal variances) or the t-test corrected for unequal variances (Welch test, Armitage et al., 2002). With the option "Automatic" the software will select the appropriate test based on the F-test (comparison of variances).

## Results

The results for the Independent samples t-test include the summary statistics of the two samples, followed by the statistical tests.

First an F-test is performed. If the P-value is low (P<0.05) the variances of the two samples cannot be assumed to be equal and it should be considered to use the t-test with a correction for unequal variances (Welch test, Armitage et al., 2002).

The independent samples t-test is used to test the hypothesis that the difference between the means of two samples is equal to 0 (this hypothesis is therefore called the null hypothesis). The program displays the difference between the two means, the pooled standard deviation, standard error, and the confidence interval (CI) of this difference. Next follow the test statistic t, the Degrees of Freedom (DF) and the two-tailed probability P. When the P-value is less than the conventional 0.05, the null hypothesis is rejected and the conclusion is that the two means do indeed differ significantly.

Note that on SciStat.com P-values are always two-sided.

### Logarithmic transformation

If you selected the Logarithmic transformation option, the program performs the calculations on the logarithms of the observations, but reports the back-transformed summary statistics.

For the t-test, the difference and its confidence interval are given, and the test is performed on the log-transformed scale.

Next, the results of the t-test are transformed back and the interpretation is as follows: the back-transformed difference of the means of the logs is the ratio of the geometric means of the two samples (see Bland, 2000).

## See also

## Link

Go to Independent samples t-test.