fsml_ttest_paired Interface

public interface fsml_ttest_paired

The paired sample t-test (or dependent sample t-test) determines if the mean difference between two sample sets are zero. It is mathematically equivalent to the 1-sample t-test conducted on the difference vector $d$ with $\mu_0 = 0$.

Hypotheses:

The null hypothesis $H_{0}$ and alternative hypothesis $H_{1}$ can be written as: $H_{0}$: $\bar{d} = 0$, and $H_{1}$: $\bar{d} \neq 0$

Procedure:

The test statstic $t$ is calculated as follows: $$t = \frac{\bar{d} - 0}{s_d / \sqrt{n}}$$ where $\bar{d}$ is the mean of the differences between the sample sets, $s_d$ is the standard deviation of the differences, and $n$ is the number of paired samples.

The degrees of freedom $\nu$ is calculated as follows: $$\nu = n -1$$

Module Procedures