fsml_signedrank_1sample Interface

public interface fsml_signedrank_1sample

The 1-sample Wilcoxon signed rank test is a non-parametric test that determines if data comes from a symmetric population with centre $mu_0$. It can be regarded as a non-parametric version of the 1-sample t-test.

Hypotheses:

If the data consists of independent and similarly distributed samples from distribution $D$, the null hypothesis $H_0$ can be expressed as:

$D$ is symmetric around $\mu = \mu_0$.

The default alternative hypothesis $H_1$ is two-sided and also be set explicitly (h1 = "two"). It can be expressed as:

$D$ is symmetric around $\mu \neq \mu_0$

If the alternative hypothesis is set to "greater than" (h1 = "gt"), it is:

$D$ is symmetric around $\mu > \mu_0$

If the alternative hypothesis is set to "less than" (h1 = "lt"), it is:

$D$ is symmetric around $\mu < \mu_0$

Procedure:

The test statistic $W$ is the smaller of the sum of positive and negative signed ranks: $$W = \min \left( \sum_{d_i > 0} R_i, \sum_{d_i < 0} R_i \right)$$

The procedure takes into consideration tied ranks.

Module Procedures