_critical_value#

normtest.ryan_joiner._critical_value(sample_size, alpha=0.05)[source]#

This function calculates the critical value of the Ryan-Joiner test [1].

Parameters:

sample_sizeint: The sample size. Must be equal or greater than 4;
alphafloat, optional: The level of significance (\(\alpha\)). Default is 0.05;

Returns:

criticalfloat: The critical value of the test;

See also

rj_test

Notes

The critical values are calculated using [1] the following equations:

\[ \begin{align}\begin{aligned}R_{p;\alpha=0.10}^{'} = 1.0071 - \frac{0.1371}{\sqrt{n}} - \frac{0.3682}{n} + \frac{0.7780}{n^{2}}\\R_{p;\alpha=0.05}^{'} = 1.0063 - \frac{0.1288}{\sqrt{n}} - \frac{0.6118}{n} + \frac{1.3505}{n^{2}}\\R_{p;\alpha=0.01}^{'} = 0.9963 - \frac{0.0211}{\sqrt{n}} - \frac{1.4106}{n} + \frac{3.1791}{n^{2}}\end{aligned}\end{align} \]

where \(n\) is the sample size.

References

[1] (1,2)

RYAN, T. A., JOINER, B. L. Normal Probability Plots and Tests for Normality, Technical Report, Statistics Department, The Pennsylvania State University, 1976. Available at www.additive-net.de. Access on: 22 Jul. 2023.

Examples

>>> from normtest import ryan_joiner
>>> critical = ryan_joiner._critical_value(10, alpha=0.05)
>>> print(critical)
0.9178948637370312