fi_test#

normtest.filliben.fi_test(x_data, alpha=0.05)[source]#

This function applies the Filliben Normality test [1].

Parameters:

x_datanumpy array: One dimension numpy array with at least 4 observations.
alphafloat, optional: The level of significance (\(\alpha\)). Default is 0.05;

Returns:

resulttuple with

statisticfloat (positive): The test statistic;
criticalfloat: The critical value of the test;
p_valuefloat or str: The probability of the test;
conclusionstr: The test conclusion (e.g, Normal/Not Normal).

Notes

The test statistic (\(F_{p}\)) is estimated through the correlation between the ordered data and the Normal statistical order:

\[F_p = \frac{\sum_{i=1}^n \left(x_i - \overline{x}\right) \left(z_i - \overline{z}\right)}{\sqrt{\sum_{i=1}^n \left( x_i - \overline{x}\right)^2 \sum_{i=1}^n \left( z_i - \overline{z}\right)^2}}\]

where \(z_{i}\) values are the z-score values of the corresponding experimental data (\(x_{{i}}\)) value, and \(n\) is the sample size.

The correlation is estimated using scipy.stats.pearsonr().

The Normality test has the following assumptions:

☕

\(H_0:\) Data was sampled from a Normal distribution.

\(H_1:\) The data was sampled from a distribution other than the Normal distribution.

The conclusion of the test is based on the comparison between the critical value (at \(\alpha\) significance level) and statistic of the test:

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if critical \(\leq\) statistic:: Fail to reject \(H_0:\) (e.g., data is Normal)
else:: Reject \(H_0:\) (e.g., data is not Normal)

The critical values are obtained using _critical_value().

Warning

The estimated \(p_{value}\) may not be accurate as it is calculated using linear interpolation.

References

[1]

FILLIBEN, J. J. The Probability Plot Correlation Coefficient Test for Normality. Technometrics, v. 17, n. 1, p. 111-117, 1975.

Examples

>>> from normtest import filliben
>>> from scipy import stats
>>> data = stats.norm.rvs(loc=0, scale=1, size=30, random_state=42)
>>> result = filliben.fi_test(data)
>>> print(result)
Filliben(statistic=0.9905837698603658, critical=0.964, p_value=0.7791884930182895, conclusion='Fail to reject H₀')