fit#

pycafee.normalitycheck.abdimolin.AbdiMolin.fit(self, x_exp, alfa=None, details=None)#

This function is a wraper around statsmodels.stats.diagnostic.lilliefors() [1] to estimate the statistic of the AbdiMolin Normality test. Only the statistic value is used.

The main difference between this method and the original one is that this wrap only allows the comparison of a sample with the Normal distribution, using dist="norm". The method to estimate the p-value is set to table. Hence:

>>> statsmodels.stats.diagnostic(x_exp, dist="norm", pvalmethod="table")

Parameters

x_expnumpy array

One dimension numpy array with at least 4 sample data.

alfafloat, optional

The level of significance (ɑ). Default is None which results in 0.05 (ɑ = 5%).

detailsstr, optional

The details parameter determines the amount of information presented about the hypothesis test.

If details = "short" (or None), a simplified version of the test result is returned.
If details = "full", a detailed version of the hypothesis test result is returned.
if details = "binary", the conclusion will be 1 (\(H_0\) is rejected) or 0 (\(H_0\) is accepted).

Returns

resulttuple with

statisticfloat: The test statistic.
criticalfloat or None: The critical value for alpha equal to 1%, 5%, 10%, 15% or 20%. Other values will raise ValueError.
p_valueNone: The p-value for the hypothesis test (always None).

conclusionstr

The test conclusion (e.g, Normal/ not Normal).

See also

pycafee.normalitycheck.andersondarling.AndersonDarling.fit
pycafee.normalitycheck.kolmogorovsmirnov.KolmogorovSmirnov.fit
pycafee.normalitycheck.lilliefors.Lilliefors.fit
pycafee.normalitycheck.shapirowilk.ShapiroWilk.fit

Notes

The critical values [2] includes samples with sizes between 4 and 50 for ɑ equal to 1%, 5%, 10%, 15% or 20%.

For data with a sample size higher than 51 (n_rep > 50), the critical value returned is the aproximation proposed by the authors.

The AbdiMolin Normality test [3] has the following premise:

☕

\(H_0:\) data comes from Normal distribution.

\(H_1:\) data does not come from Normal distribution.

The conclusion is based on the comparison between the critical value (at ɑ significance level) and statistic of the test. In summary:

if critical >= statistic:
    Data is Normal
else:
    Data is not Normal

If ɑ is not 0.01, 0.05, 0.10, 0.15 or 0.20, the function will raise a ValueError.

References

1: STATSMODELS. statsmodels.stats.diagnostic.lilliefors. Available at: www.statsmodels.org. Access on: 10 May. 2022
2: SALKIND, N. J. Encyclopedia of measurement and statistics. California: SAGE Publications, Inc., 2007. DOI: 10.4135/9781412952644.
3: MOLIN, P.; ABDI, H. New Tables and numerical approximation for the Kolmogorov- Smirnov/Lillierfors/Van Soest test of normality. p. 1–12, 1998. Available from MolinAbdi1998-LillieforsTechReport.pdf.

Examples

Applying the test with default values

>>> from pycafee.normalitycheck import AbdiMolin
>>> import scipy.stats as stats
>>> x = stats.norm.rvs(loc=5, scale=3, size=100, random_state=42)
>>> abdimolin_test = AbdiMolin()
>>> result, conc = abdimolin_test.fit(x)
>>> print(result)
AbdiMolinResult(Statistic=0.05177647360597687, Critical=0.0888513848903008, p_value=None, Alpha=0.05)
>>> print(conc)
Data is Normal at a 95.0% of confidence level.

Applying the test with alfa=0.10

>>> from pycafee.normalitycheck import AbdiMolin
>>> import numpy as np
>>> x = np.array([1.90642, 2.22488, 2.10288, 1.69742, 1.52229, 3.15435, 2.61826, 1.98492, 1.42738, 1.99568])
>>> abdimolin_test = AbdiMolin()
>>> result, conc = abdimolin_test.fit(x, alfa=0.01)
>>> print(result)
AbdiMolinResult(Statistic=0.17709753067016487, Critical=0.3037, p_value=None, Alpha=0.01)
>>> print(conc)
Data is Normal at a 99.0% of confidence level.

Applying the test with alfa=0.10 and details="full"

>>> from pycafee.normalitycheck import AbdiMolin
>>> import numpy as np
>>> x = np.array([5.1, 4.9, 4.7, 4.6, 5.0, 5.4, 4.6, 5.0, 4.4, 4.9])
>>> abdimolin_test = AbdiMolin()
>>> result, conc = abdimolin_test.fit(x, alfa=0.10, details="full")
>>> print(result)
AbdiMolinResult(Statistic=0.15459867079959644, Critical=0.241, p_value=None, Alpha=0.1)
>>> print(conc)
Since the critical value (0.241) >= statistic (0.154), we have NO evidence to reject the hypothesis of data normality, according to the AbdiMolin test at a 90.0% of confidence level.

Applying the test with details="full"

>>> from pycafee.normalitycheck import AbdiMolin
>>> import numpy as np
>>> x = np.array([0.8, 1, 1.1, 1.15, 1.15, 1.2, 1.2, 1.2, 1.2, 1.6, 1.8, 2, 2.2, 3, 5, 8.2, 8.4, 8.6, 9])
>>> abdimolin_test = AbdiMolin()
>>> result, conc = abdimolin_test.fit(x, details="full")
>>> print(result)
AbdiMolinResult(Statistic=0.3072356484569813, Critical=0.1965, p_value=None, Alpha=0.05)
>>> print(conc)
Since the critical value (0.196) < statistic (0.307), we HAVE evidence to reject the hypothesis of data normality, according to the AbdiMolin test at a 95.0% of confidence level.

Abdi Molin

to_xlsx