normaltest

Normaltest is a statistical test used to assess whether a sample of data follows a normal (Gaussian) distribution. In SciPy, normaltest refers to the function scipy.stats.normaltest, an omnibus normality test based on D'Agostino's K^2 method. The test combines measures of skewness and kurtosis to evaluate departures from normality.

The calculation proceeds by computing the sample skewness and sample kurtosis, converting these to z-scores, and forming the K^2 statistic as the sum of the squared z-scores. Under the null hypothesis that the data are drawn from a normal distribution, the K^2 statistic follows a chi-square distribution with 2 degrees of freedom. A p-value is reported to indicate the probability of observing such a deviation under normality.

Input and output: normaltest accepts a one-dimensional array-like object of numeric data, or data arranged along a specified axis. It may handle missing values according to a nan_policy parameter (for example, 'omit' or 'propagate'), depending on the SciPy version. The function returns a tuple (statistic, pvalue), where statistic is the K^2 value and pvalue is the tail probability.

Interpretation and considerations: A small p-value suggests that the data deviate from normality. The test is sensitive to sample size: with large samples, even small departures may be detected, while with small samples the test may lack power. Normaltest is univariate and should not be used to assess multivariate normality; for that purpose, alternatives or multivariate tests are needed. Other normality tests include the Shapiro-Wilk test and the Anderson-Darling test.