Statistical Functions
The Statistical Functions processor tests how closely a window of data matches a normal distribution, using the goodness-of-fit tests you enable, and returns a p-value for each indicating the strength of that match.
Why use Statistical Functions
Use this processor to check whether your data behaves like a normal distribution before applying downstream statistics that assume normality, for example, before running control charts or capability calculations that rely on that assumption.
How it works
Enable one or more of five goodness-of-fit tests via their checkboxes. Each observes a window of data and returns a p-value: the smaller the p-value, the less likely the data came from a normal distribution.
- Jarque-Bera compares the window's skewness and kurtosis to what a normal distribution would produce, calculated as JB = (n/6)(skewness² + (1/4)(kurtosis - 3)²). The further the result is from zero, the less the data resembles a normal distribution.
- Cramer-von Mises calculates the window's mean, standard deviation, and Z-scores, then compares the summed squared differences between the data's distribution and the expected normal distribution: cramerVonMises = (1/12n) + Σ((2i-1)/(2n) - Φ(Z))².
- Anderson-Darling uses the same mean, standard deviation, and Z-score calculations as Cramer-von Mises, but weights the tails of the distribution more heavily.
- D'Agostino-Pearson combines a skewness test and a kurtosis test to check whether the window's shape matches a normal distribution.
- Kolmogorov-Smirnov (using the Lilliefors variant for testing normality) calculates the window's mean, standard deviation, and Z-scores, then finds D+ and D-, the largest gaps between the data's distribution and the expected cumulative distribution. The test statistic is max(D+, D-) × √n.
Parameters
Parameter | Details |
|---|---|
Window Size | The window of data used for each enabled test. |
Jarque-Bera | Enables the Jarque-Bera test. |
Anderson-Darling | Enables the Anderson-Darling test. |
Cramer-von Mises | Enables the Cramer-von Mises test. |
D'Agostino-Pearson | Enables the D'Agostino-Pearson test. |
Kolmogorov-Smirnov | Enables the Kolmogorov-Smirnov test (using the Lilliefors variant). |