GrubbsTest Routine

Summary

Grubb's test for outliers.

Declaration

Function GrubbsTest(Data: TVec; out hRes: THypothesisResult; out Signif: TSample; out ConfInt: TTwoElmReal; hType: THypothesisType = htTwoTailed; Alpha: TSample = 0.05): TSample;

Parameter	Description
Data	dataset.
hRes	Returns the result of the null hypothesis (default assumption is there are no outliers).
Signif	(Significance level) returns the probability of observing the given result by chance given that the null hypothesis is true.
ConfInt	Returns the 100*(1-Alpha) percent confidence interval for the Rs coefficient.
hType	Defines the type of the null hypothesis (one or two - tailed, default value two-tailed).
Alpha	Defines the desired significance level. If the significance probability (Signif) is bellow the desired significance (Alpha), the null hypothesis is rejected.

Result

Grubb's (G) statistic.

Description

Performs the Grubbs test for outliers. Test is used to detect outliers in a univariate data set. It is based on the assumption of normality. That is, you should first verify that your data can be reasonably approximated by a normal distribution before applying the Grubbs' test. Grubbs' test detects one outlier at a time. This outlier is expunged from the dataset and the test is iterated until no outliers are detected. However, multiple iterations change the probabilities of detection, and the test should NOT be used for sample sizes of six or less since it frequently tags most of the points as outliers. Grubbs' test is also known as the maximum normed residual test. Grubbs' test is defined for the hypothesis:

H0: There are no outliers in the data set.
Ha: There is at least one outlier in the data set.

More about the test can be found here.