SAP HANA Predictive Analysis Library (PAL)

3.7.5 Grubbs' Test
Grubbs’ test is used to detect outliers from a given univariate data set Y={Y 1 ,Y 2 ,...,Y n }. The algorithm
assumes that Y comes from Gaussian distribution.
The basic steps of the algorithm are as follows:
1. Define the hypothesis.
H0: There are no outliers in the data set Y.
H1: There is at least one outlier in data set Y.
2. Calculate Grubbs’ test statistic.
Here
3. Given the significance level α, if
The algorithm will reject the hypothesis at the significance level α, which means that the data set contains
outlier. Here
denotes the quantile value of t-distribution with n-2 degrees and a significance level
.
The above is called two-sided test. There is another version called one-sided test for minimum value or
maximum value.
●
For minimum value:
●
For maximum value:
Note that you must replace with for one-sided test.
Suppose Y max is an outlier from Grubbs’ test, you can calculate the statistic value U as shown below:
1. Remove Y max from original data and get Z={Z 1 ,Z 2 ,...,Z n-1 .
514 P U B L I C
SAP HANA Predictive Analysis Library (PAL)
PAL Functions