2.13.1.8 grubbs

1 Menu Information
2 Brief Information
3 Additional Information
4 Command Line Usage
5 X-Function Execution Options
6 Variables
7 Description
8 Algorithm
9 References
10 Related X-Functions

Menu Information

Statistics:Descriptive Statistics:Grubbs Test

Brief Information

Grubbs outlier test

Additional Information

Minimum Origin Version Required: 9.0 SR0

Menu accessible from 9.1 SR0

Command Line Usage

1. grubbs

2. grubbs ix:=col(2) alpha:=0.1

3. grubbs ix:=col(1) alpha:=0.05 box:=1

X-Function Execution Options

Please refer to the page for additional option switches when accessing the x-function from script

Variables

Display Name	Variable Name	I/O and Type	Default Value	Description
Input	ix	Input vector	<active>	Must be a column or a range within a column
Significance Level	alpha	Input double	0.05	Option list: 0.1 0.05 0.01
Data Point with Largest G	ox	Output double	<unassigned>	The value of the suspected point
Data Index with Largest G	index	Output int	<unassigned>	Row index of suspected point
G Test Statistic	gstat	Output double	<unassigned>	The calculated G value from suspected point
Critical Value	critical	Output double	<unassigned>	The critical G value at the specified significance level
Approximate P Value	pval	Output double	<unassigned>	The p value for the test
Test Significance	sig	Output int	<unassigned>	sig=1 means there is an outlier, sig=0 means there is no outlier
Conclusion	conclusion	Output string	<unassigned>	A statement of conclusion indicating the statistical result
Outlier Plot	box	Input int	0	Specify whether to generate an outlier plot. box=1 means to generate, and box=0 means not to generate.
Grubbs Plot Data	rd	Output ReportData	[<input>]<new>	The worksheet range to put the plot data for outlier plot, if generating an outlier plot is selected.
Grubbs Report	rt	Output ReportTree	[<input>]<new>	The worksheet range to put the report table.

Description

Used to test outlier for a dataset with more than 3 data points, at significance level 0.01, 0.05 or 0.1.

Algorithm

1. Calculate G

$G= \left | \frac{ox-mean}{SD} \right |$

where ox is the value of suspected point (usually highest or lowest observation), mean is the mean value of data set, and SD is the standard deviation.

Compare G with the critical value.

2. Calculate p

$t=\sqrt{\frac{N\left ( N-2 \right )Z^{2}}{\left ( N-1 \right )^2-NZ^2}}$

where Z is the largest G, N is the number of samples.

The p value is then calculated as the two-tailed P value for the student t distribution of the t value.

References

Stephen L R. Ellison, Vicki J. Barwick and Trevor J Duguid. Farrant. 2009. Practical Statistics for the Analytical Scientist. The Royal Society of Chemistry, Cambridge, UK.