# 2.13.1.8 grubbs

Statistics:Descriptive Statistics:Grubbs Test

## Brief Information

Grubbs outlier test

Minimum Origin Version Required: 9.0 SR0

## Command Line Usage

 1. grubbs 

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

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

## 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.

## Related X-Functions

Keywords:significance level