# 17.1.11 Grubbs' Test

## Supporting Information

To open the Grubbs' test dialog box from the menu:

1. Click Statistics: Descriptive Statistics: Grubbs' Test (Open Dialog...)

## Dialog Box Controls

Results Log Output Select to output results to the Results Log. Controls recalculation of analysis results: None Auto Manual For more information, see: Recalculating Analysis Results Must be a column or column range. For help with range controls, see: Specifying Your Input Data Option list: 0.1 0.05 0.01 Select to generate an outlier plot. Scatter plot with upper and lower confidence limits and dataset mean as line plots. Worksheet range to output the outlier plot data (available if Outlier Plot is selected). Flat sheet lists upper and lower confidence values. For help with the range controls, see: Output Results The worksheet range to output the report table.

## Algorithm

1. Calculation of the Grubbs test statistic $G$:

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

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. Calculation of the p value:

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

where $Z$ is the largest $G$ and $N$ 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.

## Handling Missing Values

The missing values in the data range will be excluded in the analysis

## 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.