# Grubbs test to detect outliers in Excel tutorial

This tutorial shows how to compute and interpret a Grubbs test to detect outliers analysis in Excel using the XLSTAT software.

## Dataset for testing outliers with Grubbs test

The data have been obtained from a normal distribution with mean 0 and variance 3. One outlier has been added. We wish to test if there is one outlier in the sample.

## Goal of this tutorial

We would like to detect an outlier from a sample using Grubbs test.

## A bit of theory: how does the Grubbs test work?

First, we state the null hypothesis that there are no outliers in the dataset. Here is how to calculate the Grubbs test statistic:

$G = \frac{\max{|Y_{i} - \bar{Y}|}} {s}$

If this statistic is above the value of significance in the Grubbs table, we reject the null hypothesis and consider that the dataset contains outliers.

## Setting up a Grubbs test to detect outliers

To start the Grubbs test go to the menu Testing outliers / Grubbs test. In the General tab, select the data and the Grubbs test option (the Double Grubbs test can be used to detect two outliers). As an alternative hypothesis choose the two-sided option. The default significance level is left as is: 5%. When ready click on OK.

## Interpreting a Grubbs test for detecting outliers

The result is that the p-value for this test is slaller than 0.0001. That means that the null hypothesis should be rejected. In the following table, the detected outlier is given. You can also find the Z score to detect outliers in the output of this test. 