# Learn How to Calculate Tukey's Post HOC Test - Tutorial

## How to Calculate Tukey Post Hoc HSD Test - Definition, Formula and Example

##### Definition:

Tukey's post-hoc test is a method that is used to determine which groups among the sample have significant differences. This method calculates the difference between the means of all the groups. Tukey's HSD test values are number which acts as a distance between the groups. It works by defining a value known as Honest Significant Difference.

##### Example :

Nisha predicts that students will learn most efficiently with a constant background sound, as opposed to an unpredictable sound or no sound at all.
She randomly divides twenty-four students into three groups of eight. All students study a passage of text for 30 minutes.
Those in group 1 study with background sound at a constant volume in the background. Those in group 2 study with noise that changes volume periodically. Those in group 3 study with no sound at all. After studying, all students take a 10 point multiple choice test over the material. She begins by conducting a One-way, between-subjects Analysis of Variance.
She finds a significant F score. The relevant variables from her ANOVA table are: Mean M1 = 30 , Mean M2= 20 , MS_{w} = 25 , n = 2

##### Given,

Mean M1 = 30 , Mean M2= 20 , MS_{w} = 25 , n = 2

##### To Find,

HSD (Honest Significant Difference)

##### Solution:

###### Step 1:

Substitute the values in the HSD Formula,

HSD = 30 - 20 / sqrt (25/2)

HSD = 10 / 3.5355

HSD = 2.8288

Learn how to calculate Tukey Post Hoc HSD Test in this tutorial, which is given with the definition, formula and example.