Enter the mean square between and within groups, the number of observations, and the number of groups to determine the Scheffe Test Statistic.

## Scheffe Test Formula

The following formula is used to calculate the Scheffe Test statistic.

S = (MSR / MSE) * (n - k)

Variables:

- S is the Scheffe Test statistic MSR is the mean square between groups MSE is the mean square within groups n is the total number of observations k is the number of groups

To calculate the Scheffe Test statistic, divide the mean square between groups by the mean square within groups. Multiply the result by the difference between the total number of observations and the number of groups.

## What is a Scheffe Test?

A Scheffe Test is a statistical method used in analysis of variance (ANOVA) for conducting post hoc comparisons. It is used to determine the differences between group means after a null hypothesis has been rejected in an ANOVA test. The Scheffe Test is conservative and controls the experiment-wise error rate, making it suitable for all possible comparisons, including pairwise and complex contrasts. It is named after the American statistician Henry Scheffé.

## How to Calculate Scheffe Test?

The following steps outline how to calculate the Scheffe Test statistic.

- First, determine the mean square between groups (MSR).
- Next, determine the mean square within groups (MSE).
- Next, gather the formula from above = S = (MSR / MSE) * (n – k).
- Finally, calculate the Scheffe Test statistic.
- After inserting the variables and calculating the result, check your answer with the calculator above.

**Example Problem : **

Use the following variables as an example problem to test your knowledge.

mean square between groups (MSR) = 120

mean square within groups (MSE) = 80

total number of observations (n) = 50

number of groups (k) = 5