Scheffe Test Calculator

Formula

The formula to calculate the Scheffe Test Statistic (S) is:

\[ S = \frac{MSR}{MSE} \times (n - k) \]

Where:

\(S\) 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

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.

Example Calculation

Let's assume the following values:

Mean Square Between Groups (MSR) = 25
Mean Square Within Groups (MSE) = 5
Total Number of Observations (n) = 30
Number of Groups (k) = 3

Using the formula:

\[ S = \frac{25}{5} \times (30 - 3) = 5 \times 27 = 135 \]

The Scheffe Test Statistic (S) is 135.