# Critical Mean Difference

Given the comparison of multiple groups, the Critical Mean Difference (CMD) is the minimum difference between any two of these group means that are significant at the given level of alpha. Four methods are available: Tukey, Bonferroni, Scheffe or unprotected t-tests.

## Calculations

### Tukey

### Bonnferroni

### Scheffe

### t-test

Where:

- k is the number of Groups or Tests
- MSE is the Mean Square Error term
- n1 is the first group sample size
- n2 is the second group sample size
- Q is the Studentized Range Statistic

### Menu

**File**provides the ability__Save__or Print the output, or return to the__Main Form__.**Edit**allows__Editing Output Text__by cutting, copying, pasting, and undoing entry.**View**provides the ability to enlarge/reduce the Form size for easier viewing.**Help**provides access to this Website.

### Speed Buttons

These buttons provide quick access to the following tasks.

- Returns to last Form or the
__Main Form__. -
__Saves__the output to a file. - Prints the Text.
- Copies Selection to the clipboard.
- Pastes Text from the clipboard
- Enlarges/Reduces Form size for easier viewing.
- Brings up the
__Main Form__. - Brings up the Help file.
- Hides the form.

### Action Button

Performs calculations and displays output.

### Output Text

The calculation output is displayed here when is clicked. You may save, print, edit, cut, copy, and paste text in this area.

### Decimal Place Change

Changes the number of decimal places, from 0 to 9. Change may be made by selecting and typing in the number, or by using the incrementing buttons.

### Alpha

Enter the level of Alpha here.

### Groups

Enter the number of Groups in the comparison (or Tests for Bonferroni) here.

### MSE

Enter the Mean-Square Error term here.

### df(MSE)

Enter the Degrees of Freedom for the Mean-Square Error Term here.

### n1

Enter the first sample size for one of the groups in the comparison here.

### n2

Enter the second sample size for one of the groups in the comparison here.

### Method Selection

Select Tukey, Bonferroni, Scheffe or t-test Critical Mean Differences to be calculated.