Multiple Comparisons Using Dunnett’s Test

  Dunnett’s test is designed to compare multiple treatments against a control in order to detect significant differences. As with other post-hoc tests, Dunnett’s test is considered conservative and requires a prior ANOVA to be conducted. The test relies on a specific t-table that depends on the number of treatments.


1 Equation:

\[ dms = d \sqrt{\frac{2qmr}{r}} \]

Where:

  • dms = minimum significant difference;
  • qmr = mean square of residuals;
  • d = tabulated critical value (5% significance level).

2 Files:

  1. Dunnet1matrix program, critical d table, and 1ANAVA1matrix
  2. Program source code
  3. Table of critical d values at 5% significance

3 Usage and example

# Input:
1. Enter a matrix containing the dataset;
   Note: the control group must be placed in the 1st column of the matrix;
2. Run the program "1ANAVA1matrix" from the main page ("hp50");
3. Run the program "Dunnet1matrix".

# Output:
1. Statistical quantities: sqtr, sqt, qmtr, qmr;
2. F-value;
3. p-value;
4. R², coefficient of determination;
5. Results of comparisons between each treatment and the control group
   (positive values indicate significant differences);
6. dcrit5%: calculated value from the distribution;
7. dms: minimum significant difference;
8. "HSD": minimum significant difference value;
9. Matrix containing comparison values for each pair of groups.


(a) Insertion of data matrix.
(b) ANOVA results obtained.
(c) Results of Dunnett’s test.
Figure 1: Dunnet1matrix program running on the Android version of the HP50G calculator (Go49gp), showing data input, ANOVA, and test results.


  The dms result is identical to that reported in the reference source (Vieira, 2000).

4 References:

  1. Vieira, Sônia. Analysis of Variance: ANOVA. Atlas Publishing, 2000.
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