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## What is Dunnett’s Test?

**Dunnett’s Test** (also called* Dunnett’s Method* or *Dunnett’s Multiple Comparison)* compares means from several experimental groups against a control group mean to see is there is a difference. When an ANOVA test has significant findings, it doesn’t report *which *pairs of means are different. Dunnett’s can be used *after *the ANOVA has been run to identify the pairs with significant differences.

One fixed “control” group is compared to all of the other samples, so it should only be used when you have a control group. If you don’t have a control group, use Tukey’s Test.

## Calculation

As Dunnett’s compares two groups, it acts similarly to a t-test. The following formula gives you a value that you can use to compare mean differences.The formula is:

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Step 1: Look up the t_{Dunnett} critical value in the Dunnett-critical value table. You’ll need:

- Your chosen alpha level (usually 5%),
- Sample size, n,
- Degrees of freedom from the ANOVA “Within Groups” output. This is the “n” in the left hand column of the table.

For example, let’s say you had an alpha level of 5%, a sample size of 5 and 20 df. The Dunnett critical value is 2.65.

Plug the value into the formula:

Step 2: Find the mean squares (MS) of the within group in the ANOVA source table. Plug that value into the above formula. For example, let’s say your MS within is 15.39:

Step 3: Find “n”, the number in one group. For this example, that’s 5:

Solving the formula, we get:

**D _{Dunnett} = 2.65 * 2.481 = 6.575.**

**The answer (6.575) is the critical distance between means.** If the distance between a control group mean and an experimental group mean is greater than 6.575, then that distance is significant. For example, let’s say you had a control group mean of 52 and three experimental group means of 55, 64 and 72. The differences between means (absolute values) are:

- Group 1 55 – 52 = 3
- Group 2 64 – 52 = 12
- Group 3 72 – 52 = 20

Only groups 2 and 3 exceed the Dunnett’s distance of 6.575, so they are the significant pairs.

## References

Upton G. & Cook I. (2006.) A Dictionary of Statistics, 2nd edition, Oxford University Press, Oxford, United Kingdom.

Everitt B. S. & Shrondal A. (2010.) The Cambridge Dictionary of Statistics, 4th edition, Cambridge University Press, Cambridge, United Kingdom

Rumsey, Deborah (2009). Statistics II for Dummies. Wiley.

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**Stephanie Glen**. "Dunnett’s Test / Dunnett’s Method: Definition" From

**StatisticsHowTo.com**: Elementary Statistics for the rest of us! https://www.statisticshowto.com/dunnetts-test/

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