If you are curious as to whether the means of greater than 2 groups are statistically different or not you could use a 1-way ANOVA. But, if you have multiple treatment groups and want to compare the means to a control group, then you can use Dunnett’s 1-way ANOVA.

ANOVA stands for Analysis of Variance. ANOVA is a statistical method used to compare the means of two or more groups of data. It is based on the comparison of the variability between the different groups to the variability within each group. The method aims to determine if the observed differences between the groups are due to chance or to some systematic effect.

ANOVA tests the null hypothesis (Ho) that there is no significant difference between the means of the groups against the alternative hypothesis (Ha) that at least one group has a different mean than the others. The test calculates an F-statistic, which is the ratio of the between-group variation to the within-group variation. If the calculated F-statistic exceeds a critical value, the null hypothesis is rejected, and you can conclude that at least one group mean is significantly different from the others.

## Overview: What is Dunnett’s 1-way ANOVA?

Dunnett’s 1-way ANOVA is a statistical method used to compare the means of multiple data groups to a control group, while controlling for the overall type I error rate. It is a variation of the one-way ANOVA test, which is used to compare the means of more than two groups. Fisher’s one-way ANOVA and Tukey’s one-way ANOVA are similar tests.

In Dunnett’s test, the control group serves as a reference or comparison group against which the other groups are compared. The test assumes that the observations in each group are independent and identically distributed, and that the variances of the groups are equal.

The test calculates a test statistic that measures the difference between each group mean and the control group mean and compares it to a critical value based on the number of groups and the chosen significance level. If the test statistic exceeds the critical value, the null hypothesis (that the means of all groups are equal) is rejected, and you can conclude that at least one group mean is statistically different from the control group mean.

## An industry example of Dunnett’s 1-way ANOVA

Suppose a pharmaceutical company is testing the effectiveness of a new drug for lowering blood pressure. They recruit 4 groups of patients: a control group receiving a placebo, and three treatment groups receiving different doses of the new drug.

The company wants to determine if any of the treatment groups have a significant effect on blood pressure compared to the control group. They measure the blood pressure of 10 patients in each group and obtain the following data:

Control group: 130, 140, 135, 145, 140, 135, 130, 138, 142, 140

Treatment group 1: 125, 130, 128, 132, 135, 130, 135, 132, 138, 133

Treatment group 2: 118, 122, 125, 128, 130, 126, 132, 129, 133, 127

Treatment group 3: 115, 118, 120, 122, 125, 128, 123, 127, 129, 126

To analyze these data using Dunnett’s test, you start by calculating the overall mean and variance of the groups. Next, you calculate the test statistic for each treatment group by comparing its mean to the control group mean. Finally, you compare each test statistic to the critical value for Dunnett’s test, which depends on the chosen significance level (e.g., 0.05) and the number of treatment groups (e.g., 3). For a significance level of 0.05 and 3 treatment groups, the critical value is 2.92.

When all your calculations are done, your conclusion will be that treatment groups 2 and 3 have a significant effect on lowering blood pressure compared to the control group. You cannot conclude that there is a significant difference between treatment groups 2 and 3, only that they are both significantly different from the control group.

### What is the difference between Dunnett’s test and the Tukey test?

Dunnett’s test compares each treatment group mean to a control group mean, while Tukey’s test compares every pair of group means. Dunnett’s test is more appropriate when there is a clear control group, while Tukey’s test is better suited for situations where all groups are equal.

### How is the critical value for Dunnett’s test calculated?

The critical value for Dunnett’s test depends on the number of data groups and the chosen significance level. It is calculated using a formula that takes into account the overall type I error rate and the degrees of freedom.

### What is the assumption of equal variances in Dunnett’s test?

Dunnett’s test assumes that the variances of all groups are equal. This assumption is important because it affects the calculation of the test statistic and the critical value.

### Can Dunnett’s test be used for non-normal data?

Dunnett’s test assumes that the data in each group are normally distributed. If this assumption is not met, it may be necessary to use a different test or to transform the data to achieve normality.

### How is Dunnett’s test interpreted?

If the test statistic exceeds the critical value, you can conclude that at least one group mean is significantly different from the control group mean. The test does not identify which group(s) differ significantly, only that there is a significant difference somewhere among the groups.