Hossam Sabbour | Lean Six Sigma Consultant

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Why should we check for equal Variances before using ANOVA?

Sampling is prone to errors because of different reasons. Using Hypothesis Testing is essential when using sampling to get reasonable statistical confidence when you make decisions.

One of the types of Hypothesis Testing is the "Analysis of Variance" ANOVA. Before using ANOVA, you should check that data are following the Normal Distribution, and the different populations are having equal variances.

What is the reason for checking for equal variances?
When we have populations of different variance, the probability of not detecting a real difference increases, thus making a wrong decision.

The following example will explain this.

Three groups of data (A, B & B1) are created as shown below.

 Notice that there is a difference between the mean of group A (9,985) and the means of the other two groups B & B1 (10.13 & 10.14). The means of B & B1 are the same.

Variances of groups A & B are almost equal, while the Variance of Group B1 is much higher.

If we found a statistical difference between the means of groups A & B, then we might expect the same for groups A & B1, but because variance is significantly different between A & B1, the difference couldn’t be detected.

Below are the outputs of the ANOVA made for A & B, then for A & B1
The difference between A & B is detected, while it was not for A & B1

One-way ANOVA: A, B 

Analysis of Variance

Source    DF   Adj SS  Adj MS  F-Value  P-Value
Factor     1     9.86        9.855     9.62      0.002


One-way ANOVA: A, B1 

Analysis of Variance

Source    DF   Adj SS  Adj MS  F-Value  P-Value
Factor      1     12.0      12.009     2.29      0.130