XLSTAT: Fisher's F-test to Compare Two Variances in Excel

Background

Fisher's F-test is a method used to compare the variability of two groups of data. Variability tells us how much the values in a group differ from each other. Some groups have values that are very close together, while others have a wide range of values.

Dataset for Example

The attached data from Fisher (1936) includes sepal length and width for 100 Iris flowers of two species: setosa and versicolor. The goal is to determine if there are significant differences between species for these variables. First, normality tests confirm all four samples follow a normal distribution. Next, Fisher's F-test will assess whether the variances are equal, enabling comparison of the means.

Setting Up

To realize a two-sample comparison of variances test, once XLSTAT is activated select the Test a hypothesis section/ Parametric test/ Two-sample comparison of variances.

 

Click the button to open the dialog box.

In the General tab, select column B for Versicolor sepal length as Sample 1, and column E for Setosa sepal length as Sample 2.

 Ensure "Column labels" is enabled since each column has a label.

In the Options tab, select the test for equality of variances with the alternative hypothesis that Variance 1 ≠ Variance 2 (R=1). Keep the default significance level of 5%.

With no missing data, go to the Outputs tab and enable "Descriptive statistics." You can select additional outputs if desired.

Press OK

Interpreting the Results

The results indicate we should reject H0, as the p-value of 0.009 is below 5%.

Variances are unequal, and the sepal length distributions for Versicolor and Setosa differ.

To update, select column C for Sample 1 and column F for Sample 2.

This time the variances can be considered as equal as the p-value of the test (0.189) is superior to 0.05. 

Since variances are unequal, proceed with a comparison of means.

The descriptive statistics show Versicolor's sepal width mean is less than Setosa's, so a one-tailed test is appropriate.

In the parametric tests section, select the two-sample t-test, using the Student’s option, and choose the same samples as before for sepal width.

In the Options tab elect the alternative Mean 1 – Mean 2 < D where D is 0. We can Assume equality for the variances as we just computed the test before.

Click on OK.

The test results show a significant difference: Versicolor's sepal width is smaller than Setosa's.

The two populations do not have the same distribution.