Homogeneity of Variances Tool

Data Analysis Tool

Real Statistics Data Analysis Tool: The Real Statistics Resource Pack provides the Homogeneity of Variances data analysis tool that provides several tests to determine whether two or more groups have a significant difference in variance.

Example

Example 1: Determine whether the homogeneity of variances assumption is met for the data in range A2:D11 of Figure 1 (the group variances are shown in row 12).

Figure 1 – Homogeneity of Variances Tests

Press Ctrl-m and choose the Homogeneity of Variances data analysis tool from the Desc tab. Fill in the dialog box that appears as shown in Figure 2.

Figure 2 – Homogeneity of Variances dialog box

The output is shown on the right side of Figure 1. We see that there are fairly large differences in the p-values among the seven tests.

Example with two groups

Example 2: Determine whether there is a significant difference between the variance of Treat 1 and Treat 4 based on the data in Figure 1.

This time, press Ctrl-m and choose the Homogeneity of Variances data analysis tool from the Desc tab. Fill in the dialog box that appears as shown in Figure 2, except that this time insert A2:A11 in Input Range 1 and D2:D11 (or D2:D10) in Input Range 2. The output is shown in Figure 3.

Figure 3 – Testing whether there is a significant difference between two variances

Both tests show there is a significant difference between the variances of the two treatment groups.

Example with two contiguous groups

Example 3: Determine whether there is a significant difference between the variance of Treat 1 and Treat 2 based on the data in Figure 1.

This time, press Ctrl-m and choose the Homogeneity of Variances data analysis tool from the Desc tab. Fill in the dialog box that appears as shown in Figure 2, except that this time insert A2:B11 in Input Range 1. The output is shown in Figure 4.

Figure 4 – Testing whether two variances are significantly different

Note that all the tests from Example 1 as well as Example 2 are performed. This will be the case when the data from the two treatment groups are found in contiguous columns whose range is inserted into Input Range 1 (with Input Range 2 not filled in).

Examples Workbook

Click here to download the Excel workbook with the examples described on this webpage.

References

Wikipedia (2015) Levene’s test
https://en.wikipedia.org/wiki/Levene%27s_test

Field, A. (2009) Discovering statistics using SPSS. 3^rd Ed. SAGE.

Ramsey, P. H. (1994) Testing variances in psychological and educational research
https://psycnet.apa.org/record/1994-28101-001

Wang, Y. et al. (2016) Comparing the performance of approaches for testing the homogeneity of variance assumption in one-factor ANOVA models
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5965542/#bibr32-0013164416645162

Hitchcock, D. (2017) Test about several variances. Nonparametric statistics
https://people.stat.sc.edu/hitchcock/notes518fall13sec53filledin.pdf

Conover, W. J., Johnson, M. E.,  Johnson, M. M. (1981) A comparative study of tests for homogeneity of variances, with applications to the outer continental shelf bidding data. Technometrics, 23(4), 351-361.
https://www.academia.edu/3492119/A_comparative_study_of_tests_for_homogeneity_of_variances_with_applications_to_the_outer_continental_shelf_bidding_data