k-sample comparison of variancesk-sample comparison of variances is part of:
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Accessible - Available in many languages
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Automatable and customizable Most of the statistical functions available in XLSTAT can be called directly from the Visual Basic window of Microsoft Excel. They can be modified and integrated to more code to fit to the specificity of your domain. Adding tables and plots as well as modifying existing outputs becomes easy. Furthermore, XLSTAT includes some special tools on the dialog boxes to generate automatically the VBA code in order to reproduce your analysis using the VBA editor or to simply load pre-set settings. This effortless automation of routine analysis will be a huge time saver on your part.
Principles of the k-sample comparison of variances
Take k samples S1, S2, …, Sk, comprising n1, n2, …, nk observations with variances s1², s2², …, sk². The k-sample comparison of variances will test if all the Si are equal or not.
k-sample comparison of variances in XLSTAT
XLSTAT offers two parametric tests for the comparison of the variances of k independent samples (k > 2).
Levene's test can be used to compare two or more variances. This is a two-tailed test for which the null and alternative hypotheses are:
- H0: s1² = s2² = … = sk²
- Ha: There is at least one pair (i, j) such that si² ≠ sj²
The statistic from this test involves absolute deviations at the mean or at the median. The use of the mean is recommended for symmetrical distributions with averagely thick tails. The use of the median is recommended for asymmetric distributions.
The Levene statistic follows a Fisher distribution with k-1 and n1+n2-2 degrees of freedom.
Bartlett’s homogeneity of variances test
Bartlett's test can be used to compare two or more variances. This test is sensitive to the normality of the data. In other words, if the hypothesis of normality of the data seems fragile, it is better to use Levene's or Fisher's test. On the other hand, Bartlett's test is more powerful if the samples follow a normal distribution.
This also is a two-tailed test which can be used with two or more variances. The hypothesis are similar to the ones in the Levene’s test. Bartlett's statistic follows a Chi² distribution with k-1 degree of freedom.