Klotz Test

TL;DR

A test for whether variances across groups are equal (used in experimental research).
For two samples, it compares the two sample variances using a simple ratio of their difference to their sum.
Variances are first computed by squaring deviations from each sample mean and averaging.

Definition

The Klotz test is a statistical procedure that is used to determine whether two or more samples have equal variances. It is commonly used in experimental research to assess the homogeneity of variances between different groups of subjects.

Explanation

Steps described in the source:

Compute the variance for each sample. This is done by finding the difference between each value in the sample and the sample mean, squaring those differences, and then taking the average of the squared differences.
For the two-sample case, apply the Klotz test formula:

\text{Klotz test statistic} = \frac{s1^2 - s2^2}{s1^2 + s2^2}

where s1 and s2 are the variances for the two samples.

Decision rule given in the source:

If the resulting Klotz test statistic is greater than or equal to 0, the variances between the two samples are considered to be equal.
If the statistic is less than 0, the variances are considered to be unequal.

Examples

Comparing cognitive abilities in children

A study compares cognitive abilities of two groups of children: one group exposed to a specific educational program and one not exposed. The researchers use the Klotz test to determine whether the variance in cognitive abilities between the two groups is equal.

Comparing effectiveness of weight loss programs

A study compares two weight loss programs: group A follows program A and group B follows program B. The researchers use the Klotz test to determine whether the variance in weight loss between the two groups is equal.

Use cases

Commonly used in experimental research to assess the homogeneity of variances between different groups of subjects.

Variance
Homogeneity of variances