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I have monthly data of sales for 3 firms (A, B and C) for 10 years (12*5=60 data points per firm). I want to test if the variance of sales in A is more than the variance in B which is more than the variance in C.

I calculated variances for each year. Thus, I had 10 values of variances for each firm. Then what? I am not comfortable with grouping in a year as it is clearly an arbitrary grouping.

How should I look at this problem? What is the ideal way to test? The average sale for the three firms is different, so, should COV be used instead of variance?

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  • $\begingroup$ How come you have 60 data points? Did you mean 120? $\endgroup$
    – yoav_aaa
    Commented Oct 30, 2016 at 16:04
  • $\begingroup$ did you look at repeated measures anova? $\endgroup$
    – Estimate the estimators
    Commented Jan 17, 2023 at 8:08

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One approach would be to fit a regression model that equates the residual variance between the groups (which is the usual regression model assumption) and then compare this to a model that allows the residual variance to be unequal. When comparing these models using a likelihood ratio test, a statistically significant test statistic will indicate that the model with unequal variance is a better fit. This of course will only give you the omnibus test for differences, and not which specific groups differ. To get the pair-wise differences in variance you could take the same approach but constrain two of the three groups to have the same variance.

These types of regression models where heterogenous variance can be modeled are commonly found as options in a glm or mixed model.

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  • $\begingroup$ Your approach sounded like a reasonable way of using some kind of weighted least squares until your last comments about a GLM or a mixed model. $\endgroup$
    – Dave
    Commented Aug 15, 2020 at 2:17
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It seems to me like you would like to know whether the variance in the "sales" variable is equal or not between the treatments "firm". There are a number of tests for heterogeneity of variances, the one to chose depends on the distribution of the variable "sales". For count data, I personally used the Fligner-Killeen test. There are other, which are well described on this page : http://www.sthda.com/english/wiki/compare-multiple-sample-variances-in-r

There is no need to calculate the variance by yourself before using one of these tests.

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