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For my current project, I am interested in comparing groups of percentages. For example, say that we would like to estimate the total number of customers in a month, when we are only a few weeks in.

Let us take the current month and day (for me), which is May 11th. In this case, I would like to estimate the total amount of customers in May. We have daily data of the number of customers in previous years, as well as in May. To not overcomplicate, say that we will only base our estimate on the previous numbers in May of 2018, 2019 and 2020.

Now assume that for May 11th in the previous 3 years, we have the following percentages: (0.1, 0.12, 0.14). For May 6th in the previous 3 years, we have the following percentages: (0.04, 0.05, 0.045) (both are just examples). This means that on May 11th in 2018, the cumulative number of customers relative to the total number of customers in May 2018 was 10%.

I would like to find the date which has the most stable behaviour, which I believe would involve variation. I read about the Coefficient of variation, but because these are percentages, I'm not sure if the Coefficient of variation would be an adequate statistic to find the more 'stable' day for.

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You can try using repeated measures ANOVA (or Friedman Test as non-parametric alternative test). For the effect size you could also calculate fold change.

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