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For each day of the week, I observe $n_i$ independently chosen values from some process. I would like to be able to answer the following two questions.

Are the distributions from which the samples are drawn the same for each day?

If not, can we split the days into two groups of days so the distributions are the same in each group?

If I only had two days then it seems you could do a two sample Anderson-Darling test.

Can my two questions be answered?

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  • $\begingroup$ You can check the answers and the comments for the question below for an Andersen Darling test for more than one sample. stats.stackexchange.com/questions/12285/… $\endgroup$
    – Daniel
    Sep 27, 2014 at 19:22
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    $\begingroup$ k-sample Anderson-Darling type tests exist. However, you may want to consider the possibility of serial correlation over time. $\endgroup$
    – Glen_b
    Sep 28, 2014 at 7:20
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    $\begingroup$ Can you say more about what you want to check for? Are you wondering if the mean differs by day, the SD, the skew, etc? Are you wondering if the data come from different types of distributions (eg, normal vs uniform)? Something else? $\endgroup$ May 19, 2021 at 18:19

1 Answer 1

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One approach is to

  1. Fit each day's n values to a non-parametric kernel density estimation
  2. At the end of the week you will have 7 estimated PDFs
  3. Show these PDFs on a single plot
  4. Any PDF that overlays another may indicate that their data came from the same distribution
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    $\begingroup$ "Overlay" of PDFs is vague, non-quantitative, and generally does not work as a useful statistic for testing equality of distributions. Moreover, the result might be (and will be) sensitive to the choice of kernel radius. $\endgroup$
    – whuber
    Jan 17, 2022 at 15:22

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