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I want to preface this with: I am not the best statistician. So please bear with me if this is either really simple or riddled with errors.

I have a dataset of geographic areas classified by decile. I have been able to gather a number of events in each decile and calculate an expected number of events in each decile based on population sizes. These are not the true numbers as this is a dummy dataset, but the pattern is very similar. Red is observed.

Dummy Chart

Decile 5 and 6 are obviously very similar. However, there is a difference in Obs/Exp on the lower and higher ends. My question is: how can I show if the differences are statistically significant or not?

I recognise that each individual point on its own does not have enough degrees of freedom (N-1 = 0 as I have one point for each decile). There are several areas included in each decile, so I do have more degrees of freedom available. However, many have a value an observed value of 0. Can anyone advise before I go too far down a rabbit hole of wrongness? Thanks very much in advance.

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    $\begingroup$ Assuming the "expected" values are meaningful Can I use a chi-squared test to compare two empirical distributions? $\endgroup$ Dec 21, 2022 at 10:01
  • $\begingroup$ How do you obtain the 'expected values'? What is the point behind the deciles? In what way are they computed (what do the deciles mean, in what way do you create the order?) and why do you want to use those aggregrated statistics for statistical analysis? $\endgroup$ Dec 21, 2022 at 21:20
  • $\begingroup$ Expected results are calculated based on the population "share" (% of total population in the * sum of total observed values). in the are and the total of the observed values. Perhaps I am going wrong here? Deciles are calculated based on a score. It's a standard way of classifying areas here, it seems. I want to use these values because, if I show them in a meeting, I know someone is going to ask "are those differences statistically significant?" Decile 1 is very likely a significant difference just looking at it, but it's not so clear for 3 and 4; maybe even 8. $\endgroup$
    – JamesW
    Dec 23, 2022 at 14:16
  • $\begingroup$ That doesn't make it much clear. What is 'population share' and how does it allow you to turn it into an expectation value. Deciles as calculated based on score, but what 'score'? ..... Explain the situation. .... Currently we are only staring at a figure with dots that do not overlap, but we have no idea what it means and can not give an insight on the statistics behind it. $\endgroup$ Dec 23, 2022 at 14:25

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