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for my high school statistics course I got myself daily CSV files from the Corona ARCGIS at JHU (cumulative cases, cumulative deaths, etc). I'd like to try to model and compare the distributions of cases for two states during a given period.

So far we've learned about ChiSquared tests, t-tests, z-tests, normal and binomial distributions, and also bit about smoothing.

I'm having a bit of trouble deciding, though, which test would work best for my idea, since I see daily increasing numbers, so no mean values, right? Also, populations are different in each state... Perhaps a goodness of fit chi square might work?

Can anyone point me in the right direction? I'm not averse to teach myself new tests (as long as it doesn't take a university degree to understand it).

Thanks!

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  • $\begingroup$ What exactly do you want to compare? The tests that you mentioned work on parameters of the distribution. $\endgroup$
    – user2974951
    Commented Jan 7, 2021 at 11:42
  • $\begingroup$ Well, the frequencies of the distributions might be one idea. That could work with goodness of fit, perhaps $\endgroup$
    – AmazingAnita
    Commented Jan 7, 2021 at 12:40
  • $\begingroup$ Before deciding what statistical test to do, you will benefit massively from getting your "idea" (or hypothesis) to a form that can be subjected to a statistical test. You sketched out that you want to "compare the distributions of cases for two states during a given period", can you refine the statement to a point where you can compute a single-number statistics out of it? Examples can be: "compare if the average case per day differs between two states", which you can then use # confirmed cases (per 100,000 population) per day as a statistic and run statistical tests. $\endgroup$
    – B.Liu
    Commented Jan 7, 2021 at 14:26
  • $\begingroup$ Aside, if your hypothesis is indeed "the distributions of cases for two states during a given period is different", there are statistical tests that does so. Though one needs to be very careful on the context (how it comes by) and implications (what does that lead to) of such hypothesis, and it appears you may need some work to demonstrate that you know these things. $\endgroup$
    – B.Liu
    Commented Jan 7, 2021 at 14:32
  • $\begingroup$ Thank you for your pointers! I'd be very happy to compare prevalences or daily incidences. The data would also allow to establish mortalities, perhaps even some kind of case fatality ratio (a bit of a stretch due to mortality being delayed). $\endgroup$
    – AmazingAnita
    Commented Jan 7, 2021 at 18:37

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You can use a $\chi^2$-test for count data whose distribution is binomial or Poisson distributed and can be estimated with a normal distribution.

You might have this situation with counts of covid-19 cases but you should keep in mind that the data can be over or under dispersed. For the binomial or Poisson distribution the dispersion of the distribution follows a particular relationship with the expected value of the distribution. Many methods assume that this relation holds. In a practical situation you might have a different relationship.

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