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I have three clinics that are testing for Zika virus. We know the proportion of positives aggregated across all clinics, i.e., the first clinic has identified 20% of all positives across the three clinics, the second 30% and the third 50%. Now we know there are 100 new cases but these proportions change with respect to previous cases, i.e., they are now 10% 50% and 40%. Is there a distribution that can tell me if these proportions are significantly different than would be expected given the original proportions? I have run a Monte Carlo simulation to figure this out, but I was wondering if there was a distribution that describes this.

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  • $\begingroup$ If you know nothing about the volumes, then you can't simulate this with Monte Carlo either. $\endgroup$
    – Aksakal
    Jun 27 '16 at 18:05
  • $\begingroup$ Thanks for you comment. However, I think if we make an assumption that the relative volumes are constant it is ok. $\endgroup$
    – jtam
    Jun 27 '16 at 20:56
  • $\begingroup$ It's not enough. You'd need an assumption of what are these relative volumes. $\endgroup$
    – Aksakal
    Jun 27 '16 at 21:10
  • $\begingroup$ Indeed. I can do this with another assumption: that the relative volume of patients is equal to the relative number of positives. $\endgroup$
    – jtam
    Jun 27 '16 at 21:15
  • $\begingroup$ So, maybe you can add these assumptions to your question, then it'll be more realistic to come up with the distribution. Otherwise your question has too many degrees of freedom to suggest a sensible answer. $\endgroup$
    – Aksakal
    Jun 27 '16 at 21:19
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I think I figured this out: multinomial distribution!

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  • $\begingroup$ This is being automatically flagged as low quality, probably because it is so short. I recognize that this is your question, & you think this is the answer, but at present it is more of a comment than an answer by our standards. Can you expand on it? $\endgroup$ Jun 29 '16 at 17:50

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