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Re: binary data, proportions and distributions
Posted:
May 4, 2012 12:17 AM


On Thu, 03 May 2012 08:57:11 +0100, Rod wrote: > "James Waldby" wrote ... >> On Wed, 02 May 2012 13:28:47 +0100, Rod wrote: >>> If I look at a binary variable, say smoking/no smoking, and for each >>> county in the world or state in a country, calculate the proportion >>> of adults who smoke and then plot a frequency histogram of these >>> numbers. Should I expect the histogram to be from a particular >>> distribution, and if so which? >> >> If the binary variable is something that depends on locale or culture, >> percounty (country?) or perstate histograms will not in any >> meaningful sense be drawn from a particular distribution. A >> histogram itself might be thought of as drawn from some >> multivariate distribution but I don't know which; maybe Wishart? >> <http://en.wikipedia.org/wiki/Wishart_distribution>. A bit >> more obviously, the statistics of the histogram will be >> chisquared if the binary variable's causes are universal. > > thanks for this, but why chisquared?
I meant that the chisquare statistics (which, for a given histogram, is a single number computed according to the counts in the cells of the histogram) for all histograms will be from the same chisquare distribution, if the binary variable's causes are universal.
You may find Rich Ulrich's post of 03 May 2012 14:00:25 0500 in sci.opresearch / sci.stat.math / sci.math thread "Re: a combinatorial question" relevant too, in that he notes that for large tables, "each cell can be regarded as a 1 d.f. chisquared. But a chisquared is simply a normal variate, z, squared." etc.
 jiw



