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Topic: binary data, proportions and distributions
Replies: 4   Last Post: May 4, 2012 12:17 AM

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James Waldby

Posts: 347
Registered: 1/27/11
Re: binary data, proportions and distributions
Posted: May 4, 2012 12:17 AM
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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,
>> per-county (country?) or per-state 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
>> chi-squared if the binary variable's causes are universal.

>
> thanks for this, but why chi-squared?


I meant that the chi-square 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 chi-square
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.op-research / 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



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