Dear Allstatters,
I am analysing a data set which is continuous on a closed interval [a,b].
Globally, this data is symmetrically distributed across the interval, but I
need to prepare summaries at a local level (such as postcodes) including an
estimate with a confidence interval. Naturally to avoid silly confidence
intervals which breach the interval [a,b], I need to transform the interval
to an open unbounded one instead. If the interval was open i.e. (a,b) then
the logit transformation Log( (x-a)/b-x) ) would be perfect but clearly this
is not suitable when x equals a or b. I have been unable to find a suitable
alternative so I am proposing to use the transformation Log( (x-a+k)/(b-x+k)
) where k is a small number say 1% of b-a. I have used this in the past and
I recognise that this is not perfect solution so I would be grateful if
someone from the ALLSTAT list could suggest a better transformation. The
best I have found so far is this article
http://biostatistics.oxfordjournals.org/cgi/reprint/8/1/72 but I don't think
this is quite what I am looking as it doesn't deal with continuous data on
[a,b].
Regards
Nigel Marriott
Chartered Statistician
<http://www.marriott-stats.com/> www.marriott-stats.com
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