tlumley at u.washington.edu
Wed Aug 18 17:47:00 CEST 2004
On Tue, 17 Aug 2004, Peter Dalgaard wrote:
> You really need to read a theory book for this, but here's the basic idea:
> V is the theoretical variance of O-E for the first group. If O-E is
> approximately normally distributed, as it will be in large samples,
> then (O-E)^2/V will be approximately chi-squared distributed on 1 DF.
> In *other* models, notably those for contingency tables, the same idea
> works out as the familiar sum((O-E)^2/E) formula. That formula has
> historically been used for the logrank test too, and it still appears
> in some textbooks, but as it turns out, it is not actually correct
> (although often quite close).
You don't necessarily need a theory book --- sufficiently old biostat
textbooks may have this. For example, Fisher & van Belle (1993)
"Biostatistics: a methodology for the health sciences" gives both formulas
and explains that the simpler one is a useful approximation for hand
calculation, with a worked example.
Now that we have computers no-one needs to use the approximation, and most
of that information has been taken out of the second edition.
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