The idea of comparing the variances of two variables X and Y by looking at
the correlation of
X + Y with X - Y
seems to go back to Pitman (1939) A note on normal correlation, Biometrika,
31, pp 9-12.
I havn't seen the paper myself but I presume that the essentials are
summarized in Cox & Hinkley (1974) pp 140, 141. These days, of course, we
are keener on plots than formal tests.
I discovered all this around 1977 when I was interested in the case where X
and Y were measurements of quantities like %fat in cheese obtained by two
different methods or by two different labs.
Murray Jorgensen
At 10:35 PM 25-04-00 +0200, Peter Dalgaard BSA wrote:>"Christophe Declercq" <cdeclercq at nordnet.fr> writes:
>
>> > Secondly, I'm curious about the history of this kind of plot.
>> > I've only heard it called a "Tukey mean difference"
plot, (and
>> > Trellis graphics has a function, tmd(), that does it, but no one
>> > knows about it...). Does anyone know who invented it?
>>
>> Martin Bland and Doug Altman introduced it in their very successful
1986
>> paper in The Lancet (which has become a 'Citation Classic') :
>
>However, as so many other CTs, I don't think they actually invented
>the procedure... Plotting residuals vs. fitted values to avoid
>correlation, and warnings against the fallacy of plotting a difference
>against one of the terms have certainly been around long before '86.
>
>The Lancet paper is not really an introduction of a new method, rather
>it is a polemic paper against the widespread practise of publishing
>correlation coefficients as measures of agreement between two methods.
>
>[Of course, since people in the medical profession treats Lancet
>papers as The Law, and vocal statisticians like Altman as demigods,
>one occasionally meets people trying to use the Bland-Altman plot for
>comparing measurements on completely different scales!]
>
>> Bland JM, Altman DG. Statistical methods for assessing agreement
between
>> two methods of clinical measurement. Lancet 1986; i: 307-310.
>
>--
> O__ ---- Peter Dalgaard Blegdamsvej 3
> c/ /'_ --- Dept. of Biostatistics 2200 Cph. N
> (*) \(*) -- University of Copenhagen Denmark Ph: (+45) 35327918
>~~~~~~~~~~ - (p.dalgaard at biostat.ku.dk) FAX: (+45) 35327907
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Department of Statistics, University of Waikato, Hamilton, New Zealand
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