# [R] Bland Altman plot (was: [R] paste ?)

Peter Dalgaard BSA p.dalgaard at biostat.ku.dk
Wed Apr 26 11:19:55 CEST 2000

```"Zdenek Skala" <Zdenek.Skala at incoma.cz> writes:

> Dear all,
> sorry for this perhaps stupid question, but it concerns my recent
> problem as well as the current thread on B-A plot.
> I would like to plot something like x+y vs. x-y or mean(x,y) vs
> difference (x,y), but my "variables" x,y are actually pairs of
> replicates (two observed values of a growth rate by 60 clones). So
> the order x,y does not matter and each x,y pair can be arranged
> regardless the arrangement of other x,y pairs, - of course, this will
> influence the appearance of the plot. I was playing with plotting
> (x+y) vs. absolute value of (x-y), but this will yield plotting area
> limited by the x=y line (provided the x,y are nonnegative values,
> which is my case). Exists there some standard plotting procedure
> for such data?

I don't think there's a "standard plot".

Plotting absolute values is essentially equivalent to plotting *both*
x-y and y-x against x+y in the B-A plot since the latter is obtained
by reflection in the horisontal axis. Seems to make reasonable sense,
except that B-A is partially designed to detect deviations from
symmetry which is a rather moot point in your case. You could still
look for outliers and for trends in the dispersion. Actually, the
"half-plot" is equivalent to the "Scale-Location plot" that lm.plot
does for the model where there's a common mean for both values in a
pair, but a separate one for each pair

The B-A plot also has the enveloping phenomenon that you describe,
geometrically it just rotates an (x,y) plot 45 degrees clockwise, so
if all data are in the 1st quadrant...

If the effect is strong, you may have cause to look at the data on a
different scale, a log scale would be obvious, but power
transformations with small exponents could also be relevant.

--
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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