sciplot question
spencerg wrote:
Dear Frank, et al.: Frank E Harrell Jr wrote:
<snip> Yes; I do see a normal distribution about once every 10 years.
To what do you attribute the nonnormality you see in most cases?
(1) Unmodeled components of variance that can generate errors
in interpretation if ignored, even with bootstrapping?
(2) Honest outliers that do not relate to the phenomena of
interest and would better be removed through improved checks on data
quality, but where bootstrapping is appropriate (provided the data are
not also contaminated with (1))?
(3) Situations where the physical application dictates a
different distribution such as binomial, lognormal, gamma, etc.,
possibly also contaminated with (1) and (2)?
I've fit mixtures of normals to data before, but one needs to be
careful about not carrying that to extremes, as the mixture may be a
result of (1) and therefore not replicable.
George Box once remarked that he thought most designed experiments
included split plotting that had been ignored in the analysis. That is
only a special case of (1).
Thanks,
Spencer Graves
Spencer, Those are all important reasons for non-normality of margin distributions. But the biggest reason of all is that the underlying process did not know about the normal distribution. Normality in raw data is usually an accident. Frank
Frank E Harrell Jr Professor and Chair School of Medicine
Department of Biostatistics Vanderbilt University