On Sat, 23 Jan 2021 03:22:54 -0800 (PST), Cosine <
asecant@gmail.com>
wrote:
Hi:
When we only have a small-sized sample, what comes out to our mind is to use a non-parametric statistical method.
I assume that when you are say "non-parametric statistical method,"
you are referring to those methods based on ranks.
What you say: That's unfortunate, but too often it is true. I think
the idea was spread especially by psychologists who were
looking for an easy "out", to avoid dealing with those stats-
assumptions that they did not understand.
Psychologists are notoriously weak in math, for reasons I don't
know. My easiest A in college was in psy-stats; the final exam
took me less than 10 minutes. Maybe it was less than 5.
But does using a non-parametric method really solve the problem?
In the 1980s, Conover provided a fine perspective. Using those
rank-order tests is - effectively - performing a rank-transformation
on the data, followed by the usual ANOVA. That's often the text-
book prescription for the "large-sample" use of rank tests. If you
have to take into account the text-book's approximated adjustments
for "tied values", you can be /better/ off using transform-plus-ANOVA
for the small samples, too.
If the rank-transformed data are closer to "equal interval" for
scores than the raw data is, then you get better test after the rank tranformation.
Also, what are the drawbacks of solving a problem with a non-parametric method when the problem actually has some kind of distribution?
The obvious problem to which ranking offers a quick fix is the
presence of visible outliers. Those can screw up both the means
and the variances.
If you don't know anything at all about your data, including the
likely distribution of scores, you should probably put off trying
to make any sense of it until you learn something.
If you think that the arithmetic average, the mean, ought to be
meaningful, then you probably don't want the rank transform.
Or any transform, if that holds for all likely samples. I've probably
chosen to "winsorize" data (set an extreme to a moderated value)
more often than I've taken rank-transformations as the tool.
(But for winsorizing, I am speaking of large samples, weird scaling.)
Where data comes from can imply that certain transforms should
"bring in" the outliers, or otherwise fix the tails. For instance,
take the square root for (Poisson) counts; take the logit for
proportions; take the log for chemical traces in blood samples.
The "drawbacks" of using the rank-transformation approach
are (a) you throw away the mean and inter-group comparisons,
and (b) you can get a weaker test.
--
Rich Ulrich
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