On Tue, 16 Nov 1999, Cherilyn Young wrote:
> What would be the best significance test to see whether one subgroup of
> a data set has a significantly greater range of values on a variable
> than other subgroups?
If you're really interested in the _range_ of values, you may be
delving into extreme-value theory; and what you observe depends heavily
on sample sizes, which makes it difficult to make comparisons except
between subgroups of equal size -- which is more often the exception than
the rule amongst human subjects. But are you, in fact, interested in the
range _per_se_, or more in the general variability of the subgroups?
It's lots easier (and less subject to the slings and arrows of outrageous
fortune) to compare variances, e.g.
> From what I've read, a Poisson distribution *might* work, ...
What about your situation suggests Poisson distributions?
(Sounds fishy to me.. :-)
> ... but I'd instinctively prefer something nonparametric.
Ah. Do you have any idea what your instincts are trying to tell
you in this regard? (Apart from the fact that ranges are much less
parametric sorts of things to consider than are means or variances.)
> I'm working with a data set of human subjects' responses on cognitive
> and linguistic measures, if that helps any.
Not a whole lot when so tersely summarized. Are the responses
(a) ratings on scales of some sort;
(b) right vs. wrong answers to (e.g.) multiple-choice items;
(c) latency times for making responses;
(d) combinations of these;
(e) something else altogether ?
Your mention of Poisson suggests that you may be observing the number of
responses of some particular kind, made within a specified and limited
time, and possibly also that the responses are in some sense rare events.
But all this is of course pure speculation.
For some of the kinds of variables suggested above I'd recommend standard
parametric techniques; for others I might suggest a modification or two.
The following may help some. (Or it may not, in which case sorry for
wasting your time.) Some years ago a PhD candidate, interested in "human
subjects' responses on cognitive and linguistic measures" (as you put it),
was observing latencies for certain recognition-and-decision tasks. In
the nature of things, the latencies tended to cluster around a typical
value, but to be infected with infrequent but large outliers (when the
respondent was distracted, or wool-gathering, or for other essentially
irrelevant reasons). Mean latency times would therefore be misleadingly
high, and difficult to distinguish, on the average, between different
experimental groups of respondents. She therefore took the medians of
maybe 20 or so latencies (observed under homogeneous conditions) and used
these as raw data for a factorial analysis of variance in which there were
several such medians per cell. Rather neat, I thought; and there were
some interesting and evocative results for her dissertation.
-- DFB.
------------------------------------------------------------------------
Donald F. Burrill [EMAIL PROTECTED]
348 Hyde Hall, Plymouth State College, [EMAIL PROTECTED]
MSC #29, Plymouth, NH 03264 603-535-2597
184 Nashua Road, Bedford, NH 03110 603-471-7128
