> >On Tue, 9 Oct 2001, Payam Heidary wrote
> >> This week I lectured on various levels of measurement
> >> i.e., ordinal, nominal, interval, ratio, etc. in
> >> research and I found that some students have a hard
> >> time understanding these concepts. DO anyone of you
> >> have a good strategy or method for clearly explaining
> >> these concepts or any good handouts you can share with
> >> me. Would appreciate your input on this matter. Thanks
Jim Clark replied:
> >One perhaps unacceptable possibility is to skip it, and just
> >discuss the distinction between categorical (i.e., nominal) and
> >numerical (i.e., the rest). The differences among ordinal,
> >interval, and ratio do not matter for the statistics, and, I
> >suspect, will generally never be used again by undergraduates.
On Wed, 10 Oct 2001, Charlotte Manly wrote:
>
> That's not quite true. You shouldn't use a t test for
> ordinal data. I generally distinguish between nominal
> ("categorical"), ordinal ("ranked") and interval/ratio
> ("continuous") data. The interval/ratio distinction is not
> important for selecting a statistical test; however, you
> shouldn't compute a percent change on interval data (e.g. 20%
> reduction in RT is okay, but 10% improvement in SAT scores
> doesn't make sense since there is no true zero). However, I
> am teaching at the graduate level.
I also side with Jim Clark on this one. This is a debate that
split experimental psychology some years ago (Can you say "John
Gaito"?). The opinion I arrived at was that levels of measurement
is one of those topics that we like to torture students with but
has no real utility (another example is the negative/positive
reinforcement distinction). Even though the t-test is supposed
only to be used with data which satisfies a rather restrictive
set of assumptions, it turns out to be "robust" when its
assumptions are violated, so it can be happily (and justifiably)
used in lots of other cases.
Most of the literature on this question is quite old. I ransacked
my file, and came up with the following relatively recent paper
supporting this point of view. Wilkinson is a noted statistician
who invented the SYSTAT computer programme for analyzing data.
Here's the abstract of his paper with Velleman:
"The psychophysicist S.S. Stevens developed a measurement scale
typology that has dominated social statistics methodology for
almost 50 years. During this period, it has generated
considerable controversy among statisticians. Recently, there has
been a renaissance in the use of Steven's scale typology for
guiding the design of statistical computer packages. The current
use of Steven's terminology fails to deal with the classical
criticisms at the time it was proposed and ignores important
developments in data analysis over the last several decades."
It would be interesting to hear how current textbooks of
psychological statistics deal with this issue.
-Stephen
Vellleman, P. & Wilkinson, L. (1993). Nominal, ordinal, interval,
and ratio typologies are misleading. The American Statistician,
47, 65--
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Stephen Black, Ph.D. tel: (819) 822-9600 ext 2470
Department of Psychology fax: (819) 822-9661
Bishop's University e-mail: [EMAIL PROTECTED]
Lennoxville, QC
J1M 1Z7
Canada Department web page at http://www.ubishops.ca/ccc/div/soc/psy
Check out TIPS listserv for teachers of psychology at:
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