[Web4lib] Library Automation Survey Results

[Dan Lester]

The text below is still incorrect, except for your personal objection
to an ordinal scale. See below.

Thursday, January 10, 2008, 12:43:07 PM, you wrote:

> I think my mathematical explanation
> was wrong, but I do have a fundamental objection to these that assign an
> arbitrary quantitative value to purly qualitative states. You can't take
> an average of "poor", "fair", "good", and "excellent" by defining
> corralating values of 1, 2, 3, and 4, unless you mean to say that "fair"
> is twice as good as "fair", but "excellent" is only 1.333 times as good
> as "good". But perhaps you can in fact say 0 is "poor" and 9 is
> "excellent", without assigning any other qualitative properties in
> between, and that is okay then to average the results.

There are four types of scales that can be used:

Nominal  (as indicated by the name, this is for things like M/F,
dog/cat, etc. that are categorized by name)

Ordinal:  This is the type used in the survey under consideration.
Things are ranked in ORDER, so a 3.5 is halfway between a 3 and a 4.
A 4 is "one step" higher than a 3, not 1.33 times "better".  We're all
familiar with this from school grades where, say, an A is a 4, a B is
a 3, and so forth.  That does NOT mean that an A is 1.33 times as good
as a B is 1.5 times better than a C.  In fact, if you go by the other
form of ordinal scale that the prof uses, an A may represent 95, a B
85, and a C 75, where the ratio is different.  It is just an ordering,
and NOT a ratio.

Interval: Not relevant here, but works for things like temperatures.

Ratio:  These are where there is a true zero, and where a ratio is
valid, such as age, weight, height, and many other measurements.  If a
building is ten feet tall it is indeed half as tall as one that is 20
feet tall, and that half as tall as one 40, and so forth. (I was going
to use weights, but someone might have some personal problem with
that)

Anyway, you're looking at the ratings as ratio measurements, when
they're really ordinal measurements.

For another source on this, see:
http://www.math.sfu.ca/~cschwarz/Stat-301/Handouts/node5.html or any
statistics textbook.

dan (permanent ABD in statistics and research methodology)


-- 
The road goes on forever and the party never ends. REK, Jr. 
Dan Lester, Boise, ID