Dear Paul
It seems to me you are confusing the physical dimension of money
with the psychological dimension of value (or utility, as mentioned
by Alan McLean).
The difference was discussed by S S Stevens in his book on
psychophysics (1975 but I do not have the title to hand). He
comparedthe view of Bernoulli (1738) with that of Cramer (1728).
Bernoulli argued that value and money are related by a log
function, U (subjective value) = k log D where D is the amount fo
money. Cramer apparently said the relation was U = k D ^ 0.5.
Stevens says that experiments support the Cramer view, but that is
not surprising since it corresponds to Stevens' version of the
psychophysical law.
I gleaned this from an old handout of mine, which seems to exist
now only in printed copy on yellowing paper. hope it helps
Jeremy
Date sent: Sun, 4 Feb 2001 09:09:22 -0500
Send reply to: Concerned with the initial learning and teaching of statistics <[log in to unmask]>
From: "Paul W. Jeffries" <[log in to unmask]>
Subject: Levels of measurement.
To: [log in to unmask]
> I have been thinking about levels of measurement too much lately. I
> have a question that must have a simple response, but I don't see it
> right now. The textbooks say that a ratio scale has the properties of
> an interval scale plus a true zero point. This implies that any scale
> that has a true zero point should have the cardinal property of an
> interval scale; namely, equal intervals represent equal amounts of the
> property being measured.
>
> But isn't it possible to have a scale that has a true zero point but
> on which equal intervals do not always represent the same magnitude of
> the property? Income measured in dollars has a true zero point; zero
> dollars is the absence of income. Yet, an increase in income from say
> 18,000 to 19,000 is not the same as an increase in 1,000,000 to
> 1,001,000. At the low end of the income scale an increase of a
> thousand dollars is a greater increase in income than a thousand
> dollar increase at the high end of the scale.
>
> It seems the reason that an interval of $1000 is not the same on all
> parts of the scale is because the proportion of the increase in income
> is different. Going from 18,000 to 19,000 is a 6% increase in income
> and would be felt. But an increase from 1,000,000 to 1,001,000 is a
> mere .1% and would hardly be noticed.
>
> So is income in dollars measured at an interval level, and the zero is
> not a true zero point? Is income measured at a ratio level and so
> equal intervals represent equal amounts of income?
>
> I'm anxious to read what list members make of this.
>
> Paul W. Jeffries
> Department of Psychology
> SUNY--Stony Brook
> Stony Brook NY 11794-2500
Yours
Jeremy
Phone: 0161 247 2550
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