Time to get down & dirty on this one. I think the logic/word concepts
is/are in need of refinement.
Paul W. Jeffries wrote:
> 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.
I don't think so, on abstract grounds. If I set up a scale of visual
surface roughness, 0 is 'absolutely smooth,' and then I can put others
out there, out to 5 or 6. Nobody's to say if I have them spaced evenly
(by some contact surface roughness scale, as AA or RMS), but we have a
true zero.
Your argument to this point says that if an item has property A and B,
then presence of B implies item contains A. My example above shows no,
it does not.
> 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?
Yes, see above. However, I don't' think dollars is such a scale.
> 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.
Depends a great deal on what you mean by 'magnitude.' [And what 'is'
is. Sorry, I couldn't help myself.] I think you are considering
incremental value, not dollars.
Say I look at a pressure gauge. A clear 0 (absolute zero pressure -
space), and measurable, even incremented units. Increase in pressure
from 100 psi to 101 psi is the same increase as from 0.1 psi to 1.1 psi,
is the same from 10,000 to 10,001 psi. Same for dollars. We put a
different emotional value on dollars than psi, however :)
> 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.
this looks like you are looking at incremental amounts, in percentage
units/values. By this thinking, Bill Gates could drop a few million on
my favorite charity with the same elan as I drop $10. the charity
receiving these will place a different value on the $ , depending on who
makes the contribution. But if we each send the charity $100, the
charity will value the contributions equally. (at least until they see
who signed one of the checks!)
> 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.
Exactly so.
> 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 say ratio level, with equal increments. The value that you place on a
given increment depends on the percentage increase, and your perception
of that increment.
BTW, a change in pressure from 14.7 psi to 13.7 psi would signal a major
storm approaching. A change in pressure from 1000 to 1001 psi would not
make a whit of difference, if it was applied on your bod - you'd be
pretty flattened either way.
> 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
consider a single example. If the amount you receive as a raise in
salary is exactly equal to the amount your child care bill increases,
and they both get announced to you on the same day, it ain't a raise.
Jay
--
Jay Warner
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