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
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