implied about the differences between points on the scale. We do not assume, for example,
that the difference between 10 and 15 points represents the same difference in stress as the
difference between 15 and 20 points. Distinctions of that sort must be left to interval scales.
Interval Scales
With an interval scale,we have a measurement scale in which we can legitimately speak
of differences between scale points. A common example is the Fahrenheit scale of tem-
perature, where a 10-point difference has the same meaning anywhere along the scale.
Thus, the difference in temperature between 10 8 F and 20 8 F is the same as the difference
between 80 8 F and 90 8 F. Notice that this scale also satisfies the properties of the two pre-
ceding ones. What we do not have with an interval scale, however, is the ability to speak
meaningfully about ratios. Thus, we cannot say, for example, that 40 8 F is half as hot as
808 F, or twice as hot as 20 8 F. We have to use ratio scales for that purpose. (In this regard,
it is worth noting that when we perform perfectly legitimate conversions from one interval
scale to another—for example, from the Fahrenheit to the Celsius scale of temperature—
we do not even keep the same ratios. Thus, the ratio between 40 8 and 80 8 on a Fahrenheit
scale is different from the ratio between 4.4 8 and 26.7 8 on a Celsius scale, although the
temperatures are comparable. This highlights the arbitrary nature of ratios when dealing
with interval scales.)
Ratio Scales
A ratio scaleis one that has a truezero point. Notice that the zero point must be a true zero
point and not an arbitrary one, such as 0 8 F or even 0 8 C. (A true zero point is the point cor-
responding to the absence of the thing being measured. Since 0 8 F and 0 8 C do not repre-
sent the absence of temperature or molecular motion, they are not true zero points.)
Examples of ratio scales are the common physical ones of length, volume, time, and so on.
With these scales, we not only have the properties of the preceding scales but we also can
speak about ratios. We can say that in physical terms 10 seconds is twice as long as 5 sec-
onds, that 100 lb is one-third as heavy as 300 lb, and so on.
You might think that the kind of scale with which we are working would be obvious.
Unfortunately, especially with the kinds of measures we collect in the behavioral sciences,
this is rarely the case. Consider for a moment the situation in which an anxiety question-
naire is administered to a group of high school students. If you were foolish enough, you
might argue that this is a ratio scale of anxiety. You would maintain that a person who scored
0 had no anxiety at all and that a score of 80 reflected twice as much anxiety as did a score
of 40. Although most people would find this position ridiculous, with certain questionnaires
you might be able to build a reasonable case. Someone else might argue that it is an interval
scale and that, although the zero point was somewhat arbitrary (the student receiving a 0 was
at least a bit anxious but your questions failed to detect it), equal differences in scores repre-
sent equal differences in anxiety. A more reasonable stance might be to say that the scores
represent an ordinal scale: A 95 reflects more anxiety than an 85, which in turn reflects more
than a 75, but equal differences in scores do not reflect equal differences in anxiety. For an
excellent and readable discussion of measurement scales, see Hays (1981, pp. 59–65).
As an example of a form of measurement that has a scale that depends on its use, con-
sider the temperature of a house. We generally speak of Fahrenheit temperature as an inter-
val scale. We have just used it as an example of one, and there is no doubt that, to a
physicist, the difference between 62 8 F and 64 8 F is exactly the same as the difference be-
tween 92 8 F and 94 8 F. If we are measuring temperature as an index of comfort, rather than
as an index of molecular activity, however, the same numbers no longer form an interval
Section 1.3 Measurement Scales 7
interval scale
ratio scale