Measurement & Scaling Techniques (Part 1)
Introduction
As we discussed earlier, the data consists of
quantitative variables, like price, income, sales etc., and qualitative variables
like knowledge, performance, character etc. The qualitative information must be
converted into numerical form for further analysis. This is possible through measurement
and scaling techniques. A common feature of survey based research is to have
respondent’s feelings, attitudes, opinions, etc. in some measurable form.
Measurement Scaling
Before we proceed further it will be
worthwhile to understand the following two terms: (a) Measurement, and (b)
Scaling.
a) Measurement: Measurement is the process of
observing and recording the observations that are collected as part of
research. The recording of the observations may be in terms of numbers or other
symbols to characteristics of objects according to certain prescribed rules. The
respondent’s, characteristics are feelings, attitudes, opinions etc.
The most important aspect of measurement is the
specification of rules for assigning numbers to characteristics. The rules for
assigning numbers should be standardized and applied uniformly. This must not
change over time or objects.
b) Scaling: Scaling is the assignment
of objects to numbers or semantics according to a rule. In scaling, the objects
are text statements, usually statements of attitude, opinion, or feeling.
The level
of measurement refers to the relationship among the values that are assigned to
the attributes, feelings or opinions for a variable.
Typically,
there are four levels of measurement scales or methods of assigning numbers:
(a)
Nominal scale,
(b)
Ordinal scale,
(c)
Interval scale, and
(d)
Ratio scale.
1. Nominal scales
Let’s start with the
easiest one to understand. Nominal scales are used for labeling
variables, without any quantitative value. “Nominal” scales
could simply be called “labels.” Here are some examples, below.
Notice that all of these scales are mutually exclusive (no overlap) and
none of them have any numerical significance. A good way to remember all
of this is that “nominal” sounds a lot like “name” and nominal scales are kind
of like “names” or labels.
2. Ordinal
scales
With ordinal scales, the order of the values is what’s
important and significant, but the differences between each one is not really
known. Take a look at the example below. In each case, we know that
a #4 is better than a #3 or #2, but we don’t know–and cannot quantify–how much better it is. For example,
is the difference between “OK” and “Unhappy” the same as the difference between
“Very Happy” and “Happy?” We can’t say.
Ordinal scales are typically measures of
non-numeric concepts like satisfaction, happiness, discomfort, etc.
“Ordinal” is easy to remember because is
sounds like “order” and that’s the key to remember with “ordinal scales”–it is
the order that matters, but
that’s all you really get from these.
Advanced
note: The best way to
determine central tendency on
a set of ordinal data is to use the mode or median; a purist will tell you that
the mean cannot be defined from an ordinal set.
3. Interval
scales
Interval scales are
numeric scales in which we know both the order and the exact differences
between the values. The classic example of an interval scale
is Celsius temperature because the difference between each value is
the same. For example, the difference between 60 and 50 degrees is a
measurable 10 degrees, as is the difference between 80 and 70 degrees.
Interval scales are nice because the realm
of statistical analysis on these data sets opens up. For example, central tendency can be measured by
mode, median, or mean; standard deviation can also be calculated.
Like the others, you can remember the key
points of an “interval scale” pretty easily. “Interval” itself means “space in
between,” which is the important thing to remember–interval scales not only
tell us about order, but also about the value between each item.
Here’s the problem with interval scales:
they don’t have a “true zero.” For example, there is no such thing as “no
temperature,” at least not with celsius. In the case of interval scales,
zero doesn’t mean the absence of value, but is actually another number used on
the scale, like 0 degrees celsius. Negative numbers also have
meaning. Without a true zero, it is impossible to compute ratios.
With interval data, we can add and subtract, but cannot multiply or
divide.
Confused? Ok, consider this: 10 degrees C +
10 degrees C = 20 degrees C. No problem there. 20 degrees C is not
twice as hot as 10 degrees C, however, because there is no such thing as “no
temperature” when it comes to the Celsius scale. When converted to
Fahrenheit, it’s clear: 10C=50F and 20C=68F, which is clearly not twice as
hot. I hope that makes sense. Bottom line, interval scales are great, but
we cannot calculate ratios, which brings us to our last measurement scale…
4. Ratio
scales
Ratio scales are the
ultimate nirvana when it comes to measurement scales because they
tell us about the order, they tell us the exact value between units, AND they
also have an absolute zero–which allows for a wide range of both descriptive
and inferential statistics to be applied. At the risk of repeating
myself, everything above about interval data applies to ratio scales, plus
ratio scales have a clear definition of zero. Good examples of ratio
variables include height, weight, and duration.
Ratio scales provide a wealth of
possibilities when it comes to statistical analysis. These variables can be
meaningfully added, subtracted, multiplied, divided (ratios). Central
tendency can be measured by mode, median, or mean; measures of dispersion,
such as standard deviation and coefficient of variation can also be calculated
from ratio scales.
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