Levels of Measurement
Slide 1
The level of measurement is an important issue for questionnaire design. As you’ll see in this
lecture, the decisions you make regarding level of measurement have implications for the way
you’ll subsequently analyze the survey data that you collect.
Slide 2
There are four types of measurement scales: (1) nominal (also called categorical), which is used
to put things into categories; (2) ordinal (or rank ordering), which is used to rank things from
smallest to largest based on some property; (3) interval, and (4) ratio. The latter two types of
scales provide parametric measures and the first two types of scales provide non-parametric
measures. The best way to explain these different types of measurement scales is to provide
examples of each, and that’s the purpose of the next few slides.
Slide 3
Here are examples of the types of nominal or categorical data that marketers collect via
surveys: zip code of residence, employment status, marital status, gender, race, religion, and
ethnicity. It should be obvious why marketing researchers use these types of measures on
consumer surveys. Certainly, such measures indicate how representative respondents are
relative to the larger population of interest. For example, if we wanted to conduct a national
survey of adults, then we could compare surveyed respondents’ data to census data; if they’re
similar, then we may assume the sample is representative. Such measures also suggest
respondents’ predisposition to consume certain kinds of products. For example, employment
status indicates how someone spends much of his or her time and is predictive of current and
future consumption. The same applies to marital status. Such measures help classify people
into groups, and thus are important for market segmentation analysis.
Slide 4
To create ordinal data, questionnaire respondents place a series of related items in order
according to some criterion, such as most preferred to least preferred or most frequently used to
least frequently used. In this example, there are a half dozen ice creams and the respondent
has been asked to rank those ice creams by preference, from most to least preferred.
Slide 5
Here’s an example of what marketers often assume is intervally scaled data. You may
recognize some of these scales as typical attitudinal scales that appear on questionnaires. The
reason they aren’t strictly intervally scaled is that an interval scale provides information about
the intervals between choices. For these types of scales, we assume the intervals between
choices are equal to one another. For example, the difference between excellent and very good
is assumed equal to the difference between very good and good, between good and fair, and
between fair and poor. From a psychometric perspective, this is a strong assumption.
Nonetheless, marketers make this assumption because intervally scaled data can be analyzed
with parametric statistics, which are far easier and more powerful than non-parametric statistics.
Furthermore, data of this type tends to be relatively robust, so the assumption of equal intervals
is an acceptably safe one.
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Slide 6
Note that the starting point for an interval scale is arbitrary. For example, I can run a scale from
1 to 6 or I can run a scale from 0 to 5. The mean response would differ, in the sense that the
numbers that would be produced by arithmetic operations would differ, yet the way in which the
scale reflects people’s attitudes is identical. Also note that the number of scale points is
somewhat arbitrary.
Slide 7
Here are some examples of ratio level data: market share, sales (either number of units sold or
number of dollars of sales), personal income, number of sales people per territory, number of
full-time employed members of a household, and number of children in a household. All of these
are ratio-scaled data because there is a meaningful zero point. It’s possible to have zero market
share, make $0 in sales, earn $0 income, have no people in a sales territory, have no full-time
employed members of a household, or a couple have no children. Ratio-scaled data has a
meaningful zero point, unlike interval scaled data, which doesn’t.
Slide 8 (No Audio)
Slide 9
To begin formalizing the difference among nominal, ordinal, interval, and ratio scaled data, this
exhibit is especially useful. In the first line, under nominal, we see one horse—the #7 horse—
and that number identifies that horse uniquely; no other horse in the race will have that number.
The next line illustrates what we mean by ordinally scaled data. One horse finishes first (the win
horse), the next horse finishes second (the place horse), and the next horse finishes third (the
show horse). We know which horse finished first, second, and third; hence order, rank order,
ordinal data.
With intervally scaled data, we’ve got the same horses finishing in the same sequence, but now
we know the degree to which each horse finished before the other horses. With ordinal data, we
just know first, second, and third, but with intervally scaled data we know about the intervals, so
we know the winning horse beat the second place horse by two lengths and the second place
horse finished in front of the third place horse by one length. This information about the intervals
between finishes is additional information; we know which horse finished first, second, and third,
but now we also know the degree to which each horse finished before the others. Note that we
can extract simple ranking information from this interval data; the horse that finished two lengths
ahead of the pack finished first, the horse that finished two lengths behind the first-place horse
finished second, and the horse that finished one length behind the second-place horse finished
third. Thus, intervally scaled data can be transformed into ordinally scaled data, although
information is lost in that transformation.
Finally, ratio-scaled data is illustrated here in terms of dollars because there is a meaningful
zero point for dollars. The 40-to-1 odds on a $2 bet means that we know if you bet on the #7
horse and it won, then you would have won $80.00.
Slide 10
Here’s another example that I hope will illustrate the differences among nominal, ordinal,
interval, and ratio scales. In the first case, for the nominal scale there are 10 different stores;
Lord and Taylor’s is not Macy’s, Macy’s is not Kmart, Kmart is not Rich’s, and Rich’s is not J.C.
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Penney. Each name identifies a unique store or chain of stores. The second column indicates
preferences by rank order. You see the scaling is arbitrary, so in both columns the lowest
number refers to the most preferred store and the highest number refers to the least preferred
store. For this person, J.C. Penney is the most preferred store. It receives a rank of 1, or a rank
of 10 in the second column, but 10 is the smallest number in that second column. With ordinal
data, we’re assigning numbers to preferences so that the numbers will indicate relative
preference. The third column contains intervally scaled data. Here, think of the standard
preference questions that appear on questionnaires: on a scale of 1 to 7, please rate each store
on some characteristic. This third column of data shows that three of the stores are comparably
and most highly preferred: Macy’s, Kmart, and J.C. Penney. The scoring scheme is arbitrary but
the relation of the scores for each store, relative to one another, isn’t. In the first column,
Macy’s, Kmart, and Penney’s all scored a 7, and in the second column they all scored a 17; in
both cases, that’s the largest number in each column. The last column shows ratio-scaled data;
in this case, dollars spent in the last three months in each store. We see that J.C. Penney, with
$250.00, is the store in which the most money was spent. We also gain insights about this data
like the $200.00 was spent at Macy’s is twice as much as the $100.00 spent at Rich’s or Sax
Fifth Avenue.
Slide 11
The next two slides formalize the differences in the properties I’ve tried to introduce to this point
in the lecture. There are three properties of measurement scales: order, distance, and origin. By
order, we mean the numbers assigned or produced an ordering with respect to a given
characteristic, such as preference or most preferred to least preferred. Distance refers to the
differences between the numbers assigned, so that they produce an ordering with respect to a
characteristic. Think back to the race horse example; win, place, show, and the lengths to which
each horse finished in front of the others. This last set of information tells us something about
the distances between the objects as they are ordered. Finally, the third property is origin, which
basically means there is a meaningful zero point, or in this case, unique origin.
Slide 12
What do these properties mean relative to the four different types of scales? We can see that
nominal scales are used merely for classification. We can’t say anything about males being
more or less than females on any particular gender characteristic. For ordinal, we can say that
something is more than or less than or larger than or smaller than something else, in terms of a
given characteristic, and we can also use ordinal data for classification purposes. For example,
we can rank a series of things and then divide that series into the top half and the bottom half.
By taking the top and bottom half, we’ve now classified things into two groups. Ordinal
measures allow us to order things and to classify things.
With intervally scaled data, we cannot only order and classify things, but we also can say
something about the differences between the intervals on the scales. With ratio-scaled data, we
can say something about the intervals and have a meaningful zero point. We can take ratios of
numbers. We can say things like ‘something is twice as expensive as something else’ or ‘the
market share for this brand is twice the market share for another brand’ or ‘this company has
three times as many salespeople in sales district #1 as in sales district #2’.
As we go from nominal to ratio-scaled data, we can say more and make more revealing
statements about the qualities of the things we’re trying to measure. We can always move
upward in this table. If we have ratio-scaled income data on a group of respondents, we can
take their responses and divide them into quartiles. We can divide respondents into people in
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the lowest 25% of reported incomes, people between the 26th and 50th percentile of reported
incomes, people between the 51th and 75th percentile of reported incomes, and people with
incomes greater than the 75th percentile. Thus, we can form four groups of people based on
their income. In that case, we’ve taken ratio-scaled data and used it for classification purposes;
in other words, ratio-scaled data is being treated as nominal data. We can do the same thing
with interval data. We can assume that it’s usable as either ordinal or nominal data. What we
cannot do is go the other way. We cannot take ordinal data and treat it as if it’s ratio-scaled
data.
Slide 13
There are two important things to remember about measurement scales in questionnaires. Try
to use scales that measure at the highest possible level. If you’re conducting a survey research
study for this course, I’ll discourage you from writing questions that create ordinal data; for
example, asking respondents to rank several objects by preference or some other attitudinal
basis. You may back rank order data out of intervally scaled data, in the sense that you could
ask people to rate those objects on a scale of 1 to 7, take the mean scores for each of those
items, and interpret the object with the highest mean is the most preferred, the second highest
mean is the second most preferred, et cetera. You still can treat those same measures as
intervally scaled, and thus use the parametric statistics you may recall from your stat classes;
means, standard deviations, and the like. Parametric statistics are much easier to use than nonparametric statistics. So, my recommendation is as follows: when you design questionnaires, try
to take measures at the highest possible level (as close to ratio scale as possible).
With that said, a measure can’t exceed its basic nature. It’s impossible to make ratio-scale
measurements of the way things taste. You cannot say something is twice as salty as
something else or twice as sweet. You can say something is sweeter or something is saltier, but
the basic nature of the way things taste is such that it’s impossible to generate ratio scale
measures. The rule here is take measures at the highest possible level but remember that
measures can’t exceed the basic nature of the attribute that you’re trying to measure.
Slide 14 (No Audio)
Slide 15
This table formalizes what I’ve said about different levels of measurement and the appropriate
descriptive statistics. If we have nominal data, then all we can do is count, so we know the
frequency or percent of people or objects that fall into each category and we can say something
about the category with the greatest number of people or objects. If we have ordinal data, we
can rank objects according to some order or characteristic, so we can provide summary
numbers like median and the 50th percentile. (Note: The 50th percentile is that point at which half
the objects are more and half the objects are less on the attribute in question.) Recall the ACT
or SAT you may have taken as a requirement for admission to NMSU. You receive a percentile
score that tells you the percent of test takers who scored worse than you. With ordinal data, we
also can talk in terms of a range; we know the lowest score, the highest score, and the number
of points between them. Percentile and range-related numbers are the only descriptive statistics
for ordinal data. Once we have interval and ratio-scaled data (also called parametric data), as
opposed to nominal or ordinal (also called non-parametric data), we can use the statistics that
you may recall from your stat classes at NMSU. In other words, we can talk about means,
standard deviations, and variance.
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Slide 16
To summarize what has been presented in this lecture, I first talked about the different levels of
measurement: nominal, ordinal, interval, and ratio. I provided several examples of each type of
measure. I talked about the different properties for these different levels of measurement in
terms of ranking items, the distance between intervals, and knowing whether or not there’s a
meaningful zero point. In other words, I talked about order, distance, and origin. I closed by
briefly discussing the statistics that are appropriate for these different levels of measurement.
I hope that you understand the decisions you make regarding your questionnaires, in terms of
the levels of measure, will have implications when you’ve entered the data into a computer and
begin to analyze it. If you insist on using rank-order measures, then you won’t be able to say
something like ‘the average rank for item #1 was such and such and the average rank for item
#2 was so and so’, because that requires you to compute a mean for ordinal data and that’s
statistically problematic.
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