LEVELS/SCALES OF
MEASUREMENT
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Intriguing
Observation/Experience,
Intellectual Curiosity
More Careful Studying
of the Phenomenon
Defining Research
Problem & Objectives
THE PROCESS OF
Building the Theoretical
Framework and the
Research Model
Refinement of theory
EMPIRICAL RESEARCH
Testing Hypo.:
Data Analysis &
Interpretation
Developing Research
Hypotheses
Data Coding,
And
Editing
Operational Definition
& Measurement of
Research Variables
Data Collection
Sampling Design
LEVELS/SCALES OF
MEASUREMENT
MEASUREMENT: One of the pillars of science
– Only when we begin to assign numbers to
describe an object do we begin to learn about
that object.
“I often say that when you can measure what you are
speaking about and express it in numbers you know
something about it. But, when you cannot measure it,
when you cannot express it in numbers, your
knowledge is of a meager and unsatisfactory kind; it
may be the beginning of knowledge, but you have
scarcely, in your thoughts, advanced to the stage of
science, whatever the matter may be.”
Lord Kelvin (19th century physicist)3
LEVELS/SCALES OF
MEASUREMENT
Definition?
– Careful and deliberate observation of a phenomenon for the
purpose of describing study subjects (e.g., people, objects,
organizations, events) in terms of their attributes and
properties.
– Assigning numbers to attributes/characteristics of study subjects
(e.g., people, objects, events, etc.) according to a set of rules.
– Measurement represents:
“Rules for assigning symbols to objects so as to
1. represent quantities of attributes numerically (i.e., scaling)
or
2. define whether the objects fall in the same or different
categories with respect to a given attribute (i.e.,
classification)”
(Nunnally & Bernstein, 1994)
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LEVELS OF MEASUREMENT
A fundamental consideration in measurement that
influences our choice of alternative measurement
procedures is:
Levels/Scales of Measurement
Levels/Scales of Measurement reflect the precision and
amount of information contained in the data.
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LEVELS OF MEASUREMENT
QUESTION: What are some of the ways you
would measure/characterize/describe and,
thus, compare people’s heights? Weather?
Height?
Weather?
1. X feet and Y inches
1. X Degrees Fahrenheit
2. Very Tall, Tall,
Neither tall or short,
Short, Very short
2. Unseasonably hot, Hot,
Mild, Cold,
Unseasonably cold
3. Taller than average, Average,
Shorter than average
3. Hotter than last year,
Same as last year,
Colder than last year
4. Tall vs Short
4. Hot vs. Cold
These represent different levels of precision/crudeness—Levels of Measurement
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LEVEL/SCALES OF MEASUREMENT
What is the Significance of Level of
Measurement?


The choice of level of measurement
(i.e., precision/crudeness of
measurement procedure) greatly
determines what can/cannot be
done with the resulting data when
attempting to analyze them—i.e.,
determines what statistical
methods can/cannot be utilized.
Let’s examine various levels of
measurement!
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LEVEL OF MEASUREMENT
Statistical Techniques and Levels of Measurement:
INDEPENDENT Var.
NOMINAL/CATEGORICAL
N
O
M
I
N
A
L
M
E
T
R
I
C
METRIC (ORDERED METRIC or
HIGHER)
* Chi-Square
* Fisher’s Exact Prob.
* Discriminant Analysis
* Logit Regression
* T-Test
* Analysis of Variance
* Correlation Analysis
* Regression Analysis
We will come back to this later!
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LEVELS/SCALES OF MEASUREMENT
NOMINAL (CATEGORICAL/DISCRETE):
– Lowest level/crudest form
– Measure HOW MANY
– Typically for classification of people, objects, ideas, events,
etc. into discrete categories
– Typically involves a choice from a set of mutually exclusive
categories (e.g., male vs. female)
– Ideally, the list of categories is exhaustive
Nominal data represent labels or names (categories)
used to identify an attribute of the research subjects.
IMPORTANT FEATURES:
– Numbers used to designate categories are of no
quantitative or relative value--only labels (e.g., social
security number)
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LEVELS OF MEASUREMENT—
NOMINAL (Cont.)
Permissible operations?
– Counting--the only arithmetic operation
permitted, and
– Comparison of group frequencies/percentages-the only empirical operation applicable
Applicable descriptive statistics (Numbers that help describe
characteristics of a group/data set in summary form)?
–Central tendency--mode
–Spread/variability--none
Inferential statistics: Nonparametric test
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LEVELS OF MEASUREMENT
ORDINAL:
These scales typically involve forced ranking of a set of available
options.
Subjects are asked to rank (rank order) entities/ objects in terms
of the degree to which they possess the characteristic being
measured (e.g., brand preference), while NOT allowing assignments
of equal ranks to multiple items.
Ordinal data have the properties of nominal data,
but the order or rank of the data is meaningful.
– Relative magnitudes/quantitative values of numbers become
relevant--numbers not just labels anymore
– They indicate some subjects are lower or higher than others on
the characteristic being measured, but not by how much (e.g.,
preference).
IMPORTANT FEATURE:
– Intervals between consecutive ranks do not represent equal
amounts of the attribute being measured (e.g., first, second, or
third most preferred brand)
– They are more precise than nominal scales, but not yet very
precise, still crude
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LEVELS OF MEASUREMENT
ORDINAL (Con.):
• Additional empirical operations are applicable:
– Determination of greater or lesser, higher or lower, larger
or smaller, darker or lighter, etc.
– Transitivity postulate acceptable--i.e., comparison of
ranks/positions is allowed (e.g., if a>b and b>c, then a>c)
• Descriptive statistics?
– Central tendency--mode and median


Mode: For most subjects brand X was the 2nd choice
Median: For 50% (or more) of the subjects, Brand X was
among the top 3 choices
– spread/variability--range (minimum and
maximum)

Inferential statistics:
– nonparametric tests
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LEVELS OF MEASUREMENT
INTERVAL:
– Provides quantitative/metric measures (is always numeric)
– Measures HOW MUCH
Important Features:
– Very precise measures
– Numbers along the scale express a fixed unit of
measurement (are of equal size)
Interval data: intervals between consecutive points on the scale
represent equal amounts of the attribute being measures, but 0 is arbitrary

Thus, score intervals can be compared (e.g., temperature)
80 degrees – 60 degrees = 20
90 degrees – 70 degrees = 20
20 = 20 (both represent equal levels of heat differential)
Can you say the same for differences in test scores?
– But, the zero on the scale is arbitrary (e.g., altitude);

The scale does NOT have an absolute/true zero.
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LEVELS OF MEASUREMENT
INTERVAL (Con.)
– So, ratios of scores will be misleading
E.g., comparisons such as “Object A is 3-times hotter
than object B,” is typically wrong.
NOTE: There are very few technically true/pure interval scales
(i.e., exact but with an arbitrary zero, notable among
them Fahrenheit and Celsius temperature scales).


Descriptive statistics?
– Central tendency--mean, mode, median
– Spread/variability--standard deviation or variance, range,
minimum and maximum
• Inferential statistics?
–parametric tests
–nonparametric tests
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LEVELS OF MEASUREMENT
RATIO:
– Highest/most precise level of measurement
Important Features:
– Precise/exact like interval scales, but with a
true/absolute/meaningful zero indicating nothing exists.
– Meaningful ratios of scores can be derived (e.g., distance,
height, weight, income, etc.)
 “A is twice as long as B” would be a correct comparison
(e.g., income, age)

Descriptive statistics?
–Central tendency--mean, median, mode
–Spread/variability--standard deviation or variance, range,
minimum and maximum
• Inferential statistics?
–parametric tests
–nonparametric tests
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LEVELS OF MEASUREMENT
ORDERED METRIC:
– Technically/strictly speaking NOT really interval (not as precise),
but are superior to purely ordinal (forced ranking) scales.
EXAMPLES?

IQ scores, score on an exam, and many rating scales used in survey
research (e.g., Likert scales, comparative scales, etc.)
When response options follow an ordered sequence; larger
number represent more /less of what is being measured.
– In practice, can be treated as if they were interval

(They provide continuous/metric measures/ratings)
– Permit virtually all same operations and analyses that are
applicable to interval scales
– NOTE: Measures that are ordered metric or higher
(i.e., ordered metric, interval, or ratio) we
will refer to as “METRIC or QUANTITATIVE”
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LEVELS OF MEASUREMENT
IMPORTANT NOTE: Level of measurement
is a function of how you choose to measure
a variables, and often NOT an inherent
characteristic of the concept being measured.
EXAMPLE:
Height--Operationalization
Level of Measurement
• Number of feet/inches
?
Ratio
• 1=Very Short, 2=Short, 3=Average, 4=Tall, 5=Very Tall
?
Ordered Metric
• 1=Short, 2=Tall
?
Nominal
• 1=Freshman, 2=Sophomore, 3=Junior, 4=Senior, 5=Graduate ?
Ordered Metric
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LEVELS OF MEASUREMENT
NOTE:
• Appropriate statistical analysis for nominal and ordinal
measures are rather limited.
• Higher-level measures can be converted to lower-levels
and, thus, treated as such. But the opposite cannot be
done.
CONCLUSION:
– When you have a choice, measure your
variables at the higher levels of
measurement, unless there is a
compelling/practical reason for not
doing so.
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LEVEL OF MEASUREMENT
Remember: Level of measurement determines choice of
statistical method.
Statistical Techniques and Levels of Measurement:
INDEPENDENT Var.
NOMINAL/CATEGORICAL
N
O
M
I
N
A
L
M
E
T
R
I
C
METRIC (ORDERED METRIC or
HIGHER)
* Chi-Square
* Fisher’s Exact Prob.
* Discriminant Analysis
* Logit Regression
* T-Test
* Analysis of Variance
* Correlation Analysis
* Regression Analysis
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LEVELS OF MEASUREMENT
QUESTIONS
OR
COMMENTS
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