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Chapter 4: Conceptualization
and Measurement
Levels of Measurement
• Level of Measurement=Mathematical precision
with which values of a variable can be
• Nominal level of measurement:
• Qualitative
• No mathematical interpretation
Levels of Measurement
Quantitative levels of measurement:
 Ordinal
 Interval
 Ratio
Progressively more precise mathematically
Nominal Measures (Labels)
Identifies variables whose values have
no mathematical interpretation
are not ordered
only two categories:
Referred to as a dichotomous or
“Dummy” variable
Examples of Nominal Measures
Ordinal Measures
Categorical--Some categories are higher than
For example:
Income tax brackets
 Social class
 Levels of education
Cannot measure the distance between
categories, only which is higher or lower
Cannot say that someone is twice as educated as
someone else
Can be used as a dependent variable
Example: Ordinal Measures
When attributes can be rank-ordered…
 Distances between attributes do not have any meaning
 For example : code Educational Attainment as
0=less than H.S.
1=some H.S.
2=H.S. degree
3=some college
4=college degree
5=post college
Is the distance from 0 to 1 the same as 3 to 4?
Example: Ordinal Measures
Interval Measures
Variables of this type are called scalar or index
They provide a scale or index that allows us to
measure between levels.
We can not only measure which is higher or
lower, but how much so.
 Distance is measured between points on a
scale with even units.
 Example: Temperature in Fahrenheit or
Example: Interval Measures
When distance between attributes has meaning,
for example, temperature (in Fahrenheit) -distance from 30-40 degrees is same as
distance from 70-80 degrees
 A variety of statistical analysis can be done on
these data sets
 For
example, central tendency can be measured
by mode, median, or mean
 Standard deviation can be calculated
But we cannot calculate ratios
Index of feminist attitudes.
Two women were asked a series of questions. Their answers were compiled, and an
index of their feminist attitudes calculated, but the index had no absolute zero. Still,
their scores could be compared.
Do you agree or disagree with the following statements?
(SD =1, D=2, N=3, A=4, SA=5)
A woman should have the same job opportunities as a man.
Men should respect women more than they currently do.
America should pass the Equal Rights Amendment.
Women should be considered as seriously as men as candidates for the Presidency of the
United States.
Doctors need to take women's health concerns more seriously.
Women have been treated unfairly on the basis of their gender throughout most of human
Feminist Attitude index = 30 (highest score
Feminist Attitude index = 5 (lowest score
Ratio Level Measurement
Similar to interval level
 Can
measure distance between two points
 But can do so in absolute terms
Ratio measures have a true zero (unlike
interval measures)
 Example, can say that someone is twice
as rich as someone else based on the
value of their assets.
 To have no money is based on a starting
point of zero
Ratio Level Measurement
Has an absolute zero that is meaningful
Can construct a meaningful ratio (fraction), for
example, number of clients in past six months
It is meaningful to say that “...we had twice as
many clients in this period as we did in the
previous six months.
Ratio Level Measurement
Ratio scales are the ultimate when it
comes to measurement scales
 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
Types of Comparisons That Can Be Made
With Different Levels of Measurement
Measurement Hierarchy