Lindley Swartz

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Levels of Measurement
Lindley Swartz M. Thornberry Political Science
221 March 10, 2003
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Measurement the assignment of a name or number
to the observations made of a variables
qualities Examples age, weight, gender, place
of birth The measurement a subject receives for
a variable is the subjects score, or code, for
that variable.
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Unit of Measure set intervals between variables
that can be measured by unit. Examples for age
a year, for height an inch, for temperature a
degree If a variable has unit of measure it can
be marked off incrementally with one unit of
separation.
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Level of Measurement A variable fits into one
of four categories, called the level of
measurement, that determines which mathematical
operations, if any, can be performed on the data
collected on that variable. The results from
these operations are used to test hypotheses.
Nominal Variables Ordinal Variables Interval
Variables Ratio Variables
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Nominal Variables Variables that are coded by
non-numerical qualities. Examples major, social
class, gender, hair color, kind of pizza Nominal
Variables can be assigned a numerical code for
computer processing but that number is arbitrary
and does not have an actual value. Examples
Pizza cheese-1, pepperoni-2, Hawaiian-3
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Dichotomous Variable A variable with only two
possible answers. Examples Are you registered
to vote? The only possible answers are yes and
no. Participation in a lab experiment- control
group or experimental group.
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Ordinal Variables Variables that are coded by
categories but the categories can be ranked in an
order such as first to last or highest to lowest.
Examples academic class- freshman,
sophomore, junior, senior. Attitudes ranked by
agreement.
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Interval Variables Variables that combine the
categorical assignments of nominal and ordinal
variables with a numerical value. Because they
are measured numerically, interval variables can
be manipulated in mathematical equations and
formulas. Example temperature measured in
degrees.
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Ratio Variables Interval variables that have a
true zero, meaning for a value of zero there is
none of the variable. Examples distance,
weight, pieces of pizza Unlike temperature where
zero Fahrenheit indicates 32 degrees below
freezing, zero pieces of pizza means that there
are none. Pieces of pizza has an absolute zero
and therefore is a ratio variable.
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Ratio variables can be used in the same equations
as interval variables but can also be used to
produce meaningful ratios. Example Sara ate two
pieces of pizza and Sean ate four, the ratio is
24. This ratio can then be manipulated to
relate to a hypothesis. The difference between
interval variables and ratio variables is usually
not important in political research.
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Political scientists often find it useful to try
to change nominal/ordinal variables into
interval/ratio variables. An index is used to
combine arbitrary values for nominal variables
into ratio data that can be compared and
manipulated numerically. Example missing less
than 5 classes no-0 yes-1 keeping up with
reading no-0 yes-1 paying attention in class
no-0 yes-1 Measurement scale sum of three
nominal variables can be used to determine
likelihood a student will pass the class.
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Works Cited Ethridge, Marcus E., ed. The
Political Research Experience Readings and
Analysis. 3rd ed. Armonk, New York M.E.
Sharpe, 2002. 16-17. Ritchey, Ferris. The
Statistical Imagination. Boston McGraw-Hill
Higher Education, 2000. 41-46.