Conceptualization, Operationalization, and Measurement: Levels of Measurement

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Conceptualization, Operationalization, and
MeasurementLevels of Measurement

• October 27, 2004
• Sociology 487

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Lecture Topics

• Levels of Measurement
• Nominal
• Ordinal
• Interval
• Ratio
• Dichotomous Variables

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From Operationalization to Levels of Measurement

• The mathematical precision with which the values
  of a variable can be expressed is the level of
  measurement
• The nominal level of measurement is qualitative
• It has no mathematical interpretation
• Ordinal, interval, and ratio levels of
  measurement are quantitative
• They are progressively more precise mathematically

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Nominal Measures

• Identifies variables whose values have no
  mathematical interpretation
• Variables vary in kind or quality but not in
  amount.

In terms of the variable Dog Breed, you can say
that the German Shepherd is not equal to the
Terrier, but you cannot say that the German
Shepherd is dog breedier or less dog breedy
than the Terrier.
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Ordinal Measures

• Variables with attributes we can logically rank
  and order
• Specify only the order of cases
• Greater than and less than distinctions
• Nothing is specified in terms of actual numbers

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Interval Measures

• Distances separating variables
• Numbers represent fixed measurement units BUT
  have no absolute zero point
• Few true interval measures in social sciences
• One example Scores on standardized intelligence
  tests
• Why is it incorrect to state that someone with an
  IQ of 150 is 50 more intelligent than someone
  with an IQ of 100?

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Ratio Measures

• Attributes composing a variable are based on a
  true zero point
• Zero represents none of the variable
• Ratio measures can be added and subtracted, and
  multiplied and divided
• Example age
• 10 is 2 years older than 8 and 2 times greater
  than 5

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Dichotomies

• Variables having only two values
• Gender Female / Male
• Marital Status Married / Not Married
• Employment Status Employed / Not Employed
• Dichotomies indicate presence or absence of
  attribute
• Categorical but with inherent order
• What is the level of measurement of dichotomous
  variables?

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Comparison of Levels of Measurement
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You Decide Level of Measurement

• Level of measurement is not inherent in variables
• Age
• Nominal Age 65 and over (yes / no)
• Ordinal Young, Middle-Aged, Old
• Ratio Years of age

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Operationalization Choices

• Questions to consider when determining level of
  measurement
• What is the range of variation required?
• What analytical uses are planned for the
  variables?
• General guidelines
• Collect more information instead of less
  information
• Ratio measures can be converted into ordinal but
  ordinal can not be converted into ratio

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Key Points

• Levels of measurement provide a framework for
  interpreting categories of a variable
• Nominal measures are qualitative
• Ordinal, interval, and ratio are quantitative
• Levels of measurement are not inherent in
  variables
• Selected based on research question and analysis
  plans