SCALES OF MEASUREMENT

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SCALES OF MEASUREMENT

• AED 616
• Research Project Design Implementation

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Nominal

• Help investigators determine what types of
  statistical analyses are appropriate.
• The lowest level of measurement is nominal (also
  known as categorical).
• It is helpful to think of this level as the
  naming level.
• Individuals name the political parties with which
  they are affiliated.
• Individuals name their gender.
• Individuals name the state in which they reside.
• Individuals name the language they prefer to use
  at home.
• Categories named by subjects in these examples do
  not put the subjects in any particular order.

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• There is no basis on which we could all agree for
  saying that Republicans are logically higher or
  lower than Democrats.
• Same is true for gender, state of residence, and
  language preference.

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Ordinal

• Next level of measurement is ordinal.
• Puts subjects in order from high to low, but it
  does not indicate how much higher or lower one
  subject is in relation to another.
• Is helpful to think of this level as the ranking
  level.
• Individuals are ranked according to their height
  with a rank of 1 for the tallest, a rank of 2 for
  the nest tallest, and so on.
• Three brands of hand lotion are ranked according
  to consumers preferences for them, with a rank
  of 1 for the one most preferred, a rank of 2 for
  the next favorite, and so on.
• Individuals rank situation comedy programs on
  network television, giving a rank of 1 to their
  favorite, a rank of 2 to their next favorite, and
  so on.
• Examples tell us the relative standings of
  individuals but not the amount of the differences
  among the individuals.
• We know that an individual of with a rank of 1 is
  taller than an individual with a rank of 2, but
  we do not know by how much.
• First individual may be only one-quarter of an
  inch taller or two feet taller than the second.

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Interval

• Tells us how by how much individuals differ.
• Helpful to think of this as the equal distance
  level.
• Height of each individual measured to the nearest
  inch.
• Number of times each pigeon presses a button in
  the first minute after receiving a reward.
• Number of days each student is late arriving at
  school during the school year.

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• In most statistical analyses, interval and ratio
  measurements are analyzed in the same way.
• Interval scale does not have an absolute zero.
• If we measure intelligence we do not know exactly
  what constitutes zero intelligence, and, thus
  cannot measure it.
• In contrast, a ratio scale has an absolute zero.

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Ratio

• Similar to Interval scale.
• Highest level.
• Has equal intervals.
• Ratio scale has an absolute zero point that we
  know how to measure.
• Weight is an example of ratio scale because it
  has an absolute zero.
• We know where the zero point is on a tape measure
  when we measure height.

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Summary of Levels
Lowest Level Scale Characteristic
Nominal naming Ordinal ordering Interval equa
l interval w/o absolute zero Ratio equal
interval w/ absolute zero
Highest Level
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• Understanding scales of measurement is important
  in statistics because knowing them helps in the
  selection of appropriate statistics for a given
  set of data.