Lecture 4 Sep. 12, 2005

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Lecture 4Sep. 12, 2005

• Levels of Measurement
• Central Tendency
• Dispersion

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Measurement

• Assignment of numbers to objects to represent
  amounts or degrees of a property possessed by the
  objects (Togerson, 1958)
• Ex) She or he is a 10.
• Unemployment increased by 1.

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Levels of Measurement

• Nominal level numerals or other symbols are used
  to classify people, objects, or characteristics
• ex) gender (female 1, male 2)
• properties equivalent, exhaustive, mutually
  exclusive

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• 2. Ordinal level objects are ranked along some
  dimension, such as from smallest to largest.
• ex) prize (1st place, 2nd place, etc.)
• rankings of football or basketball
• teams
• Properties equivalence, order

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• 3. Interval level When a scale has all the
  properties of an ordinal scale and the intervals
  between adjacent points on the scale are of equal
  value
• ex) temperature
• Properties equivalence, order, equal difference

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• 4. Ratio level When the scale has all the
  properties of interval scales plus one more, the
  existence of a true zero point
• ex) time, distance, class size, income
• A 60,000 income is 3 times a 20,000 income.
• Properties equivalence, order, equal difference,
  true zero point

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A hierarchy of Information

• Do the numbers simply classify persons into
  common categories? (nominal)
• Do they rank or order persons? (ordinal)
• Do we interpret differences between persons?
  (interval)
• Can we interpret direct ratios of scores? (ratio)
• generally, ratio scales indicate most
  information and nominal scales the least
  information.

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Summary Statistics 1 Central Tendency

• Central Tendency What is a typical score?
• Central tendency provides information about the
  grouping or the numbers in a distribution by
  giving a single number that characterizes the
  entire distribution.

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• Mode the score or scores that occur most
  frequently.
• Median the midpoint of a distribution half of
  the scores lie above it and half lie below it.
• Mean the average of a set of scores (most
  familiar summary statistics) -gt sum of all
  scores divided by N

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Examples

• 20, 12, 11, 9, 5, 5, 3
• Mode
• Median
• Mean