Methods for Understanding by L3Yaq6O


									“If a thing exists, it exists in
some amount; and if it exists in
some amount, it can be
–E. L. Thorndike (1914)
“If you haven't measured it
you don't know what you
are talking about.”
-Lord Kelvin
            Today’s Questions

• What does it mean to measure a
  psychological variable?
• What is the difference between categorical
  and continuous variables, and why does the
  difference matter?
• [exercise on class composition]
                 Basic Terminology

• Variable: a characteristic that can vary or take on
  different values
   – Example: height is a variable
• Value: a number representing one of many possible
  “states” of the variable
   – Example: some possible values of height are 6 feet or 4 feet
     2 inches
• Score: a specific value for a given person
   – Example: my score on the variable of height is 6 feet
          Systematic Observation

• In order to systematically observe something,
  it is critical to have a well-defined or
  quantitative system of measurement.

• Simple example: How tall is Mike Marks?
         A More Complex Example

• What about a question such as “How shy is
  Tim Miura?”
• This seems a bit more tricky because
  shyness, unlike height, isn’t something that
  we’re used to measuring with an everyday
  tool. It is a bit more abstract and elusive.
     Can Psychological Properties be
• However, there are two points worth
  – Height isn’t exactly a “thing” in the way that a desk
    is a thing. Height, however, is an extremely useful
    abstraction. Is there any reason why shyness
    should be any more intractable than height?
  – There is nothing intrinsically concrete about
    inches, feet, miles, and meters. These are
    standard (i.e., conventional and agreed upon),
    but ultimately arbitrary, metrics.
     Can Psychological Properties be
• Finally, we must address a common
  complaint: Psychological variables can’t be
• We regularly make judgments about who is
  shy and who isn’t; who is suffering and who
  isn’t; which marriages are functioning well
  and which are not

• Implicit in these statements is the notion that
  some people are more shy, for example, than
• This kind of statement is inherently
  – Quantitative: subject to numeric qualification.
              Interim Summary

• Shyness, like distance, is a useful abstraction
• We use the concept of shyness, like height, in
  quantitative ways (e.g., greater than, less
• One goal of psychological measurement is to
  find standard and useful ways to
  systematically measure psychological
  constructs, such as shyness

• An important first-step in measurement is
  determining whether a variable is categorical
  or continuous.
• Why? This property of a variable determines
  how we quantify the variable, how we model
  its statistical behavior, and the way we
  analyze data regarding that variable.
                     Nominal Scale

• With categorical, taxonic, qualitative, or
  nominal variables, people either belong to a
  group or they do not
• Examples:
  –   country of origin
  –   biological sex (male or female)
  –   animal or non-animal
  –   married vs. single
• Quantitative question: How many people
  belong to each category?
 Scales of Measurement: Nominal Scale

• Sometimes numbers are used to designate
  category membership
• Example:
   Country of Origin
   1 = United States    3 = Canada
   2 = Mexico           4 = Other
• However, in this case, it is important to keep
  in mind that the numbers do not have
  numeric implications; they are simply
  convenient labels
             Continuous Variables

• With continuous variables, people vary in a
  graded way with respect to the property of
• Examples:
  – age
  – working memory capacity
  – marital discord
• Quantitative question: How much? or To
  what extent or degree?
   Scales of Measurement: Continuous
• When we assign numbers to people (i.e.,
  “scale” people) with respect to a continuous
  variable, those numbers represent something
  that is more meaningful than those used with
  nominal variables
• Exactly what those numbers mean, and how
  they should be treated, however depends on
  the exact metric of the continuous variable...
           Scales of Measurement: Ordinal
• Ordinal: Designates an ordering; quasi-ranking
• Does not assume that the intervals between numbers are equal
• Example:
   finishing place in a race (first place, second place)

      1st place         2nd place 3rd place                 4th place

 1 hour       2 hours        3 hours    4 hours   5 hours      6 hours   7 hours   8 hours
     Scales of Measurement: Interval

• Interval: designates an equal-interval
• The distance between, for example, a 1 and a
  2 is the same as the distance between a 4
  and a 5
• Example: Common IQ tests are assumed to
  use an interval metric
       Scales of Measurement: Ratio

• Ratio: designates an equal-interval ordering
  with a true zero point (i.e., the zero implies an
  absence of the thing being measured)
• Example:
   – number of intimate relationships a person has had
      • 0 quite literally means none
      • a person who has had 4 relationships has had
        twice as many as someone who has had 2
      Scales of Measurement: Additional
• In general, most observable
  behaviors can be measured on a
  ratio-scale                                        variables

• In general, many unobservable
  psychological qualities (e.g.,
  extraversion), are measured on           categorical      continuous
  interval scales
• We will mostly concern ourselves
  with the simple categorical                             ordinal
  (nominal) versus continuous
  distinction (ordinal, interval, ratio)                 interval


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