Methods for Understanding

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If a thing exists, it exists in some amount and
if it exists in some amount, it can be measured.
E. L. Thorndike (1914)
2
If you haven't measured it you don't know what
you are talking about. -Lord Kelvin
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Todays 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?

4

• exercise on class composition

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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

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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?

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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, isnt something that were used to
  measuring with an everyday tool. It is a bit
  more abstract and elusive.

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Can Psychological Properties be Measured?

• However, there are two points worth considering.
• Height isnt 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.

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Can Psychological Properties be Measured?

• Finally, we must address a common complaint
  Psychological variables cant be measured.
• We regularly make judgments about who is shy and
  who isnt who is suffering and who isnt which
  marriages are functioning well and which are not

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Quantitative

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

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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 than)
• One goal of psychological measurement is to find
  standard and useful ways to systematically
  measure psychological constructs, such as shyness

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Quantification

• 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.

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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?

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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

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Continuous Variables

• With continuous variables, people vary in a
  graded way with respect to the property of
  interest
• Examples
• age
• working memory capacity
• marital discord
• Quantitative question How much? or To what
  extent or degree?

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Scales of Measurement Continuous Variables

• 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...

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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
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Scales of Measurement Interval

• Interval designates an equal-interval ordering
• 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

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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

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Scales of Measurement Additional Comments

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

variables
categorical
continuous
ordinal
interval
ratio