Transcript Operational Definitions • In our last class, we discussed (a) what it means to quantify psychological variables and (b) the different scales of.

Operational Definitions
• In our last class, we discussed (a) what it means to
quantify psychological variables and (b) the
different scales of measurement used for
categorical and continuous variables.
• However, we deliberately side-stepped an
important question: How do we determine “what
matters” when we try to measure a variable?
Simple Example
• Let’s consider a relatively simple example: Let’s
try to measure crying.
• Before we can do so, we need to decide “what
counts” as crying behavior.
• Examples:
Definition of an Operational Definition
• It is critical that the set of rules, or operations, that
we use to measure a behavior be explicit and as
clear-cut as possible.
• These rules, or operations, constitute the
operational definition of a variable.
Complex Example
• Now let’s consider a more complex variable: the
experience of humor.
• Whether or not someone finds something funny is
a much more abstract (i.e., less tangible) thing to
measure than crying.
•
In-Class Example: Two sets of operational definitions, and three students
listening to jokes.
Important Distinction
• Latent vs. Observed variables
– An observed variable, like crying, is directly observable
and can be measured easily.
– A latent variable or construct is not directly observable.
Instead, it is inferred from variables than can be
observed.
Measuring Latent Variables
• Latent variables can be measured, but their
measurement is much more complicated than that
of observed variables.
• The first thing we need to do is identify, usually
on an intuitive or theoretical basis, the scale of the
latent variable. Is it categorical or continuous?
• Next, we need to identify the indicators of the
latent variable (i.e., the observable consequences
or manifestations of the latent variable).
Measuring Latent Variables
• Let’s answer the following question: Someone
who finds something funny should be likely to
behave in the following ways: __________.
• These things (e.g., laughing), operationally
defined, of course, can be considered as
observable indicators of the unobserved state of
“finding something humorous.”
Measuring Latent Variables
• So, to operationally define a latent variable, we
need to (a) specify the scale of the variable, (b)
identify the observable manifestations of that
latent variable, and (c) operationally define those
observable manifestations.
• Next, we need to know how the operational
definitions of the observable variables map onto
the latent variable.
Mapping
• This mapping tends to be handled differently by
different researchers.
• Two considerations:
– How many indicators to use?
– Can we assume a linear relationship between the
measured variables and the latent variable?
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Mathematical Mapping
How many indicators?
One
>1
Equivalence
relation
Multiple linear
indicators
(Simplest)
(Simple)
Single nonlinear
relationship
(Complex)
Multiple nonlinear indicators
(Very Complex)
Equivalence Relationship
• Simplest case: The equivalence relationship. In
this case, we use one indicator and assume that the
relation between the latent variable and the
manifest variable is linear.
• Example: We may operationally define laughing,
and then measure humor as if it is equal to
laughing.
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Someone who laughs
8 times would get a
humor score of 8.
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Laughing
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For each extra laugh,
we assume the person
thought the joke was
one unit more funny
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Humor
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Equivalence Relationship
• Advantages:
– Explicit and straight-forward
– Doesn’t require complicated mathematics
– Other researchers can easily determine what you did
• Disadvantages:
– Behaviors are influenced by many things. Thus, part of what
you’re measuring may be unrelated to the latent variable of
interest.
– Latent variables manifest themselves in a variety of ways. By
focusing on one variable, our measurements are not as rich or
compelling.
Multiple linear indicators
• A better scenario, but more difficult to work with,
is to use multiple indicators under the assumption
of a linear relationship.
• Example: Attraction
We assume that when someone is attracted to someone else
(a latent variable), that person is more likely to have an
increased heart rate, talk more, and make more phone calls
(all observable variables).
heart beat
talking
attraction
phone calls
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attraction
attraction
We assume that each observed variable has a
linear relationship with the latent variable.
Note, however, that each observed variable has
a different metric (one is heart beats per
minute, another is time spent talking). Thus,
we need a different metric for the latent
variable.
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allow the highest measured
value to represent the
highest value of the latent
variable
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allow the lowest measured
value to represent the
lowest value of the latent
variable
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Latent
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the line between these
points maps the
relationship between them
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talking
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heart beat
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attraction
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attraction
attraction
After the relationship has been specified between the latent
variable and each measured variable, the latent scores for
each measured variable can be averaged to scale the person
on the latent variable.
In this example: (2 + 0 + 3)/3 = 5/3 = 1.67
Multiple linear indicators
• Advantages
– By using multiple indicators, the uniqueness of each
one gets washed out by what is common to each of
them
• Disadvantages
– More complex to use
– There is more than one way to scale the latent variable,
thus, unless a scientist is very explicit, you might not
know exactly what was done to obtain the
measurements.
Multiple linear indicators: Caution
• On that last note, I should mention an important problem.
• When using multiple indicators, researchers typically sum or
average the scores to scale people on the construct
• Example:
time spent talking + heart rate = LOVE
Person A: 2 + 80 = 82
Person B: 3 + 120 = 123
Multiple linear indicators: Caution
• Why may this be a problem?
• First, the resulting metric for the latent variable
doesn’t make much sense.
Person A: 2 minutes talking + 80 beats per minute
= 82 minutes talking/beats per minute???
Multiple linear indicators: Caution
• Second, the variables may have different ranges.
• If this is true, then some indicators will count
more than others.
Multiple linear indicators: Caution
• Variables with a large range will influence the latent score
more than variable with a small range
Person
A
B
C
D
Heart rate
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120
120
Time spent talking
2
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2
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Total
82
83
122
123
* Heart rate has a greater range than time spent talking and, therefore, influences
the total score more (i.e., the score on the latent variable)
Operational Definitions
• In psychology, there is an interesting assortment of
variables that we try to measure
• Some variables are concrete and observable (e.g.,
kissing); others are abstract (e.g., love)