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.

Simple Example

• Today we’re going to discuss operational definitions.

• Let’s begin by assuming we’re interested in the question of whether the use of cell phones while driving impairs safe driving.

Definition of an Operational Definition

• There are many ways we could potentially measure “safe driving”– Examples

• It is critical that the set of rules, or operations, that we use to measure a variable be as explicit, concrete, and as quantifiable as possible.

• These rules, or operations, constitute the operational definition of a variable.

Complex Example

• Safe driving is a relatively simple example because it doesn’t involve references to abstract concepts.

• Now let’s consider a more complex, abstract variable: psychological distress.

Important Distinction

• Latent vs. Observed variables– An observed variable, like using a cell phone, is

directly observable and can be measured relatively easily once observers agree upon what counts as an instance of using a cell phone and what does not.

– A latent variable or construct, such as stress, is not directly observable. Instead, it is inferred from variables that 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 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 is distressed should be likely to do the following things: __________.

• These things—which also need to be operationally defined—can be considered observable indicators of the unobserved state of stress.

Measuring Latent Variables

• Let’s focus on one potential indicator for the moment: The number of things a person has to do by Friday—a “to do” list.

• We could operationalize this in a relatively simple way by asking people “How many things do you need to do before Friday?” and recording the response.

• The answer essentially becomes the person’s score on the latent variable: an equivalence relationship.

Stress

Num

ber

of th

ings

to d

o by

Fri

day

For each extra task, we assume the person is more distressed.

Someone who has 8 things to do would get a stress score of 8.

Person Numb of things to do

Latent score

estimate

Prof. Fraley

13 13

b

c

d

e

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, the indicator

(e.g., “things to do”) might be a better measure of “being employed” rather than “stress” per se.

– Latent variables manifest themselves in a variety of ways. By focusing on one indicator, our measurements are not as rich or compelling.

Multiple indicators

• A more ideal situation is to use multiple indicators to assess a latent variable.

• Example: Stress

stress

heart rate complaints To do list

We assume that when someone is experiencing stress (a latent variable), that person is more likely to have an increased heart rate, complain more, and report having more things to do (all of these need to be operationally defined).

Person Indicator 1

complaints

Indicator 2

To do list

Average

Prof. Fraley

10 13 11.5

b

c

d

e

Multiple indicators: Caution

• When using multiple indicators, there is a temptation to average the observed scores to scale people on the construct

• Example:

(complaints + heart rate)/2 = stress

Person A: (2 + 80)/2 = 82/2 = 41

Person B: (3 + 120)/2 = 123/2 = 62

Multiple linear indicators: Caution

• This can lead to several problems if each manifest variable is measured on a different scale.

• First, the resulting metric for the latent variable doesn’t make much sense.

Person A: 2 complaints + 80 beats per minute

= 41 complaints/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 Heart rate Complaints Average

A 80 2 41

B 80 3 42

C 120 2 61

D 120 3 62

* Moving between lowest to highest scores matters more for one variable than the other

* 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)

Mapping

• One solution to this problem is to (a) define a metric for the latent variable and (b) formalize the mapping of the indicator onto the latent variable.

• Mapping—specifying the relationship between the latent and manifest/observed variable.

stress

hear

t bea

t /10

stressC

ompl

aint

sstress

Sle

ep p

robl

ems

In our example we might assume that stress is on an interval metric, with values ranging between -4 and + 4.

Note, however, that each observed variable has a different metric (one is heart beats per minute, another is number of complaints). Thus, we need to specify how the measured scores translate into the latent scores.

-4 0 4

020

4060

8010

0

Allow the lowest measured value to represent the lowest value of the latent variable.

Allow the highest measured value to represent the highest value of the latent variable.

Draw a line between these points to map the relationship between the observed and latent variable.

Latent

Obs

erve

d

Stress

hear

t bea

t / 1

0

StressC

ompl

aint

sStress

Thi

ngs

to d

o

Now we can map the observed scores for each measured variable onto the scale for the latent variable. For example, the observed heart rate score of 120 maps onto a stress score of 2. Ten complaints over a week maps onto a stress score of zero. Thirteen things to do maps to a high stress score of 3.

attraction

hear

t bea

t/10

attractionta

lkin

gattraction

phon

e ca

lls

This mapping process provides us with three estimates of the latent stress score: 2, 0, and 3. Because we are trying to estimate a single number for stress and because these numbers are on the same scale, we can simply average these three estimates to obtain our measurement of attraction.

In this example: (2 + 0 + 3)/3 = 5/3 = 1.67 (somewhat stressed)

Estimating latent scores

Person Indicator 1 (complaints)

Latent score

estimate 1

Indicator 2

(to do list)

Latent score

estimate 2

Averaged latent score

Prof. Fraley

10 0 13 3 (0+3)/2 = 1.5

b

c

d

e

Multiple indicators

• Advantages– By using multiple indicators, the uniqueness of each

indicator gets washed out by what is common to all of the indicators. (example: heart rate and running up the stairs)

• 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 he or she did to obtain the measurements.

Summary

• Recap of what we did– Identified two (or more) indicators of the latent variable and

operationally defined those.– Determined the metric of the latent variable– Mapped the relationship between the latent variable and

each observed variable– Using this mapping, we calculated the latent scores for each

person with each observed variable.– Averaged the latent score estimates for each person to get a

single estimate of where that person falls on the latent variable.

– This is often called a “composite score” and is used as an estimate of the person’s standing on the latent variable of interest.