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Goals for Today
• Review the basics of an experiment• Learn how to create a unit-weighted composite
variable and how/why it is used in psychology.• Learn how to create composite variables in
SPSS.• Learn how to compare the mean difference
between two groups using Cohen’s d.
Review
• What is an experiment? What is random assignment to conditions and why does it matter?
• What are independent vs. dependent variables in an experimental study?
• What are our dependent measures/variables in our subliminal study?
Composite Scores
• When we have multiple ways of assessing a construct (e.g., self-esteem), we often create a composite variable that captures the these scores.
Composite Scores
• Why do we average scores together to create a composite?
• We assume that a “latent” variable or “construct”, such as self-esteem, manifests itself in various ways.
Composite Scores
• Each of those manifestations, however, is an imperfect reflection of a person’s self-esteem.
• Example: A person may indicate that they feel good about themselves not because they feel especially good about themselves per se, but because they hold others in such low regard.
Composite Scores
• O = T + E• We assume that our measurement or
observation, O, is a function of at least two factors: A true score (T: the value that we expect to observe) and measurement error (E).
• If the measurement errors are random, then averaging several O’s together should give us a better approximation of T.
Reverse Scored Items
• Some items are negatively related to the construct of interest.– Ex: “I feel I do not have much to be proud of. ”
• These items cannot be weighted in the same fashion as the others when creating a composite variable.
Unit-weighted composite
• To create a “unit-weighted composite”—the most commonly used composite in personality psychology, do the following:
– 1. Reverse-key responses to items that are in the opposite direction of the construct.
• One way to do this is to use the following formula:
• (Max - X) + Min• Thus, on a 1 (Min) to 5 (Max) scale, like the one
we used:• 5 – X + 1
• 2. Once the appropriate responses have been reverse keyed, simply average the responses for each person.
Item Person 1 Person 2 Person 3
I feel that I'm a person of worth, at least on an equal plane with others
5 5 2
I feel that I have a number of good qualities. 5 4 3
All in all, I am inclined to feel that I am a failure.(Reverse)
1 (5) 2 (4) 3 (3)
I am able to do things as well as most other people.
5 5 2
I feel I do not have much to be proud of. (Reverse)
1 (5) 1 (5) 4 (2)
Sum 25 23 12
Average 5 4.6 2.4
Qualifications
• This method is the simplest, but there are more complex ways of creating composite variables.– For example, sometimes responses to each variable
are standardized (transformed to z-scores) before the averaging takes place.
– In some work, the measurements might be weighted differently. That is, some variables might count more than others.
– In other work, non-linear relationships might be assumed between the latent variable and an item response (e.g., Item Response Theory models).
Mean Differences
• The big question in our experiment is whether people’s self-esteem improves after listening to a subliminal recording containing subliminal messages designed to improve self-esteem.
• [open SPSS]
Our Experiment
• Two conditions:– A. People in the “good” condition were
presented with self-affirming subliminal messages, such as “You are a good person.”
– B. People in the “bad” condition were presented with self-defacing subliminal messages, such as “No one likes you.”
Answering the Question
• Did our manipulation have an impact on peoples’ self-esteem?
• One way of addressing the question is by determining whether people in Condition A had higher levels of self-esteem than people in Condition B. (As measured after hearing the recording.)
• Everyone has a unique self-esteem score, so we average the scores (i.e., the composite scores) for people in Condition A and separately average the scores for people in Condition B.
• We want two statistics: (a) the mean, which tells us the average self-esteem value for a person in a condition, and (b) the standard deviation (SD), which tells us the amount of variability there is around the mean in that condition.
Mean Difference
• Mean Difference between conditions:– (Mean of Group A – Mean of Group B)
– If positive, then Group A > Group B– If negative, then Group A > Group B– If zero, then no difference between conditions.
Standardized Mean Difference
• If we divide the mean difference by the average SD of the two groups, we obtain a standardized mean difference or Cohen’s d.
2/22BA
BA
SDSD
MMd
Pooled standard deviation
Standardized Mean Difference
• Cohen’s d expresses the difference between groups relative to the average standard deviation of the scores.
• For Cohen's d, an effect size of 0.2 to 0.3 might be dubbed a "small" effect. Something around 0.5 might be called a "medium" effect. And values above .80 might be called “large” effects.
• Handy online Cohen’s d calculator: http://web.uccs.edu/lbecker/Psy590/escalc3.htm
Another Calculation
• We could also ask about the amount of change that takes place in self-esteem scores from Time 1 (before the recording) to Time 2 (after the recording).
• Create a composite for the Time 1 scores.• Create a new variable in SPSS that represents
the Time 2 composite – Time 2 composite scores.