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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.
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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.
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. 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.