Goals for Today Review the basics of an experiment Learn how to create a unit-weighted composite...

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.