Correlation andCorrelationalResearch

Slides Prepared by Alison L. O’Malley

Passer Chapter 5

Correlation

•Correlations reveal the degree of statistical association between two variables, and can be computed in experimental and non-experimental research designs •Correlational research establishes whether naturally occurring variables are statistically related •How does correlational research differ from experimental research?

Correlational Research

• In correlational research, variables are measured rather than manipulated

• Manipulation is the hallmark of experimentation which enables researchers to draw causal inferences

• This distinction between measurement and manipulation drives the oft-cited mantra “correlation does not equal causation”

Thinking Critically about Correlational Research

What information do you need to know in order to determine whether a study uses an experimental or correlational research design?

Generate a research question that lends itself to a correlational research design but not an experimental research design.

Direction of Relationship: Positive

•Two variables tend to increase or decrease together •Higher scores on X are associated with higher scores on Y •Lower scores on X are associated with lower scores on Y •Envision two people in an elevator

Direction of Relationship: Negative

•Two variables tend to move in opposite directions •Higher scores on X are associated with lower scores on Y•Lower scores on X are associated with higher scores on Y •Envision two people on a see-saw

Examine the pattern of association between (a) X and Y1 and (b) X and Y2

Correlation Practice

Generate your own example of each of the following: • A positive relationship• A negative relationship • A relationship that is not significantly

different than zero

Measuring Correlations What scale of measurement are we dealing with?

•Pearson product-moment correlation coefficient• Pearson’s r•Variables measured on interval or ratio scale

•Spearman’s rank-order correlation coefficient• Spearman’s rho •One or both variables measured on ordinal

scale

Interpreting Correlations

In addition to considering the direction of the relationship (i.e., positive or negative), we need to attend to the strength of the relationship.

0.00 +1.00-1.00

Interpreting Correlation Strength

• Is the relationship between two variables weak? Moderate? Strong?

Guidelines from Cohen (1988) Absolute value

Weak .10 - .29

Moderate .30 - .49

Strong > .50

Interpreting Correlations

• Pay close attention to how variables were coded • In most (but not all) cases, higher values

reflect more of the underlying attribute [Note: this does not apply to nominal data]

Interpreting Correlations

If a psychological scientist establishes a correlation of .33 between integrity and job performance, can one say that the two variables are 33% related?

Interpreting Correlations

If a psychological scientist establishes a correlation of .33 between integrity and job performance, can one say that the two variables are 33% related?

No. r2 (coefficient of determination) reveals how much of the differences in Y scores are attributable to differences in X scores.

Interpreting Correlations How much “overlap” is there?

Y

YX

?

Interpreting Correlations How much “overlap” is there?

Y

YX

?

If r = .33, then r2 = .11 11% of the variance in Y is attributable to X

Interpreting Correlations: Scatter Plots

How are the properties of correlation coefficients – sign and strength – reflectedin each of these scatter plots?

Correlation ≠ Causation

Review the three criteria used to draw causal inferences…

Which criterion/criteria is/are impacted by the bidirectionality problem? The third-variable problem?

Correlation ≠ Causation

Strategies to Reduce Causal Ambiguity

1. Statistical approaches• Measure and statistically control for (i.e., partial out) a third variable

2. Research design approaches• When possible, conduct longitudinal studies

Why are longitudinal studies preferable to cross-sectional studies?

Longitudinal Research Designs

•Prospective design• X measured at Time 1, Y measured at Time 2 • Rules out bidirectionality problem

•Cross-lagged panel design •Measure X and Y at Time 1• Repeat X and Y measurement at Time 2• Examine pattern of relationships (i.e., cross-

lagged correlations) across variables and time

Cross-Lagged Panel Design

What does it mean when a correlation is “spurious”?

Drawing Causal Conclusions

• How do we rule out all plausible third variables (confounds) using correlational research designs?

• We can’t… only the control afforded by rigorous experimentation provides strong tests of causation.

• So what good are correlational studies?

Correlation and Prediction

• A goal of science is to forecast future events

• In simple linear regression, scores on X can be used to predict scores on Y assuming a meaningful relationship (r) has been established between X and Y in past research

Linear Regression

• E.g., Scores on a job interview (X) can be used to predict job performance (Y)

• X is the predictor; Y is the criterion• Interview scores plugged into

regression equation and hiring decisions made based on results

• This is an illustration of criterion validity

Regression

Regression line generated through application of regression equation

Multiple Regression

•Multiple predictors are used to predict a criterion measure

•Strive for as little overlap as possible between predictors (i.e., want to account for unique variance in criterion)

Multiple Regression

GeneralCAT

Criterion

Structured Interview

WorkSample

GeneralCAT

Criterion

Structured Interview

WorkSample

Which scenario is preferable?

(a) (b)

Nonlinear Relationships

Pearson’s r is useless in cases where X and Y do not relate in a linear fashion. See the curvilinear relationship below.

test performance

Alertness

sleepy alert panic

Range Restriction

Special Considerations

• Make sure to examine your scatterplot • Are X and Y related in a linear fashion?• Do your data reveal range restriction?• What scales of measurement are you dealing

with?

If the relationship of interest is nonlinear and/or you have range restriction and/or you have nominal data, calculating r will produce inaccurate, misleading results!

•Correlation is a powerful statistical tool and correlational research can shed light on important questions…•But make sure to employ these tools wisely! Unfortunately, the media and even some researchers can report misleading findings. • And remember, by itself correlation does not establish causation!

Closing Considerations