Download - Correlation and Correlational Research Slides Prepared by Alison L. O’Malley Passer Chapter 5
![Page 1: Correlation and Correlational Research Slides Prepared by Alison L. O’Malley Passer Chapter 5](https://reader031.vdocuments.us/reader031/viewer/2022032803/56649e205503460f94b0b173/html5/thumbnails/1.jpg)
Correlation andCorrelationalResearch
Slides Prepared by Alison L. O’Malley
Passer Chapter 5
![Page 2: Correlation and Correlational Research Slides Prepared by Alison L. O’Malley Passer Chapter 5](https://reader031.vdocuments.us/reader031/viewer/2022032803/56649e205503460f94b0b173/html5/thumbnails/2.jpg)
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?
![Page 3: Correlation and Correlational Research Slides Prepared by Alison L. O’Malley Passer Chapter 5](https://reader031.vdocuments.us/reader031/viewer/2022032803/56649e205503460f94b0b173/html5/thumbnails/3.jpg)
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”
![Page 4: Correlation and Correlational Research Slides Prepared by Alison L. O’Malley Passer Chapter 5](https://reader031.vdocuments.us/reader031/viewer/2022032803/56649e205503460f94b0b173/html5/thumbnails/4.jpg)
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.
![Page 5: Correlation and Correlational Research Slides Prepared by Alison L. O’Malley Passer Chapter 5](https://reader031.vdocuments.us/reader031/viewer/2022032803/56649e205503460f94b0b173/html5/thumbnails/5.jpg)
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
![Page 6: Correlation and Correlational Research Slides Prepared by Alison L. O’Malley Passer Chapter 5](https://reader031.vdocuments.us/reader031/viewer/2022032803/56649e205503460f94b0b173/html5/thumbnails/6.jpg)
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
![Page 7: Correlation and Correlational Research Slides Prepared by Alison L. O’Malley Passer Chapter 5](https://reader031.vdocuments.us/reader031/viewer/2022032803/56649e205503460f94b0b173/html5/thumbnails/7.jpg)
Examine the pattern of association between (a) X and Y1 and (b) X and Y2
![Page 8: Correlation and Correlational Research Slides Prepared by Alison L. O’Malley Passer Chapter 5](https://reader031.vdocuments.us/reader031/viewer/2022032803/56649e205503460f94b0b173/html5/thumbnails/8.jpg)
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
![Page 9: Correlation and Correlational Research Slides Prepared by Alison L. O’Malley Passer Chapter 5](https://reader031.vdocuments.us/reader031/viewer/2022032803/56649e205503460f94b0b173/html5/thumbnails/9.jpg)
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
![Page 10: Correlation and Correlational Research Slides Prepared by Alison L. O’Malley Passer Chapter 5](https://reader031.vdocuments.us/reader031/viewer/2022032803/56649e205503460f94b0b173/html5/thumbnails/10.jpg)
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
![Page 11: Correlation and Correlational Research Slides Prepared by Alison L. O’Malley Passer Chapter 5](https://reader031.vdocuments.us/reader031/viewer/2022032803/56649e205503460f94b0b173/html5/thumbnails/11.jpg)
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
![Page 12: Correlation and Correlational Research Slides Prepared by Alison L. O’Malley Passer Chapter 5](https://reader031.vdocuments.us/reader031/viewer/2022032803/56649e205503460f94b0b173/html5/thumbnails/12.jpg)
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]
![Page 13: Correlation and Correlational Research Slides Prepared by Alison L. O’Malley Passer Chapter 5](https://reader031.vdocuments.us/reader031/viewer/2022032803/56649e205503460f94b0b173/html5/thumbnails/13.jpg)
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?
![Page 14: Correlation and Correlational Research Slides Prepared by Alison L. O’Malley Passer Chapter 5](https://reader031.vdocuments.us/reader031/viewer/2022032803/56649e205503460f94b0b173/html5/thumbnails/14.jpg)
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.
![Page 15: Correlation and Correlational Research Slides Prepared by Alison L. O’Malley Passer Chapter 5](https://reader031.vdocuments.us/reader031/viewer/2022032803/56649e205503460f94b0b173/html5/thumbnails/15.jpg)
Interpreting Correlations How much “overlap” is there?
Y
YX
?
![Page 16: Correlation and Correlational Research Slides Prepared by Alison L. O’Malley Passer Chapter 5](https://reader031.vdocuments.us/reader031/viewer/2022032803/56649e205503460f94b0b173/html5/thumbnails/16.jpg)
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
![Page 17: Correlation and Correlational Research Slides Prepared by Alison L. O’Malley Passer Chapter 5](https://reader031.vdocuments.us/reader031/viewer/2022032803/56649e205503460f94b0b173/html5/thumbnails/17.jpg)
Interpreting Correlations: Scatter Plots
How are the properties of correlation coefficients – sign and strength – reflectedin each of these scatter plots?
![Page 18: Correlation and Correlational Research Slides Prepared by Alison L. O’Malley Passer Chapter 5](https://reader031.vdocuments.us/reader031/viewer/2022032803/56649e205503460f94b0b173/html5/thumbnails/18.jpg)
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?
![Page 19: Correlation and Correlational Research Slides Prepared by Alison L. O’Malley Passer Chapter 5](https://reader031.vdocuments.us/reader031/viewer/2022032803/56649e205503460f94b0b173/html5/thumbnails/19.jpg)
Correlation ≠ Causation
![Page 20: Correlation and Correlational Research Slides Prepared by Alison L. O’Malley Passer Chapter 5](https://reader031.vdocuments.us/reader031/viewer/2022032803/56649e205503460f94b0b173/html5/thumbnails/20.jpg)
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?
![Page 21: Correlation and Correlational Research Slides Prepared by Alison L. O’Malley Passer Chapter 5](https://reader031.vdocuments.us/reader031/viewer/2022032803/56649e205503460f94b0b173/html5/thumbnails/21.jpg)
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
![Page 22: Correlation and Correlational Research Slides Prepared by Alison L. O’Malley Passer Chapter 5](https://reader031.vdocuments.us/reader031/viewer/2022032803/56649e205503460f94b0b173/html5/thumbnails/22.jpg)
Cross-Lagged Panel Design
What does it mean when a correlation is “spurious”?
![Page 23: Correlation and Correlational Research Slides Prepared by Alison L. O’Malley Passer Chapter 5](https://reader031.vdocuments.us/reader031/viewer/2022032803/56649e205503460f94b0b173/html5/thumbnails/23.jpg)
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?
![Page 24: Correlation and Correlational Research Slides Prepared by Alison L. O’Malley Passer Chapter 5](https://reader031.vdocuments.us/reader031/viewer/2022032803/56649e205503460f94b0b173/html5/thumbnails/24.jpg)
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
![Page 25: Correlation and Correlational Research Slides Prepared by Alison L. O’Malley Passer Chapter 5](https://reader031.vdocuments.us/reader031/viewer/2022032803/56649e205503460f94b0b173/html5/thumbnails/25.jpg)
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
![Page 26: Correlation and Correlational Research Slides Prepared by Alison L. O’Malley Passer Chapter 5](https://reader031.vdocuments.us/reader031/viewer/2022032803/56649e205503460f94b0b173/html5/thumbnails/26.jpg)
Regression
Regression line generated through application of regression equation
![Page 27: Correlation and Correlational Research Slides Prepared by Alison L. O’Malley Passer Chapter 5](https://reader031.vdocuments.us/reader031/viewer/2022032803/56649e205503460f94b0b173/html5/thumbnails/27.jpg)
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)
![Page 28: Correlation and Correlational Research Slides Prepared by Alison L. O’Malley Passer Chapter 5](https://reader031.vdocuments.us/reader031/viewer/2022032803/56649e205503460f94b0b173/html5/thumbnails/28.jpg)
Multiple Regression
GeneralCAT
Criterion
Structured Interview
WorkSample
GeneralCAT
Criterion
Structured Interview
WorkSample
Which scenario is preferable?
(a) (b)
![Page 29: Correlation and Correlational Research Slides Prepared by Alison L. O’Malley Passer Chapter 5](https://reader031.vdocuments.us/reader031/viewer/2022032803/56649e205503460f94b0b173/html5/thumbnails/29.jpg)
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
![Page 30: Correlation and Correlational Research Slides Prepared by Alison L. O’Malley Passer Chapter 5](https://reader031.vdocuments.us/reader031/viewer/2022032803/56649e205503460f94b0b173/html5/thumbnails/30.jpg)
Range Restriction
![Page 31: Correlation and Correlational Research Slides Prepared by Alison L. O’Malley Passer Chapter 5](https://reader031.vdocuments.us/reader031/viewer/2022032803/56649e205503460f94b0b173/html5/thumbnails/31.jpg)
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!
![Page 32: Correlation and Correlational Research Slides Prepared by Alison L. O’Malley Passer Chapter 5](https://reader031.vdocuments.us/reader031/viewer/2022032803/56649e205503460f94b0b173/html5/thumbnails/32.jpg)
•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