Psychology 3450W: Experimental Psychology

Psychology 3450W: Experimental Psychology
Fall, 2017 Professor Delamater

Correlational Research
Outline of Todays Lecture: Basic Ideas Regarding Correlations Scatterplots Direction, Strength & the correlation coefficient Prediction & Least Square Regression Multiple Regression Interpretive Problems When Using Correlations Use of Correlations in Psychological Research Psychometrics Individual Difference Research (e.g., IQ & Twin Studies) Cognitive Studies 4. More Advanced Correlational Ideas Multivariate Analysis Factor Analysis

Basic Ideas Regarding Correlations – Used to examine a relationship between two naturally occurring variables.

Basic Ideas Regarding Correlations – Used to examine a relationship between two naturally occurring variables. e.g., sun spots & aurora borealis (“Northern Lights”)

Basic Ideas Regarding Correlations – Used to examine a relationship between two naturally occurring variables. e.g., sun spots & aurora borealis

Basic Ideas Regarding Correlations – Used to examine a relationship between two naturally occurring variables. e.g., sun spots & aurora borealis But Where and When does this natural phenomenon occur?

Basic Ideas Regarding Correlations – Used to examine a relationship between two naturally occurring variables. e.g., sun spots & aurora borealis Sun spots reflect solar flares – emission of highly charged particles that could enter the earth’s atmosphere at the poles

Basic Ideas Regarding Correlations – Used to examine a relationship between two naturally occurring variables. e.g., sun spots & aurora borealis Sun spot cycles fluctuate over time (11-yr cycles) and these correlate with aurora borealis citings.

Basic Ideas Regarding Correlations – Used to examine a relationship between two naturally occurring variables. Scatter Plot – Illustrates the relationship # Aurora Citings # Sun Spots # of Aurora sightings is positively related to # sun spots in different time periods.

Basic Ideas Regarding Correlations – Used to examine a relationship between two naturally occurring variables. Scatter Plot – Illustrates the relationship Correlation Coefficient: -1 < r < +1 Indicates: Direction Strength # Aurora Citings # Sun Spots # of Aurora sightings is positively related to # sun spots in different time periods.

Basic Ideas Regarding Correlations – Used to examine a relationship between two naturally occurring variables. Scatter Plot – Illustrates the relationship Correlation Coefficient: -1 < r < +1 Indicates: Direction Strength Range restriction problem # Aurora Citings # Sun Spots # of Aurora sightings is positively related to # sun spots in different time periods.

Basic Ideas Regarding Correlations – Used to examine a relationship between two naturally occurring variables. Scatter Plot – Illustrates the relationship The sign of r indicates the direction of the relationship, and how close the value is to +1 or -1 indicates its strength.

Basic Ideas Regarding Correlations – Used to examine a relationship between two naturally occurring variables. Scatter Plot – Illustrates the relationship Panel 1 shows a strong positive correlation, panel 2 a weak positive correlation, and panel 3 no correlation.

Basic Ideas Regarding Correlations – Used to examine a relationship between two naturally occurring variables. Scatter Plot – Illustrates the relationship How tightly clustered the data are around a “best fitting line” indicates the strength of the correlation. The more tightly clustered the stronger the correlation.

Basic Ideas Regarding Correlations – Used to examine a relationship between two naturally occurring variables. Scatter Plot – Illustrates the relationship But what is a “best fitting” line?

Basic Ideas Regarding Correlations – Used to examine a relationship between two naturally occurring variables. Scatter Plot – Illustrates the relationship But what is a “best fitting” line? Another name for it is the “least squares regression” line. This is the line that minimizes the sum of the squared differences between each point and the line.

Basic Ideas Regarding Correlations – Used to examine a relationship between two naturally occurring variables. Scatter Plot – Illustrates the relationship Equation for the Least Squares Regression Line: y = mx + b # Aurora Citings # Sun Spots

Basic Ideas Regarding Correlations – Used to examine a relationship between two naturally occurring variables. Scatter Plot – Illustrates the relationship Equation for the Least Squares Regression Line: y = mx + b This can be used for prediction - You can estimate how much of y you’d expect with a given level of x. # Aurora Citings # Sun Spots

Basic Ideas Regarding Correlations – Used to examine a relationship between two naturally occurring variables. 3-d Scatter Plots – 2 predictor variables (Multiple Regression) Equation for the Least Squares Regression Line: y = b + m1x1 + m2x2 This can be used for prediction - You can estimate how much of y you’d expect with a given level of x. Also, you can determine the relative importance of multiple predictor variables. y x1 x2

Basic Ideas Regarding Correlations – Used to examine a relationship between two naturally occurring variables. 3-d Scatter Plots – 2 predictor variables (Multiple Regression) Equation for the Least Squares Regression Line: y = b + m1x1 + m2x2 This can be used for prediction - You can estimate how much of y you’d expect with a given level of x. Also, you can determine the relative importance of multiple predictor variables – size of slopes (m). y x2 x1

Basic Ideas Regarding Correlations – Used to examine a relationship between two naturally occurring variables. Multiple Regression with more than 2 predictor variables Suppose you have a questionnaire and you are trying to determine the relative importance of different predictor variables for some response variable of interest. For example, you might be interested in determining which variables might best predict when someone would be likely to get the common cold. The various predictor variables you ask about include: Equation for the Least Squares Regression Line: y = b + m1x1 + m2x2 + … + mnxn This can be used for situations with more than 2 predictor variables as well. # times w cold in past year, amount of sleep, stress rating, # people in work place, commuting distance, etc.

Interpretive problems with correlations. Correlation does NOT mean Causation. Why? Amount of Aggressive Behavior # Hrs Watching Violence on TV

Interpretive problems with correlations. Correlation does NOT mean Causation. Why? Amount of Aggressive Behavior # Hrs Watching Violence on TV 3 Problems: (1) Spurious Correlations, (2) Directionality Problem, & (3) Third Variable Problem

Spurious Correlations: Refers to relationships that are truly unconnected. SAT Scores Inter-Galactic Distance While the universe is expanding, the distance between the galaxies increases. At the same time the average SAT scores have been decreasing. But these have nothing to do with one another!

Directionality Problem: We don’t know in which the direction a causal influence may be operating. Amount of Aggressive Behavior # Hrs Watching Violence on TV Does being aggressive cause one to watch more violence on TV, or does watching more violence on TV cause aggression?

Third Variable Problem: Are two things correlated because they are both caused by some common 3rd variable? Variable A Amount of Aggressive Behavior Variable B Variable C Variable A has a causal effect on both B and C, but we only measure the relationship between B and C. # Hrs Watching Violence on TV Maybe some 3rd variable, like exposure to violence, causes both of the variables we have measured.

Directionality Problem: Cross-lagged correlations can help assess the direction of influence. Time Time2 Aggression Aggression TV Violence TV Violence Amount of Aggressive Behavior # Hrs Watching Violence on TV Assess Agg:TV correlations at Time 1 and Time 2, but also assess the correlations between Aggression at Time 1 and TV Violence at Time 2 as well as TV Violence at Time 1 and Aggression at Time 2. If one has more causal influence on the other, this will be reflected in the cross—lagged correlations.

Third Variable Problem: Partial correlations can help address the 3rd variable problem. Variable A (IQ) Reading Score Variable B Variable C (Reading) (Comprehension) Variations in IQ cause variations in both reading and comprehension. Comprehension Score Also measure IQ and calculate a “partial correlation” between reading and comprehension. This asks whether any correlation remains after removing the contribution made by IQ. If no, then you’ve identified a likely 3rd variable. If yes, then perhaps the two are directly related.

Examples in Psychological Research: Psychometrics Individual Difference Research Cognitive

Psychometrics: Devising a test for anxiety, depression, or some other personality trait. Two key issues concern assessing the reliability and validity of the test (usually a paper and pencil questionnaire). 1. Test-Retest Reliability – Are the scores similar when taken at separate times? 2. Split-Half Reliability – Choose a random half of the items (questions) on the questionnaire, analyze those, and compare the results to the score you get from evaluating the other half of the items. If the items (questions) are all assessing the same underlying construct (anxiety, depression, etc), then you should get similar scores on the different split halves.

Psychometrics: Devising a test for anxiety, depression, or some other personality trait. Two key issues concern assessing the reliability and validity of the test (usually a paper and pencil questionnaire). 3. Predictive Validity – Once a reliable test has been constructed, one can ask how valid it is at predicting behavior relevant to the construct of interest. For instance, can your test of depression predict treatment effectiveness? More severe cases would be more treatment-resistant than less severe cases, etc. Notice that all of these issues are related to the more general question of developing measures of psychological constructs that we discussed at the beginning of term.

Individual Difference Research: This form of research is focused on the study of individual variations in some psychological attribute. For example, is intelligence genetically or environmentally determined? Twin Studies – Investigators have administered IQ tests to members of twin pairs and determined how well correlated are their scores as a function of their shared genetics.

Twin Studies – Investigators have administered IQ tests to members of twin pairs and determined how well correlated are their scores as a function of their shared genetics. Identical Twins (reared together) r = 0.86 Identical Twins (reared apart) r = 0.72 Fraternal Twins (reared together) r = 0.60 Siblings (reared together) r = 0.47 Siblings (reared apart) r = 0.24 Cousins r = 0.15 What can we say about the heritability of intelligence?

Twin Studies – Investigators have administered IQ tests to members of twin pairs and determined how well correlated are their scores as a function of their shared genetics. Identical Twins (reared together) r = 0.86 Identical Twins (reared apart) r = 0.72 Fraternal Twins (reared together) r = 0.60 Siblings (reared together) r = 0.47 Siblings (reared apart) r = 0.24 Cousins r = 0.15 100% 50% 12.5%

Twin Studies – Investigators have administered IQ tests to members of twin pairs and determined how well correlated are their scores as a function of their shared genetics. Actual ID Actual Fraternal r = ? r = ? Perceived ID r = ? r = ? Perceived Fraternal

Twin Studies – Investigators have administered IQ tests to members of twin pairs and determined how well correlated are their scores as a function of their shared genetics. Scarr & Carter-Saltzman, 1979 Actual ID Actual Fraternal r = ? r = ? r = Perceived ID r = ? r = ? Perceived Fraternal r > r These results are more consistent with a genetic than an environmental view.

Cognitive: Studies how organisms “think,” i.e., how they process, store, and retrieve information. Individual subjects may differ in their processing systems, so one can correlate performance to some individual trait measure. Correlate: Perceptual Priming with Stroop interference effect.

Advanced Correlational Techniques: Multivariate Analysis – Multiple regression (considered earlier) Factor Analysis – Study how many basic ”components” or “factors” there are underlying a complex data set.

Advanced Correlational Techniques: Multivariate Analysis – Multiple regression (considered earlier) Factor Analysis – Study how many basic ”components” or “factors” there are underlying a complex data set. e.g., Is Intelligence unitary or multi-faceted?

Sir Francis Galton & Intelligence: Look at grade-school records and examine the correlation matrix. History Geo Math Lit Science X + + + + History Geo X + + + X + + Math Lit Science X + X Correlation matrix is symmetrical Grades in every class are positively correlated with grades in every other class. Implies a single “factor” underlying these results – general intelligence (g)

But more recent studies with IQ implies a more complex pattern… Compr Spelling Analogy Rot Fig Logic Algebra X + + Compr Spelling X + X Analogy Rot Fig Logic X + + + X X Algebra

But more recent studies with IQ implies a more complex pattern… Compr Spelling Analogy Rot Fig Logic Algebra X + + Compr Spelling X + X Analogy Rot Fig Logic X + + + X X Algebra In this dataset there appear to be 2 basic factors – linguistic & analytical/spatial

Psychology 3450W: Experimental Psychology

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