Psych220 Quiz2
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passer2e_lectureslides_ch05.pptxResearch Methods Second Edition
CHAPTER 5
Michael W. Passer
RESEARCH METHODS | CONCEPTS AND CONNECTIONS Michael W. Passer | Second Edition
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CORRELATION AND CORRELATIONAL RESEARCH
CHAPTER 5
RESEARCH METHODS | CONCEPTS AND CONNECTIONS Michael W. Passer | Second Edition
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Correlation: Basic Concepts (part 1)
CORRELATIONAL RESEARCH
Basic concepts
A correlation is a statistical association between two variables. Variable score are associated in nonrandom fashion.
A correlation exists between two variables (X and Y) when the scores or values of X are associated with the scores or values of Y in a nonrandom fashion.
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Key Distinctions Between Experiments and Correlational Research
Experiments: Steps
Manipulate independent variable, X.
Measure dependent variable, Y.
Statistically analyze whether different conditions of X produced differences in Y.
Attempt to eliminate confounding variables by controlling experimental environment.
Correlation Research: Steps
Measure variable X.
Measure variable Y.
Statistically analyze whether there is an association between X and Y.
Attempt to reduce influence of confounding variables through statistical control and special research designs.
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Correlation: Basic Concepts (part 2)
CORRELATIONAL RESEARCH
Basic concepts
In correlational research, variables are measured not manipulated.
Possible sources of association in correlational research.
X and Y are characteristics of the same people.
X and Y are characteristics of different, but related, sets of people.
X is a personal characteristic and Y is an environmental characteristic.
Can you provide an example for each source?
A correlation exists between two variables (X and Y) when the scores or values of X are associated with the scores or values of Y in a nonrandom fashion.
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Correlation: Basic Concepts (part 3)
POSITIVE AND NEGATIVE CORRELATION
Positive correlation means that higher scores or levels of one variable tend to be associated with higher scores or levels of another variable.
Negative correlation means that higher scores or levels of one variable tend to be associated with lower scores or levels of another variable.
Positive correlation
As X increases, Y also tends to increase; as X decreases, Y also tends to decrease.
Negative correlation
Scores on X and Y tend to move in opposite directions: As X increases, Y tends to decrease; as X decreases, Y tends to increase.
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Correlation: Basic Concepts (part 4)
UNDERSTANDING POSITIVE AND NEGATIVE CORRELATION
This table presents a set of hypothetical data for 10 participants. Perceived crime-risk scores can range from a probability of zero to 100% in increments of 10 percentage points. Trust scores can range from 5 to 25, with higher scores indicating greater trust.
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Correlation: Basic Concepts (part 5)
MEASURING AND GRAPHING CORRELATIONS
Pearson’s r
Measures direction and strength of the linear relation between two variables measured on an interval or ratio scale
Has correlation strength reflected by absolute value of the correlation
Ranges from values of +1.00 to −1.00
r2 (coefficient of determination)
Represents proportion of variance in Y accountable for by variance of X
Informs the extent to which differences among the X statistically account for differences among the Y scores (based on linear relation between two variables)
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Correlation: Basic Concepts (part 6)
MEASURING AND GRAPHING CORRELATIONS
Spearman’s rho (Spearman rank-order correlation coefficient)
Measures the relation between two quantitative variables when one or both variables measured on an ordinal scale
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Correlation: Basic Concepts (part 7)
MEASURING AND GRAPHING CORRELATIONS
Positive or negative?
Coding of measurement scales affects whether the statistical analysis yields a plus or minus sign for that coefficient.
Researcher conceptualization of a variable affects whether a correlation emerges as positive or negative.
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Correlation: Basic Concepts (part 8)
MEASURING AND GRAPHING CORRELATIONS
A scatter plot (scattergram) is a graph in which data points portray the intersection of X and Y values.
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Correlation: Basic Concepts (part 9)
THREE SCATTER PLOTS
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Correlation: Basic Concepts (part 10)
INTERPRETING THE STRENGTH OF A CORRELATION
Guidelines for absolute values of Pearson’s r (Cohen, 1988)
Small association: .10 to .29
Medium association: .30 to .49
Large association: .50 to 1.00
No universally agreed-upon standard for these terms
Subjective criteria for judging strength varies by different areas in psychology
No universally agreed-upon standard for these terms
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Correlation: Basic Concepts (part 11)
DIFFERENCES IN THE STRENGTH OF CORRELATIONS
Figure 5.4 Differences in the strength of correlations. In each of these four diagrams, the entire circle represents the total variance in Y (i.e., perceived crime risk). The part of the entire circle shaded in pink represents the proportion of variance in Y that is accounted for by the variance in X (weekly hours of TV watched).
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Correlation: Basic Concepts (part 12)
Key criteria used in drawing causal inference
Covariation of X and Y
Temporal order
Absence of plausible alternative explanations
Can you apply these criteria to Gerbner and Gross correlational research?
“Watching TV influences perceived crime risk.”
Covariation of X and Y. As X changes, Y changes.
Temporal order. Changes in X occur before changes in Y.
Absence of plausible alternative explanations. Other than the changes in X, there are no changes in other factors that might reasonably have produced the changes in Y.
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Correlation Does Not Establish Causation (part 1)
The bidirectionality problem (also two-way causality problem)
Ambiguity about whether X has caused Y or Y has caused X; also possible that each variable influences the other
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Correlation Does Not Establish Causation (part 2)
The third-variable problem
Third variable, Z, may be the true cause of why X and Y appear to be related.
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Another Third-Variable Example
For some correlations, bidirectionality can be ruled out.
The third-variable problem must still be considered.
See Table 5.2 for additional information for identifying potential third variables.
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Correlation Does Not Establish Causation (part 3)
CAN WE GAIN A CLEARER CAUSAL PICTURE?
Statistical approaches
Measuring potential variables during data collection and statistically adjusting for these in data analysis
Partial correlation
Path analysis
Structural equation modeling
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Measuring and Statistically Adjusting
Percentage of light- versus heavy-TV viewers who greatly overestimated the risk of being a crime victim.
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Correlation Does Not Establish Causation (part 4)
CAN WE GAIN A CLEARER CAUSAL PICTURE?
Research design approaches
Longitudinal designs
Prospective design
(Adapted with permission from “Religious Participation, Interleukin-6, and Mortality in Older Adults,” by S. K. Lutgendorf, D. Russell, P. Ullrich, T. B. Harris, and R. Wallace, 2004, Health Psychology, 23[5], p. 465.)
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Correlation Does Not Establish Causation (part 5)
Research design approaches
Longitudinal designs
Cross-lagged panel studies
(a) Correlations between violent TV preference and aggression in a sample of 211 boys. The correlations between aggression in Grade 3 and violent TV preference, measured in Grade 13, and between violent TV preference in Grade 3 and aggression in Grade 13, are called cross-lagged correlations. (b) Two causal hypotheses. Focusing only on this portion of the cross-lagged panel design highlights the potential third-variable problem. Children’s aggression, as measured in Grade 3, would be the third variable. The pattern of findings from the complete cross-lagged panel design indicates, however, that violent TV preference in Grade 3 remains correlated with aggression in Grade 13, even after statistically controlling for the possible influence of this third variable. (Adapted with permission from APA from “Does Television Violence Cause Aggression?” by L. D. Eron, L. R. Huesmann, M. M. Lefkowitz, and L. O. Walder, 1972, American Psychologist, 27, pp. 253–263 [Figure 1, p. 257].)
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Correlation Does Not Establish Causation (part 6)
NOW CAN WE DRAW CLEAR CAUSAL CONCLUSIONS?
It is always possible that researchers have overlooked other plausible third variables.
Thus, correlational studies do not provide as clear a test of causal relations as experiments do.
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Correlation Does Not Establish Causation (part 7)
High-quality reporting is not always present or evident in the news media.
What consequences might this have for you?
Your family? Your university?
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Correlation and Prediction (part 1)
USING ONE PREDICTOR
Regression analysis (simple linear regression)
Explores the quantitative, linear relation between two variables and is often used to predict the scores of one variable based on the score of another variable
Criterion variable
Predictor variable
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Using One Predictor
(a) A scatter plot of SAT scores and first-year college GPA for a hypothetical sample of 50 students. (b) A scatter plot with a regression line added. The SAT–GPA correlation is .45.
Scatter plots, with and without a regression line.
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Correlation and Prediction (part 2)
USING TWO OR MORE PREDICTORS
Multiple regression
Explores the linear relations between one variable and a set of two or more variables
To be retained in the final regression, each new predictor must enhance the ability to estimate Y beyond what can be achieved by the other predictor variables already in the equation.
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Benefits of Correlational Research
Correlational research provides many benefits.
Prediction in daily life
Test validation
Venturing where experiments cannot tread
Hypothesis and model testing
Convergence with experiments
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Special Issues: Nonlinear Relations
Curvilinear relation between employee job satisfaction and the proportion of co-ethnic coworkers.
Curvilinear relation between age and overall negative affect.
When variables have a nonlinear relation, Pearson’s r will underestimate or fail to detect variable relations.
Figure 5.13 Curvilinear relation between employee job satisfaction and the proportion of co-ethnic coworkers. Each data point represents the average job satisfaction rating of participants who reported having a particular proportion of co-ethnic coworkers. (Information from Enchautegui-de-Jesús et al., 2006.)
Figure 5.12 Curvilinear relation between age and overall negative affect. Higher values on the y-axis indicate greater overall negative emotion. Each data point represents the average negative emotion score at a particular age. (Adapted with permission from APA from “Aging and Negative Affect: The Rise and Fall and Rise of Anxiety and Depression Symptoms,” by B. A. Teachman, 2006, Psychology and Aging, 21, pp. 201–207 [Figure 1].)
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Special Issues: Range Restriction
Range restriction occurs when the range of scores obtained for a variable has been artificially limited in some way.
Range restriction can lead to erroneous conclusions about the strength, direction, and linear versus nonlinear nature of the relation between two variables.
Figure 5.14 Range restriction and correlation, based on hypothetical data from 40 job applicants. In this example, range restriction substantially reduces a correlation’s strength.
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Special Issues: Associations Involving Qualitative Variables
The concept of linear relations does not apply for associations involving qualitative variables.
The absence of ordinal, interval, or ratio scaling makes it impossible to say such variables are positively or negatively correlated.
Figure 5.15 College majors in relation to ethnicity and gender. Each horizontal bar shows the percentage of students from a particular ethnic/gender group majoring in various fields. (Adapted with permission from American Psychological Science from “Questioning a White Male Advantage in STEM Examining Disparities in College Major by Gender and Race/Ethnicity,” by C. Riegle-Crumb and B. King, 2010, Educational Researcher, 39, pp. 656–664 [Figure 1].)
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