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Psychology
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PSYC 2001
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Guy Lacroix
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Psychology

PSYC 2001

Guy Lacroix

Fall

Description

Correlational research
Correlational research
- What are correlations?
• Scatterplots
• Correlations and causality
- What are regressions?
• y = mx + b
• Multiple regressions
- Examples
• Siddiqui, West, and Stanovich (1998)
Correlational research
- The purpose of correlational research is to establish that a relation exists between
variables and to describe the nature of this relationship.
• Rubin’s (1970) love scale and “being in love”
• Reliability coefficient is .87 to 1.0 (Bowker et al., 2009)
Pearson correlation coefficient
- The Pearson correlation (r) coefficient is the statistic that indicates the degree to which
two variables are related to one another in a linear fashion.
- Range r is between – 1.00 and + 1.00
- Positive correlation (r > .00). Positive, direct relationship between two variables
- Negative correlation (r < .00). Negative, inverse relationship between two variables
No relation between the variables Perfect relation between the variables
Strong relation between the variables Weak relation between the variables
How can we tell that a correlation is significant?
- What is the probability that a “lucky result” was obtained?
- The probability is calculated using the Student’s t statistic.
Critical values of r
Number of participants Minimum r that is significant (for a p
value of .05)
10 .52
20 .37
30 .30
40 .26
50 .23
60 .21
80 .18
100 .16 1000 .05
Correlation matrix
- When multiple correlations are used, the results are typically shown in a correlation
matrix.
Index 1 2 3
1. Grades 1.0 - -
2. Performance IQ .65 1.0 -
3. Hours of study .34 .01 1.0
Correlations and causality
- ACorrelation does not imply causality!
- Three criteria must be satisfied to conclude that one variable causes another:
• Covariation. There is a correlation between variables X and Y.
• Directionality. Variable X (the cause) precedes Variable Y (the effect).
• Elimination of extraneous variables. No other variable may be responsible for the
relationship between X and Y.
Directionality problem
- Correlational studies do not allow us to determine which variable is the cause and which
variable is the effect.
- Self-esteem school achievement (Stanovich example 2007)
Third-variable problem
- Although a correlational study may establish that two variables are related, it does not
necessarily mean that there is a direct relationship between them. Linear regressions
- Another way of looking at the relation between two variables.
- The best fitting linear function is estimated and then used to “explain” the changes in one
variable using a second variable.
- Criterion. The variable to be explained.
- Predictor. The variable used to predict, to “explain”.
- Correlation between women owning a toasting and being on contraceptives; not causal
y = mx + b
Effect size for regressions
- Using the regression equation, we know that the predictor (x) explains a 31% change in
the criterion (y).
2
- r . The measure of effect size for regressions. Multiple regression
- Regressions allow for multiple predictors.
- Example. Suppose you want to explain grades using both IQ and number of hours of
study.
Index 1 2 3
1. Grades 1.0 - -
2. Performance IQ .65 1.0 -
3. Hours of study .34 .01 1.0
Multiple regression
- R. Measure of relation for multiple variable.
- R . The measure of effect size for multiple regressions Hierarchical multiple regressions
- What if I want to see the relation between study time and grades independently of IQ?
- Mathematically, the variance explained by IQ is removed after step 1. Hence, the
variance explained by study time is “unique”.
- Final F= probability that the result is due by chance
• Percentage that results could be lucky; is it significant or not. 0.12 explains 12% of
the leftover variable that has not be explained by IQ
Criterion = Grades
Variable R R 2 Final F
Step 1
1. IQ .65 .42*** 26.82***
Step 2
2. Study time .73 .12** 20.82***
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