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Correlation
Nonexperimental method that describes a relationship between two variables.
Allow us to make predictions If smoking is correlated with lung cancer, then we can predict,
with some accuracy, that a person who smokes can develop lung cancer.
Used when: Unethical to conduct experimental study (i.e., smoking
condition) Researchers want to assess the relationship among many
variables at once. Ex: variables that correlate with personality traits
Characteristics of Correlations
Magnitude strength of the relationship measured by a correlation coefficient
- 1 -.7 -.3 0 .3 .7 +1
weak weakmoderate moderate
strongstrong
no relationship
Scatterplots
Graphical representation of the relationship between 2 variables.
8.007.006.005.004.003.00
Hours of Sleep per Day
8.00
7.00
6.00
5.00
4.00
3.00
2.00
Du
rati
on
of
Co
ld (
in d
ay
s)
Hours of Sleep and Duration of Cold Symptomsr = -.60
Interpretation Difficulties
Only experiments allow us to infer causality and directionality factor A caused factor B to change.
Correlational studies no inferences of causality or directionality “Correlation does not imply causation” be a critical consumer of information
Third- Variable Problem
Despite strong correlation, the results could be due to something else… Third-variable problem: the correlation between 2
variables is dependent on another variable. Ex: teenage delinquency increases with sales of ice-
cream
Restrictive Range
Occurs when a variable has limited variability due to restrictions in range.
0 6 12exposure to noise (months)
1 5 10exposure to noise (years)
Heari
ng
ab
ility
Heari
ng a
bili
ty
Pearson’s r
Duration of Cold symptoms
Hours of sleep zCold zHours
zCold*zHours
8.00 3.00 1.83 -1.73 -3.17
7.00 4.00 1.27 -1.05 -1.33
6.00 5.00 0.71 -0.36 -0.26
5.00 5.00 0.15 -0.36 -0.05
6.00 5.00 0.71 -0.36 -0.26
4.00 6.00 -0.41 0.32 -0.13
3.00 7.00 -0.97 1.01 -0.97
2.00 8.00 -1.53 1.69 -2.58
5.00 4.00 0.15 -1.05 -0.16
6.00 5.00 0.71 -0.36 -0.26
4.00 5.00 -0.41 -0.36 0.15
3.00 5.00 -0.97 -0.36 0.35
2.00 6.00 -1.53 0.32 -0.49
4.00 7.00 -0.41 1.01 -0.41
6.00 8.00 0.71 1.69 1.20
Mean = 4.73 Mean = 5.53 N = 15 SUM = - 8.37SD = 1.79 SD = 1.46 r = - 0.60
Population
r = ∑ (zA)(zB) __________ N
Sample
r = ∑ (zA)(zB) __________ N - 1