Correlational Methods and Statistics

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

How strong is an association?

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

Curvilinear relationship No Correlation

Negative Correlation Positive Correlation

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