What are three characteristics of relationships?
- Direction (positive vs. negative)
- Strength of association (strong vs. weak; perfect vs. imperfect)
- Form (linear vs. non-linear)
How can relationship direction and strength of association vary?
positive vs. negative
strong vs. weak; perfect vs. imperfect
How can relationship form vary?
linear: positive or negative
vs.
non-linear: independent or curvilinear
Correlation coefficient
expresses the strength and direction of a relationship
- perfect negative relationship: -1
- perfect positive relationship: 1
- no relationship (variables are independent): 0
Pearson r
a type of correlationship coefficient used to describe LINEAR relationships; a measure of the extent to which paired scores occupy the same or opposite positions within their own distributions
- leading zeros (before the decimal point) are not used when reporting
- a non-linear relationship may have a Pearson r value of 0, but this doesn’t mean there is no relationship (just no linear relationship)
Line of best fit
straight line in a scatterplot drawn so that number of points above and below the line is about equal
- outliers can have a large effect
What should you do before calculating correlation coefficients?
- create a scatterplot
- look for outliers
- check for linearity
- consider whether the ranges of the two variables are sufficient to show their true relationship
Range restriction
the limitation of the full range of the total possible scores to only a narrow portion of that total
via:
- sampling
- measurement procedures
- other aspects of experimental design
How do you calculate Pearson r?
- convert to z-scores to put variables on the same scale
- calculate X2, Y2, and XY for all raw values
- calculate the sum for all columns
(Subject X Y X2 Y2 XY)
How do you interpret Pearson r?
