Correlation Flashcards
(43 cards)
How can we assess the relationship/correlation between two variables?
Pictorially - Scatterplot. Useful when have wide range of scores or large sample size. Allows to see levels of association between variables
Numerically - Correlation coefficient
What happens when there is a negative association between two variables
Higher values on variable A corresponding to lower levels on variable B
As one variable deviates from the mean, the other deviates from the mean in the opposite direction.
What happens when there is a perfect positive association between two variables?
Higher values on variable A perfectly corresponding to higher values on variable B.
As one variable deviates from the mean, the other variable deviates in the same direction.
What happens when there is a perfect negative association between two variables?
Higher values on variable A perfectly correspond to lower values on variable B
What happens when there is no association between two variables?
Higher values on variable A corresponding to either high or low values on variable B
What happens when there is a non-linear association between two-variables?
- There is an association, but it is not linear
- E.g. if practice too much then performance decreases
What does the strength of a relationship refer to?
How closely bunched around the imaginary line the dots are in the scattergraph
What are the two axes on a scattergram called?
- Ordinate and abscissa
- Vertical and horizontal axis
- Y-axis and x-axis
What does the direction of a relationship refer to?
- If points upward from bottom left to right = positive relationship
- If points down from top left to bottom right = negative relationship
What does the form of a relationship refer to?
- Linear = Straight line cutting across dots fits data nicely
- Non-linear = If a curve fits better
Correlation coefficient
Numerical way of expressing a linear relationship
Tells you how strong the relationship is between variables
What are the steps for calculating Pearson’s r?
- Transform raw scores into z-scores
- Multiply the two z-scores for each participant
- Sum all of the products of the paired z-scores then divided the result by the number of cases - 1
Provide an example of a negative relationship from Pearson’s r
-0.61
Provide an example of no relationship from Pearson’s r
0.00
Provide an example of a small positive relationship from Pearson’s r
0.06
Pearson’s r forumla
The mean of the products of paired z-scores
Numerator = Sum of all the products of the paired z-scores Denominator = Number of cases - 1
Values range from -1 (perfect negative correlation) to +1 (perfect positive correlation). Value of 0 implies no linear correlation. The stronger from 0, the stronger the relationship.
Which values can the Pearson’s r take?
From -1 to 1
Undefined Correlation
- When you assess the correlation between two variables and one of them is constant.
- Scatterplot will be perfectly horizontal
One-tailed
Hypotheses specify direction
Two-tailed
Hypotheses don’t specify direction
How do you report the results of correlation?
- Describe magnitude of relationship, direction, whether statistically significant
- E.g. “There was a strong, positive, statistically significant relationship between class test scores and number of revision scores; r(10) = 0.82, p = 0.001.
What happens when the relationship between two variables departs from linearity?
When it is u-shaped - Pearson’s r will underestimate the correlation between X and Y
When serious departure - Pearson’s r is not appropriate
What happens when you calculate the correlation for two variables using a restricted range of scores?
Correlation is…
- Reduced
- Inflated
What happens to the value of Pearson’s r when there are outliers?
Value of r will be inflated or reduced
