Lecture 2

Question 1

What is the Pearson Correlation r?

Answer 1

Pearson’s correlation coefficient r is a standardized index of the linear relationship between 2 continuous (or dichotomous*) variables

• In case of 2 dichotomous variabels (= nominal variables with only 2 categories) r algebraic equal to Φ

Question 2

Assumptions of Pearson correlation r

Answer 2

Scores of the X and Y variables:
1. are quantitative (or both dichotomous)
2. are linearly related
3. have a bivariate normal distribution
4. do not have extreme outliers
5. Homoscedasticity: Y-scores have the variance across levels of X (and vice versa)

Question 3

Influence of outliers

Question 4

Distributional assumptions

Question 5

Homoscedasticity/heteroscedasticity

Question 6

Computation of Pearson’s r

Question 7

Strength of Pearon’s r is related to patterns of the data

Answer 7

It is helpful to divide a X,Y scatterplot in 4 quadrants
We can divide the data points in:
◦ Concordant data points:data points that lie above the mean of both X and Y or
below the mean of both X and Y
◦ Discordant data points: data points that lie below the mean of X and above the
mean of Y, or above the mean of X and below the mean of Y

Question 8

‘The cross’

Question 9

Factors that can influence Pearson’s r

Answer 9

1. Data patterns in X,Y plot (see above)
2. Biased sample selection
   - Restricted Range
   - Selection of Extreme Groups
3. Correlations of samples with combined groups
4. Extent to which r is controlled by other variables (more on this later at regression)
5. Bivariate outliers
6. Different shapes of distribution of X and Y
7. Curvilinear or nonlinear relationships
8. Transformation of data (e.g. log)
9. Attenuation as a result of unreliability of measurement*; unreliable measurements weaken the correlation between such measurements
10. Artificial part-whole correlations
11. Aggregated data

Question 10

Pearson’s rxy and causal conclusions

Answer 10

Large r can have many causes
We can only conclude that‘X is the cause of Y’if we can eliminate all these alternative explanations; non-experimental design does not fully allow this
Therefore, a larger correlation between X and Y does not provide sufficient
proof of a causal relationship!

Question 11

Some reasons for a large Pearson r xy

Answer 11

1. X causes Y
2. Y causes X
3. X causes Z, and Z causes Y; variable Z mediates effect of X on Y
4. X is related to another variable Z, and Z causes Y
5. X and Y measure the same construct
6. X and Y are both influenced by Z
7. Chance (sampling error)