Lecture 8 - Correlations Flashcards
Correlation is not…
Causality
When is correlation measured?
When it is not possible or ethical to manipulate the variable of interest (e.g. smoking)
Why are correlations useful?
- they highlight possibilities
- null effects may allow to discount theories
What are the four measures of association?
- covariance (parametric)
- Pearson’s Coefficient of Correlation (parametric)
- Spearman’s Coefficient of Rank Correlation (non-parametric)
- variance explained
What is covariance?
The mean of the product of the deviations from the mean divided by number of participants. The higher the number, the stronger the correlation - 0 indicates no correlation and - and + indicate direction
What are the pros and cons of covariance as a measure of association?
+ as a single number, it is very easy to interpret
- it is related to variance - when x and y vary a lot, the covariance is large.
How is Pearson’s (Product-Moment) Coefficient of Correlation (r) calculated?
Divide the covariance by the standard deviations of the variables, meaning it is independent of the overall variability.
Pearson’s r takes values between…
-1 and 1
Indicates the strength of the linear relationship.
In what situations can and cannot Pearson’s r be used?
Can’t be used for ordinal data, as there is no mean or standard deviation
It can, however, be used for experimental data as well as for correlations to determine linear relations
When is Spearman’s Rho (Spearman’s Coefficient of Ran Correlation) used?
For ordinal data, as it does not assume that data are evenly spaced or normally distributed
How does Spearman’s Rho work?
The data is first ranked, and then Pearson’s R is calculated on the ranks.
How do you carry out a correlation in SPSS?
- Plot data on a scatter plot (graphs|legacy dialogs|scatter/dot) and add a trend line (linear fit line)
- Compute the coefficients - analyse|correlation|bivariate - and select Pearson and/or Spearman
This can also be done with multiple pair-wise comparisons.
How do you report a correlation?
There was(n’t) a significant correlation, as demonstrated by a … test (r=…, n=…, p</>0.05) as shown in Figure 1.
How is variance accounted for expressed and calculated?
Expressed as a percentage or fraction, calculated by squaring Pearson’s r
If the correlation between variables A and B can be explained by variable C, a … can be used to measure the part of the correlation not caused by C.
Partial correlation
