Deductive the third variable problem.
There could be a common factor/process feeding into the 2 observed variables.
Describe concordant pairs of variables.
As X increases, Y increases.
Describe discordant pairs of variables.
As X increases, Y decreases.
What fire Goodman-Krystal gamma actually measure?
The number of concordant and discordant pairs.
Why is it so key to check the scatter plot when analysing covariance?
Covariance only detects straights line relationships, so you must check if any alternative relationships may be there.
What are the problems with covariance being affected by scale?
Comparisons between studies are very hard and evaluation of significance is very hard.
The distribution of Pearson’s r is (normal/skewed).
The distribution of Fischer’s transform is (symmetric/asymmetric).
What is r^2?
The coefficient of determination.
What does r^2 convey?
The proportion of variance that one variable explains another.
How is Pearson’s r reported?
r(df) = x.xx, p = 0, r^2 = 0.xx
What is the main purpose of Fischer’s transformation?
To get meaningful confidence intervals.
In very brief terms, what is variance?
What is correlation most effective for?
Exploration and description.
What is regression most effective for?
Explanation and prediction.
What is the consequence of regression assuming iid distributions of depends variables?
Not all error deviations are the same, and they can form a pattern, so we must look at a plot of the residuals.
Give 2 situations when residuals show that regression is not appropriate?
When they do not lend themselves to a straight line of best fit and when Devil’s triangle occurs.
What is Devil’s triangle?
As X increases, the variability of Y increases.