11. Analysis of associations I: Correlation versus causation

Question 1

When there is a linear correlation how do we work out variance?

Answer 1

Sums of squares (like anova)

Question 2

What is covariance?

Answer 2

measure of joint variability

Question 3

How do we work out the covariance if there is a linear corrilation?

Answer 3

sums of product

Question 4

What is the standard error of a linear correlation coefficient?

Answer 4

the difference bertween

sample of two variables and its correlation

the populations correlation (phi)

Question 5

What is the standard error of a linear correlation coefficient?

Answer 5

the difference between

sample of two variables and its correlation

the populations correlation (phi)

Question 6

Why is the standard error of linear correlation coefficient useful?

Answer 6

as we cant assume data is normally distributed.

in addition correlation coeffects are bounded between +/- 1 but normal distributions are not.
- so we must transform our data using the Fisher’s-Z transformation

Question 7

how do we hypothesis test with correlations

Answer 7

we assume normality and that coefficients are bivariate normal

H0: phi =0
H1: phi <>0

we use a one sampled t-test

Question 8

what test do we use if there is non-linear correlation?

Answer 8

spearman’s rank correlation
(non-parametric)