Correlation

Question 1

Correlation

Answer 1

relation of two, typically continuous, variables

Question 2

Draw a positive, negative and no correlation on a scatter plot.

Answer 2

.

Question 3

calculating correlation coefficient

Answer 3

r= correlation in sample (pearsons r)
P= correlation in population

rXY = ΣZxZy/n

Question 4

Formula for r (z-score method)

Answer 4

rXY = Σ ZxZy / n

sum of the product of standardised scores, over population

Question 5

Note on r

Answer 5

r is sensitive only to linear relationships

• this is normally good enough to describe the data, though far from perfect

assumption being made when running analysis

• it is very rare to get a purely linear relationships between X and Y, but it is enough for our purposes to approximate it that way

Question 6

Sampling Distribution for r

Answer 6

when p=0, it can be shown that the ratio:

r / √(1-1)^2/(n-2)

is distributed as t with df= n-2

Question 7

Hypothesis Test for h0:p=0

Answer 7

Step 1: h0: p = 0 vs h1: p ≠ 0 (non-directional)

Step 2: choose a level; find tc with df = n-2 (convert r to t)

Step 3: calculate

t = r √n-2/1-r^2

Step 4: Apply decision rule, reject h0 if |t|> or = to tc

Step 5: Conclusion (with focus on directionality)

Question 8

Sampling Distribution of rXY

Answer 8

mean is Pxy

• SD is Or = 1-P^2xy / √n-1
• Or gets smaller as n gets larger
• Or gets smaller as P gets larger
• shape of sampling distribution is not normal

Question 9

Draw an example of what a correlation distribution appears like.

Answer 9

.

Question 10

Features of sampling distribution for correlations.

Answer 10

when p=0, sampling distribution is symmetrical and nearly normal

when p does not = 0, sampling distribution is skewed, and the degree of skew increases the closer P is to -+ 1

Question 11

Note on Correlation Analysis

Answer 11

when running correlation analysis you need. fairly large sample size, otherwise there is no statistically significant power to reject h0 when you generally should have

• do not do a correlation analysis on data thst does not have a linear relationship

Question 12

Power and Sample size for r

Answer 12

want to find 1-B, given y, n and a

• in this case r represents the size of effect, and so it would be equivalent to y

Step 1: obtain all relevant values
Step 2: find o~ = y = √n-1
Step 3: use table 3 to find 1-B, given y (r) and a

Question 13

Guide to Effect Sizes for Correlations (Cohen vs Everyone else)

Answer 13

small effect .1 vs .3

medium effect .3 vs .5

large effect .5 vs .7

Question 14

Calculating Sample Size

Answer 14

step 1: specify y, a and 1-B to solve for n
step 2: find o~ using table 4
step 3: calculate n = (o~/y)^2 +1