Pearson's r

Question 1

What is the formula for Pearson’s r?

Answer 1

r = sample covariance / SRT sample variance (x) x SQRT sample variance (y)

Simply = r = shared variance / total variance

Question 2

What does Pearson’s r tell us?

Answer 2

What proportion of the total variance is shared variance

Question 3

What does Pearson’s r statistic vary between?

Answer 3

-1 and 1

Question 4

If data is distributed evenly amongst all 4 quadrants, this is called…?

Answer 4

Low correlation

Question 5

What is low correlation?

Answer 5

If data is distributed evenly amongst all 4 quadrants

No apparent relationship

Question 6

What value of Pearson’s r is considered a perfect (negative or positive) correlation?

Answer 6

+1 or -1

Question 7

What value of Pearson’s r is considered a strong (negative or positive) correlation?

Answer 7

+0.9, +0.8, +0.7 or -0.9, -0.8, -0.7

Question 8

What value of Pearson’s r is considered a moderate (negative or positive) correlation?

Answer 8

+0.6, +0.5, +0.4 or -0.6, -0.5, -0.4

Question 9

What value of Pearson’s r is considered a weak (negative or positive) correlation?

Answer 9

+0.3, +0.2, +0.1 or -0.3, -0.2, -0.1

Question 10

What value of Pearson’s r is considered zero correlation?

Answer 10

0

Question 11

Data are collected for three participants on two variables (X, Y). The data are described below:

P1: (1, -0.5)

P2: (2, -1.0)

P3: (3, -1.5)

a) The mean for variable X is:

b) The mean for variable Y is:

c) The sample covariance of the X and Y data is:

d) Pearson’s r for this data is (note the s.d. for variable X is 1.0 and that for variable Y is 0.5):

Answer 11

a) 2
b) -1
c) -0.5
d) -1

Question 12

Alien visitors from planet Ziltoidia 10 believe that their athletic ability depends upon the size of the bald patch in their favoured ‘skullet’ hairstyle (i.e. the area of central hair loss). The annual Ziltoidian games involves 20 competitors who take part in a series of 10 athletic trials. You measure the overall score in the games and skullet area (in cm^2) for each competitor. Given that:

1) The variance of skullet area scores is 14.5

2) The variance for scores in the games is 99.98

3) The covariance between skullet area and score in the games is 21.15

Pearson’s r measure of the correlation between skullet area and games score is …

Answer 12

0.56

Pearson’s r = shared variance / total variance

r = 21.15 / (SQRT (14.5) x SQRT (99.98))