Spearman's rho

Question 1

What is Spearman’s rho?

Answer 1

Alternative to Pearson’s r

Question 2

What is Spearman’s rho used for?

Answer 2

Used when the assumptions required for Pearson’s r have not been met

e.g. Hypothesis: IQ (X) is correlated with the number of hours spent gaming per month (Y)

Question 3

If we have a relatively small sample size, do we use Pearson’s r or Spearman’s rho? Why?

Answer 3

Spearman’s rho

Because we’re not sure about the normality of data

Question 4

What is the formula for Spearman’s rho?

Answer 4

p = 1 - ((6 x difference^2) / n(n^2-1))

Question 5

How do you calculate Spearman’s rho step by step?

Answer 5

1) Convert scores A and B into ranks
2) Calculate the difference in ranks for A and B
3) Square the difference
4) Multiply the squared difference by 6 and divide by n(n^2-1)
5) Subtract 1 from the results achieved in (4)

Question 6

You are running the experiment described in the previous video to examine a potential relationship between IQ and hours spent gaming per month. The data for N = 10 participants (ordered by the participant) are summarised below. Note that in these data ranks are perfectly positively correlated:

IQ: {86, 97, 99, 100, 101, 103, 106, 110, 112, 113}

Hours: {0, 6, 7, 12, 17, 20, 27, 28, 29, 50}

a) The sum of the squared differences in ranks for the IQ and Hours data is:

b) The quantity N x (N^2-1), which is useful for our calculation of Spearmans rho below is:

To work out spearman’s rho:

i) calculate 6 times the quantity you worked out in a)

ii) divide this by the quantity you worked out in b)

iii) subtract this from 1

c) Spearman’s rho is:

Answer 6

a) 0
b) 990
c) 1.00

Question 7

You are running the experiment described in the previous video to examine a potential relationship between IQ and hours spent gaming per month. The data for N = 10 participants (ordered by participant) are summarised below. Note that in these data ranks are perfectly negatively correlated:

IQ: {86, 97, 99, 100, 101, 103, 106, 110, 112, 113}

Hours: {50, 29, 28, 27, 20, 17, 12, 7, 6, 0}

a) The sum of the squared differences in ranks for the IQ and Hours data is:

b) The quantity N x (N^2-1), which is useful for our calculation of Spearman’s rho below is:

To work out spearman’s rho:

i) calculate 6 times the quantity you worked out in a)

ii) divide this by the quantity you worked out in b)

iii) subtract this from 1

c) Spearman’s rho is:

Answer 7

a) 330
b) 990
c) -1.00

Question 8

You are running the experiment described in the previous video to examine a potential relationship between IQ and hours spent gaming per month. The data for N = 10 participants (ordered by participant) are summarised below. Note that these are the data presented in the video:

IQ: {86, 97, 99, 100, 101, 103, 106, 110, 112, 113}

Hours: {0, 20, 28, 27, 50, 29, 7, 17, 6, 12}

a) The sum of the squared differences in ranks for the IQ and Hours data is:
(enter a whole number)

b) The quantity N x (N^2-1), which is useful for our calculation of Spearman’s rho below is:

To work out spearman’s rho:

i) calculate 6 times the quantity you worked out in a)

ii) divide this by the quantity you worked out in b)

iii) subtract this from 1

c) Spearman’s rho is:

Answer 8

a) 194
b) 990
c) -0.176