Correlation Coefficient

Question 1

What is correlation coefficient used to test?

Answer 1

used to test the strength of the relationship (correlation) between two variables.

Question 2

What is correlation coefficient simply?

Answer 2

as you change one variable, does it affect the other variable and is that significant?

Question 3

What is the equation for correlation coefficient?

Answer 3

Rs = 1 - 6(Σ d^2) / n(n^2-1)

Question 4

What is “Rs”?

Answer 4

correlation coefficient

Question 5

What is “Σ”?

Answer 5

sum of

Question 6

What is “n”?

Answer 6

number of pairs

Question 7

What is “d”?

Answer 7

difference between each pair of ranks

Question 8

1) What do you do first?

Answer 8

You have to rank the data from group 1 ( so from the highest to lowest (40 - 1, 35 - 2)

You then rank the data from group 2 (rank the highest value 1, and lowest value 9 → 20.2 = 1)

Question 9

What do you do if when you are ranking the data you have two of the same numbers?

Answer 9

If you have two of the same numbers e.g. 19.6, they are going to be equally ranked. E.g. 19.6 will be 3 and 4, so you add 3 + 4 and divide it by 2. So, 19.6 will both be 3.5.

Question 10

2) What do you calculate?

Answer 10

the difference between each pair of ranks

You subtract rank of group 1 from rank of group 2 (e.g. 9 - 3.5, 8 - 1, etc)

Question 11

3) What do you square?

Answer 11

you then square the answers from the d row (e.g. 5.5 x 5.5 = 30.25)

Question 12

4) What do you need to add up?

Answer 12

you then need to add up all of the numbers in the d^2 row (e.g. 30.25 + 49.00, etc.) to two decimal places.

Question 13

5) What do you multiply?

Answer 13

you then multiply the answer from adding up all of the d^2 values by 6 (e.g. 6 x 213.50 = 1281.0)

Question 14

6) What do you calculate?

Answer 14

n^2 - 1 (e.g. 9^2 - 1 = 80)

Question 15

7) What do you then do next?

Answer 15

n(n^2-1) (e.g. 9 x 80 = 720

Question 16

8) What do you calculate next?

Answer 16

(sum of d^2) / n(n^2 - 1) (e.g. 1281.0 / 720 = 1.779)

Question 17

9) What do you calculate lastly?

Answer 17

1 - your answer previous answer (e.g. 1 - 1.779 = - 0.78 (2.d.p) → correlation coefficient value

Question 18

After calculating your correlation coefficient, what do you have to consider?

Answer 18

is our correlation coefficient value greater than our critical value? If it is greater, we can say that there is a significant negative correlation.

Question 19

What do you say if the correlation coefficient is greater than the critical value?

Answer 19

“The correlation coefficient statistic is greater than the critical value so there is a significant negative correlation between…. (the two variables) at the P=0.05 confidence level”.