Correlation Coefficient Flashcards
What is correlation coefficient used to test?
used to test the strength of the relationship (correlation) between two variables.
What is correlation coefficient simply?
as you change one variable, does it affect the other variable and is that significant?
What is the equation for correlation coefficient?
Rs = 1 - 6(Σ d^2) / n(n^2-1)
What is “Rs”?
correlation coefficient
What is “Σ”?
sum of
What is “n”?
number of pairs
What is “d”?
difference between each pair of ranks
1) What do you do first?
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)
What do you do if when you are ranking the data you have two of the same numbers?
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.
2) What do you calculate?
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)
3) What do you square?
you then square the answers from the d row (e.g. 5.5 x 5.5 = 30.25)
4) What do you need to add up?
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.
5) What do you multiply?
you then multiply the answer from adding up all of the d^2 values by 6 (e.g. 6 x 213.50 = 1281.0)
6) What do you calculate?
n^2 - 1 (e.g. 9^2 - 1 = 80)
7) What do you then do next?
n(n^2-1) (e.g. 9 x 80 = 720
8) What do you calculate next?
(sum of d^2) / n(n^2 - 1) (e.g. 1281.0 / 720 = 1.779)
9) What do you calculate lastly?
1 - your answer previous answer (e.g. 1 - 1.779 = - 0.78 (2.d.p) → correlation coefficient value
After calculating your correlation coefficient, what do you have to consider?
is our correlation coefficient value greater than our critical value? If it is greater, we can say that there is a significant negative correlation.
What do you say if the correlation coefficient is greater than the critical value?
“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”.
