Sub lesson - Spearman's correlation coefficient

Question 1

Types of correlation:

Answer 1

• Positive (this is when both variables increase or decrease together)
• Negative (This is when one variable increases as the other decreases)
• Non-existent (This is when there is no clear relationship, indicated by a correlation coefficient close to 0.

Question 2

Results of correlation coefficient of 1:

Answer 2

indicates a perfect, positive linear correlation, where all points lie on a straight line.

Question 3

Process for calculating Spearman’s rank correlation:

Answer 3

1. Convert the raw data values of each variable into ranks from the smallest value to the largest value.
2. If two values are the same for one variable, give them an average rank
3. Determine the differences in ranks (d) for each pair of values.
4. Square these rank differences (d2).
5. Sum up all the squared rank differences
6. Calculate Spearman’s rho (p).
7. Compare p to a critical value at 5% significance level to determine significance of correlation.

Question 4

p

Answer 4

Spearman’s rank correlation coefficient

Question 5

sum of the squared differences of the ranks

Answer 5

E thing d2

Question 6

n

Answer 6

number of pairs of data

Question 7

Results:

Answer 7

• A p value near +1 indicates a strong positive correlation
• A p value near -1 indicates a strong positive correlation
• A p value around 0 implies that there is no correlation.