9.1.11 - inferential statistics

Question 1

how do you calculate correlation coefficient using Spearman’s rank?

Answer 1

1. rank the data (separate rank or data in each variable) - lowest gets a rank of 1 and so on
2. find the difference (D) between the ranks for the corresponding data for each variable
3. square D to get D^2
4. add up all the D^2s to get 𝚺d^2
5. find n (total number of pairs of data)
6. substitute the values into the equation to find R (remember to include +/- in final answer)

Question 2

when ranking data, what do you do if you have tied scores?

Answer 2

use up the same number of ranks as there are tied scores, but give all the tied scores the same rank which is the number in the middle of the ranks being used up

Question 3

what is significance?

Answer 3

the pattern in a set of data is significant if we don’t think it was caused by chance

Question 4

what do you use for a directional hypothesis?

Answer 4

a one-tailed test

Question 5

what do you use for a non-directional hypothesis?

Answer 5

a two-tailed test

Question 6

how do you carry out a significance test for Spearman’s rank?

Answer 6

1. find the right table of statistical significance
2. find the critical value based on what value n is, whether you are doing a one or two-tailed test, and the one for a probability of 0.05
3. see whether your correlation coefficient (calculated value) is higher or lower than the critical value

Question 7

how do you interpret the result of a significance test?

Answer 7

if the calculated value is equal to or exceeds the critical value, there is a less than 0.05 chance that the result was caused by chance (unlikely), so the result is significant and you reject the null hypothesis
if the calculated value is less than the critical value, there is a greater than 0.05 chance that the result was caused by chance (likely), so the result isn’t significant and you accept the null hypothesis

Question 8

what are key rules to remember when checking the significance of a Spearman’s correlation?

Answer 8

1. if the result is significant at p<0.05, check at p<0.025, and if it is significant there, check at p<0.01
2. always assume you are carrying out a two-tailed test, then check to see whether there is evidence for a one-tailed test

Question 9

what is the written structure to follow when reporting significance for Spearman’s rank?

Answer 9

The calculated value of Spearman’s R was . The critical value (n=, _ tailed, p<_) is _. Since the calculated value was less/greater than the critical value, the null hypothesis was accepted/rejected. The correlation between _ and _ is/isn’t significant.