# Spearman’s Rho

## When is the Spearman’s Rho the correct test to use?

• if you are looking at a relationship between pairs of scores, i.e. you have a correlational design; how to spot if this is the case…
• there is NO independent variable, so there are no groups or conditions
• each participant has two scores
• they have given you a picture of a scattergram!
• the level of measurement of your data is at least ordinal

## How to do a Spearmans Rho:

1. First things first, you need to rank the scores in the first condition/column
• don’t get in a pickle with those tied ranks – take the median
• slow down and double check for mistakes, especially after a tied rank, make sure you pick up again on the correct rank
• check your ranking, for example, make sure that the last rank assigned is the number of Pps that you actually have, if it isn’t something has gone wrong!
• Easy huh?!
2. Now work out the ranks for the second set of scores/second column
3. Write the ranks alongside the scores
4. Now work out the difference between rank A and rank B for each Pp (A-B)
5. Now square the differences to  give you d squared
6. Now you are ready to use that formula! So add up the d squared column and multiply by 6.
7. Now the tricky bit 😉
8. How many Pps do you have? Got it? Now square that number and subtract 1, got it?
9. Now multiply by number of Pps; do you have answer?
10. Right, now take the the answer to 6 x sigma d squared and divide it by n multiplied by n squared minus one; fun times!
11. So you have all that….Last bit;… do 1 – that number!
12. And there you have it Spearman’s Rho! SO now you can compare your observed value (calculated value of Rho with the critical value.
13. So you need to check whether your hypothesis is directional (i.e. you said there is a positive correlation or indeed you said there is a negative correlation) or non-directional (i.e. you said there would be a correlation but did not state the direction), this will determine whether you are going to do a one or a two tailed test.
14. Now remind yourself you are looking for the 0.05 level of significance
15. You also need to remind yourself how many Pps you had 🙂
16. Now it should be easy to find the critical value. Remember use two sheets of paper to guide you so your eye doesn’t wander onto the wrong column or row.
17. So is your observed value bigger than the critical value, if so you can accept your hypothesis (p<0.05)
18. If your value is smaller than the critical value, you must reject the hypothesis and accept the null (p>0.05)
19. Bravo, you are a statistical genius!

mindful spearmans colouring

Practice Questions:

1. Neil carried out a correlation. To analyse his data Neil decided to carry out a Spearman’s test. He carried out the Spearman’s test because he was …

A) looking for a difference

B) looking for a relationship

C) using an independent groups design

D) using nominal data

E) using ordinal data

2. Paulo devised a self-report questionnaire to find out how many hours pupils spend each week engaging with violent video games. He then asked their teachers to score the pupils’ aggression level on a scale of 1-10 (1 was very low and 10 was very high). He believed that there would be a positive correlation between the two variables. Paulo is half way through his Spearmans Rho calculation and has had to go and answer the phone, he wants you to finish his calculation and check whether the data is significant.

a. Use the table to see how far he has got and complete the calculation for him. First you will need to complete the D2

 Rank 1 Rank 2 D D2 1 3 -2 2.5 5 -2.5 2.5 1 1.5 4 4 0 5 7 -2 6 2 4 7.5 6 1.5 7.5 10 -2.5 9 8 1 10 9 1

Use the space here to show the rest of your workings:

R = …………………………………………

(4 marks)

b. Should Paulo reject his null hypothesis? (1 mark) ………………………………

Answer and guidance to the Paulo question

3. In a recent study by Lu et al (2017) it was suggested that the number countries you have visited, the less precise your moral compass becomes, e.g. the more you are likely to cheat on a test. They suggest that exposure to a variety of moral codes means people start to view morality as relative rather than absolute leading to more lax following of rules for example. Imagine the table contains some of their data:

 Number of countries visited No. of times the Pps was observed to cheat on a test 2 4 4 7 6 12 7 7 8 15 13 12 21 16 24 15

a. Explain which statistical test Lu should use to analyse this data and why (3)

b. Calculate the observed value (7)

c. State whether you should use a one or a two tailed test when checking for significance and why (2)

d. State the critical value (1)

e. State whether Lu would reject the null hypothesis based on this analysis and why (3)

Models answers to Lu et al (2017) stats questions