What does Spearman's rank correlation measure, and what kind of data does it need?

It measures the strength and the direction of the relationship between two variables that have been measured for the same set of cases, by comparing the rank order of each case on one variable with its rank order on the other. It needs paired data - two values for every site, person or time period - and the values must be capable of being ranked. It works with ordinal data as well as with measurements, and it is normally applied to at least ten pairs, since below that the test cannot detect anything reliably.

What range of values can Spearman's rank correlation coefficient take, and what does each end of the scale mean?

It runs from minus one to plus one. A value of plus one is a perfect positive relationship: the case ranked first on one variable is ranked first on the other, all the way down the list, so as one variable increases the other increases exactly in step. A value of minus one is a perfect negative or inverse relationship: the case ranked first on one variable is ranked last on the other, so as one increases the other decreases exactly in step. A value of zero means there is no relationship between the two rank orders at all.

A Spearman's rank calculation gives minus 0.82. What does that say, in words, about the relationship?

It says there is a strong negative relationship between the two variables: as one increases, the other consistently decreases. The minus sign gives the direction - the two rank orders run in opposite directions - and the size, 0.82 out of a possible 1, gives the strength, which is high, so the relationship holds for most of the cases with only a few departing from it. It does not say that one variable causes the other, and it must still be checked against the critical value in the significance table for the number of pairs used before it can be called significant.

CCEA A-Level Geography 3910

Processes That Shape Fluvial Environments

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Data Processing

Spearman's rank correlation

3 things to know
Unit AS 3

Overview

What the test measures and what data it needs, what the sign and the size of the coefficient each say, and how significance is read off the table provided.

What you need to know

Answer each one before you reveal it.

Your recallNot started

Key term

A Spearman's rank calculation gives plus 0.15. How would you interpret that?

Key term

What is the difference between the sign and the size of a correlation coefficient?

Key term

How do you test whether a Spearman's rank result is significant, using the table provided?

Questions from this subtopic

Each one with the model answer underneath.

1
What does Spearman's rank correlation measure, and what kind of data does it need?
Model answer
It measures the strength and the direction of the relationship between two variables that have been measured for the same set of cases, by comparing the rank order of each case on one variable with its rank order on the other. It needs paired data - two values for every site, person or time period - and the values must be capable of being ranked. It works with ordinal data as well as with measurements, and it is normally applied to at least ten pairs, since below that the test cannot detect anything reliably.
2
What range of values can Spearman's rank correlation coefficient take, and what does each end of the scale mean?
Model answer
It runs from minus one to plus one. A value of plus one is a perfect positive relationship: the case ranked first on one variable is ranked first on the other, all the way down the list, so as one variable increases the other increases exactly in step. A value of minus one is a perfect negative or inverse relationship: the case ranked first on one variable is ranked last on the other, so as one increases the other decreases exactly in step. A value of zero means there is no relationship between the two rank orders at all.
3
A Spearman's rank calculation gives minus 0.82. What does that say, in words, about the relationship?
Model answer
It says there is a strong negative relationship between the two variables: as one increases, the other consistently decreases. The minus sign gives the direction - the two rank orders run in opposite directions - and the size, 0.82 out of a possible 1, gives the strength, which is high, so the relationship holds for most of the cases with only a few departing from it. It does not say that one variable causes the other, and it must still be checked against the critical value in the significance table for the number of pairs used before it can be called significant.
4
A Spearman's rank calculation gives plus 0.15. How would you interpret that?
Model answer
As a very weak positive relationship, effectively no relationship at all. The positive sign indicates the two rank orders tend very slightly in the same direction, but at 0.15 the value is so close to zero that the ranking of a case on one variable tells you almost nothing about its ranking on the other. A value this low would fall well short of the critical value in the significance table at any normal sample size, so the null hypothesis of no relationship would stand.
5
What is the difference between the sign and the size of a correlation coefficient?
Model answer
The sign gives the direction of the relationship - positive means the variables increase together, negative means one increases as the other decreases - and says nothing about how strong it is. The size, meaning the value ignoring the sign, gives the strength, with figures near one indicating a close relationship and figures near zero indicating almost none. So minus 0.9 is a much stronger relationship than plus 0.3, even though one is negative; students who assume a minus sign means a poor result have misread the test.
6
How do you test whether a Spearman's rank result is significant, using the table provided?
Model answer
Find the row of the table for the number of pairs of data used, and read off the critical value for the significance level chosen, normally the 95 per cent or 0.05 level. Compare your calculated coefficient with that critical value, ignoring the sign. If your value is equal to or greater than the critical value, the result is significant and the null hypothesis is rejected; if it is smaller, the result could reasonably have arisen by chance and the null hypothesis is accepted. Because the tables are provided in the examination, the marks are for using them correctly and stating the conclusion, not for remembering them.

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