Spearman's Rank Interpretation
Spearman's rank correlation coefficient is a number between -1 and 1 that measures how strongly two ranked sets of data are related. At Foundation tier you are given a calculated coefficient and must interpret its size and sign, rather than working it out yourself. A value close to 1 or -1 shows a strong link, while a value close to 0 shows almost no link.
Before you start
Make sure you're comfortable with these topics first:
Method
- Note the value of the coefficient, rs, given in the question; it will always be between -1 and 1.
- Look at the sign: a positive value means as one variable increases the other tends to increase; a negative value means as one increases the other tends to decrease.
- Look at the size: values close to 1 or -1 show a strong relationship, and values close to 0 show a weak or negligible relationship.
- Write a conclusion in context, naming the actual variables from the question rather than just saying 'x and y'.
- If asked to compare two coefficients, compare their sizes ignoring the sign (their absolute values); the one further from 0 is the stronger relationship.
- Remember that a strong correlation does not prove that one variable causes the other to change.
Worked example
The Spearman's rank correlation coefficient between the number of hours 10 students spent revising and their exam scores was calculated as rs = 0.82. Interpret this value in context.
- rs = 0.82 is positive, so as revision hours increase, exam scores tend to increase.
- 0.82 is close to 1, so this is a strong relationship rather than a weak one.
- So the final answer is: there is a strong positive correlation between hours spent revising and exam score, meaning students who revised more tended to score higher.
Practice questions
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Q1The Spearman's rank correlation coefficient between temperature and ice cream sales for 8 days is rs = 0.95. Describe the correlation.Show answer
Answer: Very strong positive correlation - as temperature rises, ice cream sales rise.
Q2The Spearman's rank correlation coefficient between the age of a used car and its price is rs = -0.88. Describe the correlation.Show answer
Answer: Strong negative correlation - older cars tend to cost less.
Q3For a class, the Spearman's rank correlation coefficient between shoe size and spelling test score is rs = 0.15. Describe the correlation.Show answer
Answer: Very weak (almost no) correlation between shoe size and spelling score.
Q4The Spearman's rank correlation coefficient between hours spent watching TV and test score is rs = -0.4. Describe the strength and direction of the correlation.Show answer
Answer: Weak to moderate negative correlation - more TV time is weakly linked to lower scores.
Q5Two data sets give correlation coefficients rs = 0.6 and rs = -0.9. Which shows the stronger relationship?Show answer
Answer: rs = -0.9, since its size (0.9) is greater than 0.6, even though it is negative.
Q6A researcher finds rs = 0.99 between a town's number of ice cream vans and its number of sunburn cases, and concludes the vans cause sunburn. Explain why this conclusion may be wrong.Show answer
Answer: Correlation does not imply causation - a third factor (hot, sunny weather) likely increases both, so the vans do not directly cause sunburn.
Exam-style questions
Written in the style of a GCSE Statistics exam paper, with a full mark scheme.
The Spearman's rank correlation coefficient for the relationship between a runner's age and their marathon time is rs = 0.73. State what this value tells you about the relationship, referring to both the direction and the strength.
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A student calculates the Spearman's rank correlation coefficient between the price of 8 second-hand phones and the number of scratches visible on each phone, getting rs = -0.79. (a) State whether this shows a positive or negative correlation, and explain what this means in context. (b) Comment on the strength of the correlation.
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Two Spearman's rank correlation coefficients are calculated: rs = 0.34 between a plant's amount of sunlight and its height, and rs = 0.91 between a plant's amount of water and its height. (a) State which relationship is stronger, giving a reason. (b) A gardener claims that because rs = 0.91 is high, more water definitely causes the plant to grow taller. Comment on this claim.
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Free printable worksheet
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This topic is chapter 10 of GCSE Statistics Foundation Workbook 2, the whole course as one free printable PDF.
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