Spearman's Rank Interpretation: Fluency and Exam Drill - Worksheets, Questions and Revision

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F07D Spearman's Rank Interpretation: Fluency and Exam Drill

EDEXCEL 1ST0 · Calculator allowed · about 50 minutes

Total Marks

Name: _______________________________ Date: ____ / ____ / ______

Answer ALL questions. Show all your working.

State whether rs = 0.72 shows a positive or negative association.

(Total for Question 1 is 1 mark)

State whether rs = -0.55 shows a positive or negative association.

(Total for Question 2 is 1 mark)

Write down whether rs = 0.98 is closer to 0 or closer to 1.

(Total for Question 3 is 1 mark)

Write down whether rs = -0.12 is closer to 0 or closer to -1.

(Total for Question 4 is 1 mark)

Write down the value of rs that shows perfect positive agreement between two rankings.

(Total for Question 5 is 1 mark)

Write down the value of rs that shows perfect negative agreement (a complete reversal) between two rankings.

(Total for Question 6 is 1 mark)

State whether rs = 0 shows a strong association or no clear association.

(Total for Question 7 is 1 mark)

Two examiners rank 5 essays. The Spearman's rank correlation coefficient between their rankings is rs = 0.85. Describe the strength and direction of the association.

(Total for Question 8 is 2 marks)

For a pair of judges scoring a competition, rs = -0.77. Describe the strength and direction of the association.

(Total for Question 9 is 2 marks)

Two coefficients are given: rs = 0.63 for Pair X and rs = 0.29 for Pair Y. Write down which pair shows the stronger association, explaining your reasoning.

(Total for Question 10 is 2 marks)

Two coefficients are given: rs = -0.81 for Group P and rs = 0.35 for Group Q. Write down which group shows the stronger association, regardless of sign, explaining your reasoning.

(Total for Question 11 is 2 marks)

In a design competition, two judges score 4 entries. Judge B gives two entries the same score, which would otherwise occupy positions 2 and 3. Work out the rank that should be given to each of these two tied entries.

(Total for Question 12 is 2 marks)

In a separate competition, three entries tie and would otherwise occupy positions 3, 4 and 5. Work out the rank that should be given to each of these three tied entries.

(Total for Question 13 is 2 marks)

Two coaches independently rank 7 sprinters by predicted finishing position for an upcoming race. The Spearman's rank correlation coefficient between their two rankings is rs = 0.92.

(a)State the type of association (positive or negative) shown by rs = 0.92.(1)

(b)Describe the strength of this association.(1)

(c)Interpret rs = 0.92 in the context of the two coaches' rankings.(1)

(Total for Question 14 is 3 marks)

Two recruiters independently rank 6 candidates by suitability for a job. The Spearman's rank correlation coefficient between their rankings is rs = -0.2.

(a)State whether rs = -0.2 shows a strong or a weak association.(1)

(b)Explain what this value suggests about the two recruiters' views on the candidates, and explain why 'weak' is a better description than 'no association at all'.(2)

(Total for Question 15 is 3 marks)

Three weather stations each compare their rainfall ranking with their sunshine-hours ranking for three different months. The Spearman's rank correlation coefficient is given for each month.

Month	rs
April	0.81
May	-0.92
June	0.06

(a)Write down which month shows the weakest association.(1)

(b)Write down which month shows the strongest association, regardless of sign, giving a reason.(2)

(Total for Question 16 is 3 marks)

At an art exhibition, Critic A and Critic B each score 5 paintings out of 25. Critic B gives two paintings the same score.

Painting	Critic A score	Critic A rank	Critic B score	Critic B rank
1	22	1	23	1
2	15	3	17	?
3	12	4	17	?
4	18	2	15	4
5	8	5	9	5

(a)Painting 2 and Painting 3 both scored 17 from Critic B. Work out the rank that should be given to each of these two paintings.(2)

(b)Explain why Painting 2 and Painting 3 are given the same rank instead of one being placed above the other.(1)

(c)The Spearman's rank correlation coefficient for this data is calculated to be rs = 0.95. Interpret this value in the context of the two critics' rankings.(1)

(Total for Question 17 is 4 marks)

A five-a-side league organiser wants to know whether teams' pre-season prediction rank is a good predictor of their end-of-season rank. She calculates the Spearman's rank correlation coefficient between the two rankings for 9 teams to be rs = 0.74.

(a)State whether this value shows a positive or negative association.(1)

(b)Comment on whether the organiser could reasonably claim the pre-season prediction is 'an excellent predictor of final league position'.(2)

(Total for Question 18 is 3 marks)

Three pairs of examiners each mark and rank the same set of history essays. The Spearman's rank correlation coefficient is given for each pair.

Pair	rs
J	0.94
K	-0.58
L	0.11

The exam board wants to know which pair can be trusted to mark consistently together, and which pair actively disagree.

(a)Write down which pair shows the strongest agreement.(1)

(b)Explain why pair K should be described as disagreeing with each other, rather than simply showing a weak association.(2)

(c)Explain why a coefficient of rs = 0.11 for pair L does not necessarily mean either examiner is a poor marker.(2)

(Total for Question 19 is 5 marks)

Mark scheme · F07D Spearman's Rank Interpretation: Fluency and Exam Drill

Question 1

B1 Positive cao
Answer: Positive

Question 2

B1 Negative cao
Answer: Negative

Question 3

B1 Closer to 1 cao
Answer: Closer to 1

Question 4

B1 Closer to 0 cao
Answer: Closer to 0

Question 5

B1 1 cao
Answer: 1

Question 6

B1 -1 cao
Answer: -1

Question 7

B1 no clear association, oe
Answer: No clear association

Question 8

B1 Positive
B1 Strong (close to +1)
Answer: Strong positive association.

Question 9

B1 Negative
B1 Strong (close to -1)
Answer: Strong negative association.

Question 10

M1 compares the sizes of the coefficients, 0.63 and 0.29
A1 Pair X cao
Answer: Pair X

Question 11

M1 compares the sizes of the coefficients ignoring sign, 0.81 and 0.35
A1 Group P cao
Answer: Group P

Question 12

M1 recognises the tied entries would occupy positions 2 and 3, oe
A1 2.5 for both cao
Answer: 2.5 (for both entries)

Question 13

M1 recognises the tied entries would occupy positions 3, 4 and 5, oe
A1 4 for all three cao
Answer: 4 (for all three entries)

Question 14

(a) B1 Positive cao
(a) Answer: Positive
(b) B1 Strong cao
(b) Answer: Strong
(c) B1 the two coaches largely agree on the order in which the sprinters will finish, oe
(c) Answer: The two coaches largely agree on the order in which the sprinters will finish; their rankings are very similar.

Question 15

(a) B1 Weak cao
(a) Answer: Weak
(b) B1 there is little agreement/link between the two rankings, oe
(b) B1 -0.2 is close to but not exactly 0, so there is a very slight tendency for the rankings to disagree, not none at all, oe
(b) Answer: There is little agreement between the two recruiters' rankings; -0.2 shows only a very slight tendency for their views to disagree, not a total lack of any association.

Question 16

(a) B1 June cao
(a) Answer: June
(b) M1 compares the size of each coefficient ignoring sign (0.81, 0.92, 0.06)
(b) A1 May cao
(b) Answer: May

Question 17

(a) M1 recognises the two tied scores would occupy positions 2 and 3, oe
(a) A1 2.5 for both cao
(a) Answer: 2.5 (for both Painting 2 and Painting 3)
(b) B1 they scored exactly the same, so there is no fair way to place one above the other, oe
(b) Answer: They scored exactly the same, so neither can fairly be placed above the other.
(c) B1 the two critics agree very strongly on the order of the paintings, since rs is close to +1, oe
(c) Answer: The two critics agree very strongly on the order of the paintings.

Question 18

(a) B1 Positive cao
(a) Answer: Positive
(b) B1 rs = 0.74 shows a fairly strong positive association, so there is some support for the claim
(b) B1 balanced comment: since rs is well below 1, the prediction is good but not excellent/not perfectly reliable for every team, oe
(b) Answer: The claim is only partly justified: rs = 0.74 shows a fairly strong positive link, but since it is well below 1, the prediction is good rather than excellent and will not be correct for every team.

Question 19

(a) B1 J cao
(a) Answer: J
(b) B1 rs for K is negative, showing the two examiners' rankings run in opposite directions, oe
(b) B1 -0.58 is a fairly large negative value (not close to 0), so this is a fairly strong disagreement, not a weak one, oe
(b) Answer: K's coefficient is negative and fairly large in size, so the examiners' rankings tend to run in opposite directions: a real disagreement, not just a weak link.
(c) B1 rs measures agreement between the two rankings, not the quality/ability of either examiner, oe
(c) B1 a low rs simply means the two examiners are ranking the essays in largely different orders from each other, which is not the same as either ranking being wrong, oe
(c) Answer: rs only measures how closely the two rankings match each other, not whether either examiner is good at marking; a low value just means their orders differ, not that one (or both) is incorrect.

Question 19

5 marks

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Spearman's Rank Interpretation: Fluency and Exam Drill - Worksheets, Questions and Revision

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