Justify use of Spearman's

Question asks to explain why Spearman's rank correlation coefficient is more appropriate than PMCC for the given data or context.

6 questions · Standard +0.2

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OCR Further Statistics AS 2020 November Q4
9 marks Standard +0.3
4 After a holiday organised for a group, the company organising the holiday obtained scores out of 10 for six different aspects of the holiday. The company obtained responses from 100 couples and 100 single travellers. The total scores for each of the aspects are given in the following table.
AspectCouplesSingle travellers
Organisation884867
Travel710633
Food692675
Leader898898
Included visits561736
Optional visits683712
Fred wishes to test whether there is significant positive correlation between the scores given by the two categories.
  1. Explain why it is probably not appropriate to use Pearson's product-moment correlation coefficient.
  2. Carry out an appropriate test at the \(1 \%\) level.
  3. Explain what is meant by the statement that the test carried out in part (b) is a non-parametric test.
OCR FS1 AS 2021 June Q2
9 marks Moderate -0.5
2 After a holiday organised for a group, the company organising the holiday obtained scores out of 10 for six different aspects of the holiday. The company obtained responses from 100 couples and 100 single travellers. The total scores for each of the aspects are given in the following table.
QuestionAnswerMarkAOGuidance
1(a)\(\frac { 1 } { 0.2 } = 5\)M1 A1 [2]3.3 1.1Geometric distribution soi 5 (or \(5.00 \ldots\) ) only
1(b)\(0.8 ^ { 2 } - 0.8 ^ { 10 }\) \(= \mathbf { 0 . 5 3 3 } \quad ( 0.5326258 \ldots )\)M1 A1 [2]1.1 3.4
Allow for powers 2, 3, 4 and 9, 10, 11 .
Awrt 0.533, www. [5201424/976562]
Or \(0.2 \left( 0.8 ^ { 2 } + \ldots . + 0.8 ^ { 9 } \right) , \pm 1\) term at either end [0.506, 0.378, 0.275, 0.405, 0.302, 0.554, 0.426, 0.324]
1(c)
\(\mathrm { P } ( \geq 10 ) = 0.8 ^ { 9 }\)
\(= 0.1342 \ldots\)
B(30, 0.1342...)
Variance \(= n p q\) = 3.486...
M1
A1
M1
A1ft [4]
3.1b
1.1
3.1b
1.1
Or \(0.8 ^ { 10 }\). Can be implied by correct \(p\)
[0.10737... is M1A0 here]
Stated or implied, their \(0.8 ^ { 9 }\) or \(0.8 ^ { 10 }\)
In range [3.48, 3.49]
SC: 0.134(2) oe not properly shown: B2 for correct final answer.
SC: 2.875 from \(0.8 ^ { 10 }\) : M1A0M1A1ft
QuestionAnswerMarkAOGuidance
2(a)Test is for rankings/rankings arbitrary/not bivariate normal etcB1 [1]2.4OE
2(b)
\(\mathrm { H } _ { 0 } : \rho _ { s } = 0 , \mathrm { H } _ { 1 } : \rho _ { s } > 0\), where \(\rho _ { s }\) is the population rank correlation coefficient
Ranks 543612
512643
\(\Sigma d ^ { 2 } = 20\)
\(r _ { s } = 1 - \frac { 6 \times 20 } { 6 \times 35 }\)
\(= 3 / 7\) or \(0.42857 \ldots\)
<0.9429
B1
B1
M1
A1
B1
1.1
1.1
1.1
1.1
1.1
Allow \(\rho _ { s }\) not defined; allow \(\rho\).
Allow: \(\mathrm { H } _ { 0 }\) : no association between rankings.
\(\mathrm { H } _ { 1 }\) : positive association (but not \(\mathrm { H } _ { 1 }\) : association)
Do not reject \(\mathrm { H } _ { 0 }\)
Insufficient evidence of association between ranking given by the two categories
M1ft
A1ft
[7]
1.1
2.2b
FT on their \(\Sigma d ^ { 2 }\) only
2(c)Not dependent on any distributional assumptions
B1
[1]
1.2Oe (cf. Specification, 5.08f)
QuestionAnswerMarkAOGuidance
3(a)Failures occur to no fixed pattern/are not predictableB1 [1]1.1OE. NOT "independent"
3(b)Failures occur independently of one another and at constant average rate
B1
B1
[2]
1.1
1.1
Not recoverable from (a) if independence not restated here; must be contextualised
Ignore "singly". Allow "uniform" rate, not "constant rate" or "constant probability"; must be contextualised
3(c)
Variance (1.6384) \(\approx\) mean
So suggests that it is likely to be well modelled
M1
A1
[2]
1.1
3.5a
Compare variance (or SD). Allow square/square-root confusion
Correct comparison and conclusion, 1.64 or better seen
3(d)\(\mathrm { e } ^ { - 1.61 }\)
B1
[1]
3.4Exact needed, allow even if \(0 !\) or \(1.61 ^ { 0 }\) or both left in
3(e)
1\(\geq 2\)
0.3220.478
B1
B1
[2]
3.4
1.1
One correct e.g. 0.3218
Other correct e.g. 0.4783
3(f)\(\mathrm { P } ( F = 1 )\) will be smaller as single failures are less likely
B1*
depB1
[2]
3.5c
3.3
OE. Partial answer: B1
Edexcel S3 Q4
11 marks Standard +0.3
At the end of a season an athletics coach graded a random sample of ten athletes according to their performances throughout the season and their dedication to training. The results, expressed as percentages, are shown in the table below.
AthletePerformanceDedication
A8672
B6069
C7859
D5668
E8080
F6684
G5165
H5955
I7379
J4953
  1. Calculate the Spearman rank correlation coefficient between performance and dedication. [5]
  2. Stating clearly your hypotheses and using a 10\% level of significance, interpret your rank correlation coefficient. [5]
  3. Give a reason to support the use of the rank correlation coefficient rather than the product moment correlation coefficient with these data. [1]
Edexcel S3 2002 June Q4
11 marks Standard +0.3
At the end of a season an athletics coach graded a random sample of ten athletes according to their performances throughout the season and their dedication to training. The results, expressed as percentages, are shown in the table below.
AthletePerformanceDedication
A8672
B6069
C7859
D5668
E8080
F6684
G3165
H5955
I7379
J4953
  1. Calculate the Spearman rank correlation coefficient between performance and dedication. [5]
  2. Stating clearly your hypotheses and using a 10\% level of significance, interpret your rank correlation coefficient. [5]
  3. Give a reason to support the use of the rank correlation coefficient rather than the product moment correlation coefficient with these data. [1]
Edexcel S3 Q7
16 marks Standard +0.3
For one of the activities at a gymnastics competition, 8 gymnasts were awarded marks out of 10 for each of artistic performance and technical ability. The results were as follows.
Gymnast\(A\)\(B\)\(C\)\(D\)\(E\)\(F\)\(G\)\(H\)
Technical ability8.58.69.57.56.89.19.49.2
Artistic performance6.27.58.26.76.07.28.09.1
The value of the product moment correlation coefficient for these data is 0.774.
  1. Stating your hypotheses clearly and using a 1% level of significance, interpret this value. [5]
  2. Calculate the value of the rank correlation coefficient for these data. [6]
  3. Stating your hypotheses clearly and using a 1% level of significance, interpret this coefficient. [3]
  4. Explain why the rank correlation coefficient might be the better one to use with these data. [2]
WJEC Further Unit 2 Specimen Q3
9 marks Standard +0.3
A class of 8 students sit examinations in History and Geography. The marks obtained by these students are given below.
StudentABCDEFGH
History mark7359834957826760
Geography mark5551585944664967
  1. Calculate Spearman's rank correlation coefficient for this data set. [6]
  2. Hence determine whether or not, at the 5% significance level, there is evidence of a positive association between marks in History and marks in Geography. [2]
  3. Explain why it might not have been appropriate to use Pearson's product moment correlation coefficient to test association using this data set. [1]