Further Mathematics · OCR H245 · Option S · Topic 5.08

Correlation

Pearson's product-moment correlation coefficient, hypothesis tests using Pearson's coefficient, Spearman's rank correlation coefficient, hypothesis tests using Spearman's coefficient, comparison of coefficients.

  • 5 sub-topics
  • Taught in Year 13
  • 60 practice questions
  • 5 animated lessons
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What the specification says

Every sub-topic OCR can examine in this topic, with its reference number from the official specification. The Y12 and Y13 tags show when each sub-topic is usually taught.

  1. 5.08a-cPearson's product-moment correlation coefficientY13
  2. 5.08dHypothesis tests using Pearson's coefficientY13
  3. 5.08eSpearman's rank correlation coefficientY13
  4. 5.08fHypothesis tests using Spearman's coefficientY13
  5. 5.08gComparison of coefficientsY13

Try 3 questions

Easy, medium and hard questions from this topic, each with a worked solutions and the mark for every step. All 60 questions in this topic, free, no account needed.

Correlation

Easy

What each coefficient measures · Year 12 · 1 mark

  1. What does Pearson's product moment correlation coefficient measure?
    (1)

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  1. Pearson's coefficient is about straight lines. Spearman's is about order.CC: The strength of the linear association between two variables

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Correlation

Not needed for Year 12Medium

The product moment correlation coefficient · Year 13 · 4 marks

For a set of bivariate data, SxxS_{xx}=310, Syy{}= 310, \ S_{yy}=95, Sxy{}= 95, \ S_{xy}=77.2{}= 77.2.
  1. (a)
    Calculate the product moment correlation coefficient.
    (2)
  2. (b)
    Interpret your answer.
    (1)
  3. (c)
    The data are coded using u=2x+5u = 2x + 5 and v=(y−10)/3v = (y - 10)/3. State the value of the product moment correlation coefficient between uu and vv.
    (1)

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Part (a)2 marks

  1. rr=77.2310×95{}= \frac{77.2}{\sqrt{310 \times 95}}
  2. r=0.450r = 0.450

Part (b)1 mark

  1. Moderate positive linear correlation.

Part (c)1 mark

  1. Linear coding with positive scale factors does not change rr.0.4500.450

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Correlation

Not needed for Year 12Hard

Spearman's rank correlation · Year 13 · 6 marks

Two judges rank 7 contestants, PP to VV. Judge AA: P1P 1, Q2Q 2, R3R 3, S4S 4, T5T 5, U6U 6, V7V 7. Judge BB: P6P 6, Q7Q 7, R4R 4, S3S 3, T5T 5, U2U 2, V1V 1.
  1. (a)
    Calculate Spearman's rank correlation coefficient.
    (3)
  2. (b)
    Test, at the 5% level, whether there is positive agreement between the judges.
    (3)
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Part (a)3 marks

  1. ∑d2=104\sum d^2 = 104
  2. rsr_s=1{}= 1−6×1047(49−1){}- \frac{6 \times 104}{7(49 - 1)}=−0.857{}= -0.857

Part (b)3 marks

  1. H0:ρ=0, H1:ρ>0H_0: \rho = 0, \ H_1: \rho > 0
  2. n=7n = 7, one-tailed 5%.cv=0.7143\text{cv} = 0.7143
  3. Do not reject H₀: there is insufficient evidence of positive agreement between the judges.

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