4.10 Spearman's rank correlationIB Maths: Applications and Interpretation HL: Flashcards

What these 14 flashcards ask

What does Spearman's rs measure?
What does Pearson's r measure?
What is a monotonic relationship?
What range of values can rs take?
How do you find rs in an examination?
How are tied values ranked?
Scores 9,8,7,6,5,5,4, highest rank 1: ranks of the two 5s?
What does rs=1 mean?
What does rs=-1 mean?
Which coefficient is less sensitive to outliers?
Curved but always increasing data: which coefficient suits it best?
Does a low r show the variables are unrelated?
What mistake changes the sign of rs?
Does a strong correlation prove causation?

Exam questions on 4.10 Spearman's rank correlation

Six students sat a maths test and a physics test. Their marks (maths, physics) were $(45,52)$ , $(60,58)$ , $(72,80)$ , $(38,40)$ , $(55,61)$ and $(80,75)$ . In both subjects the highest mark is given rank $1$ .
Interpret the value of $r_s$ in context.2 marks
Seven dishes in a cookery competition were each given a score out of $10$ by two judges, $X$ and $Y$ . In the order of the dishes, judge $X$ gave $7,5,9,5,8,6,4$ and judge $Y$ gave $8,6,9,7,7,5,3$ . The highest score is given rank $1$ .
Write down the ranks given by judge $Y$ to the seven dishes, in the order of the dishes.2 marks
A scientist counts the bacteria in a culture, $y$ thousand, $x$ hours after the start of an experiment. For $x=1,2,3,4,5,6,7,8$ the counts are $2,4,9,17,31,52,85,140$ . Use your GDC.
(i) Find Pearson's product-moment correlation coefficient $r$ between $x$ and $y$ . (ii) Find Spearman's rank correlation coefficient $r_s$ , justifying your value.3 marks

Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).