IB Maths AI HL 4.10 Spearman's rank correlation Question Bank

Practise IB Mathematics SL/HL 4.10 by applying spearman's rank correlation methods to exam-style questions.

[Maximum number: 8]

A firm wishes to review its recruitment processes. This question considers the validity and reliability of the methods used.
Every year an accountancy firm recruits new employees for a trial period of one year from a large group of applicants.
At the start, all applicants are interviewed and given a rating. Those with a rating of either Excellent, Very good or Good are recruited for the trial period. At the end of this period, some of the new employees will stay with the firm.
It is decided to test how valid the interview rating is as a way of predicting which of the new employees will stay with the firm.
Data is collected and recorded in a contingency table.

Table for Question SL 4.10—Spearman's rank correlation question 1 — IB Maths AI HL

(a)

Without calculation, explain why it might not be appropriate to calculate a correlation coefficient for the whole sample of 18 employees.

[ 2 ]

(b)

Find $r_{s}$ for the seven employees working in the international department.

[ 4 ]

L

M

N

O

P

Q

R

Written assessment

rank

1

2

3

4

5

6

Manager score

rank

1

2.5

4.5

2.5

4.5

6
(M1)(A1)
Note: Award (M1) for an attempt to rank the data, and (A1) for correct ranks for both variables. Accept either set of rankings in reverse.

Note: The (M1) is for calculating the PMCC for their ranks.

Note: If a final answer of 0.9107 is seen, from use of $1-\frac{6 \sum d^{2}}{n\left(n^{2}-1\right)}$ , award (M1)(A1)A1.

Accept -0.909 if one set of ranks has been ordered in reverse.

(c)

Hence comment on the validity of the written assessment as a measure of the level of performance of employees in this department. Justify your answer.

The same seven employees are given the written assessment a second time, at the end of the first year, to measure its reliability. Their marks are shown in the table below.

[ 2 ]

(iii) EITHER there is a (strong) association between the written assessment mark and the manager scores.
OR
there is a (strong) agreement in the rank order of the written assessment marks and the rank order of the manager scores.
OR
there is a (strong linear) correlation between the rank order of the written assessment marks and the rank order of the manager scores.
Note: Follow through on a value for their value of $r_{s}$ in c(ii).
THEN
the written assessment is likely to be a valid measure (of the level of employee performance)

All question bank results loaded

SL 4.10—Spearman's rank correlation question 1

Question (a)

Question (b)

Question (c)