IB Maths AI HL Sl 4 10 Spearmans Rank Correlation Questions

Practise ranking data with ties, calculating Spearman’s coefficient, comparing it with Pearson correlation and judging association without claiming causation.

Syllabus
First assessment 2021
Course
Mathematics: applications and interpretation HL
Level
HL

Exam points

  • Rank data, average tied ranks and calculate or interpret Spearman’s rank correlation coefficient with technology.
  • Compare Spearman and Pearson correlation for monotonic/non-linear relationships, outliers and data type.
  • Assess the direction, strength and limitations of the association without claiming causation.

IB Maths AI HL Sl 4 10 Spearmans Rank Correlation Questions question 1

[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 IB Maths AI HL Sl 4 10 Spearmans Rank Correlation Questions question 1 — IB Maths AI HL

Question (a)

(a)

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

[ 2 ]

Question (b)

(b)

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

[ 4 ]

Question (c)

(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.

Table for Question (c) — IB Maths AI HL
[ 2 ]
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