| Exam Board | OCR |
|---|---|
| Module | Further Statistics (Further Statistics) |
| Year | 2021 |
| Session | November |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Hypothesis test of Spearman’s rank correlation coefficien |
| Type | Hypothesis test for association |
| Difficulty | Standard +0.3 This is a straightforward application of Spearman's rank correlation test with standard steps: ranking data, calculating rs, and comparing to critical values. Part (a) requires understanding when Spearman's is preferred (measurement errors, ordinal data), which is standard theory. The calculation in part (b) is routine with 9 data points and no computational complications. Slightly above average difficulty only because it's Further Maths content and requires knowledge of both correlation coefficients. |
| Spec | 5.08e Spearman rank correlation5.08f Hypothesis test: Spearman rank |
| Item | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
| Supermarket \(A\) | 17 | 28 | 41 | 43 | 62 | 69 | 75 | 93 | 115 |
| Supermarket \(B\) | 24 | 7 | 18 | 12 | 47 | 29 | 58 | 42 | 37 |
| Answer | Marks | Guidance |
|---|---|---|
| 5 | (b) | H : no association between ranks of numbers of items |
| Answer | Marks |
|---|---|
| items | B1 |
| Answer | Marks |
|---|---|
| [8] | 1.1 |
| Answer | Marks |
|---|---|
| 2.2b | Don’t insist on “population” here, but allow use of ρ in |
Question 5:
5 | (b) | H : no association between ranks of numbers of items
0
H : (positive) association between ranks
1
Ranks 1 2 3 4 5 6 7 8 9
4 1 3 2 8 5 9 7 6
Σd 2 = 38
6Σd2
r = 1−
s
9(92 −1)
= 0.683
< 0.700
Do not reject H .
0
Insufficient evidence of association between rankings of the
items | B1
M1
A1
M1
A1
B1
M1ft
A1ft
[8] | 1.1
1.1
1.1
1.2
1.1
1.1
1.1
2.2b | Don’t insist on “population” here, but allow use of ρ in
s
both, even if no explanation (not just r). Context needed,
s
but don’t worry about 1- or 2-tailed here
Compare TS (–1 ≤ TS ≤ 1) with 0.7, independent
ft on TS provided correct formula used, or on CV 0.600
In context, not too positive. FT on TS only
SC: 0.600 (2-tailed): B0 M1A05 The numbers of each of 9 items sold in two different supermarkets in a week are given in the following table.
\begin{center}
\begin{tabular}{ | l | c | c | c | c | c | c | c | c | c | }
\hline
Item & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 \\
\hline
Supermarket $A$ & 17 & 28 & 41 & 43 & 62 & 69 & 75 & 93 & 115 \\
\hline
Supermarket $B$ & 24 & 7 & 18 & 12 & 47 & 29 & 58 & 42 & 37 \\
\hline
\end{tabular}
\end{center}
A researcher wants to test whether there is association between the numbers of these items sold in the two supermarkets.
However, it is known that the collection of data in Supermarket $B$ was done inaccurately and each of the numbers in the corresponding row of the table could have been in error by as much as 2 items greater or 2 items fewer.
\begin{enumerate}[label=(\alph*)]
\item Explain why Spearman's rank correlation coefficient might be preferred to the use of Pearson's product-moment correlation coefficient in this context.
\item Carry out the test at the $5 \%$ significance level using Spearman's rank correlation coefficient.
\end{enumerate}
\hfill \mbox{\textit{OCR Further Statistics 2021 Q5 [10]}}