| Exam Board | Edexcel |
|---|---|
| Module | FS2 AS (Further Statistics 2 AS) |
| Session | Specimen |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Hypothesis test of Spearman’s rank correlation coefficien |
| Type | Hypothesis test for positive correlation |
| Difficulty | Standard +0.3 This is a straightforward application of Spearman's rank correlation coefficient with standard hypothesis testing. Students must rank data, apply the formula, compare to critical values, and interpret results—all routine procedures for Further Statistics 2. The calculations are mechanical with no conceptual challenges beyond textbook exercises, making it slightly easier than average for A-level standard. |
| Spec | 5.08e Spearman rank correlation5.08f Hypothesis test: Spearman rank5.08g Compare: Pearson vs Spearman |
| Competitor | A | B | C | D | E | F | G | H |
| J udge 1's scores | 4.6 | 9.1 | 8.4 | 8.8 | 9.0 | 9.5 | 9.2 | 9.4 |
| J udge 2's scores | 7.8 | 8.8 | 8.6 | 8.5 | 9.1 | 9.6 | 9.0 | 9.3 |
# Question 1
## 1(a)
**M1** For an attempt to rank at least one row (at least four correct)
**M1** For an attempt at $d^2$ row for their ranks
**M1** Dependent on 1st M1 for use of $r_s = 1 - \frac{6\Sigma d^2}{n(n^2-1)}$ with their $d^2$
$\Sigma d^2 = 8$
$r_s = 1 - \frac{6(8)}{8(64-1)}$
$r_s = 0.90476...$ awrt $0.905$
**A1** For awrt 0.905
(4 marks)
## 1(b)
$H_0: \rho_s = 0$
$H_1: \rho_s \neq 0$
**B1** Both hypotheses stated in terms of $\rho_s$
Critical value $= 0.8333$
**B1** For correct critical value
$r_s = 0.905$ lies in the critical region/reject $H_0$
**M1** For comparing their 0.905 with their 0.8333
The two judges are in agreement.
**A1** For a correct contextual conclusion with no contradictions seen
(4 marks)
## 1(c)
E.g. The data is unlikely to be from a bivariate normal distribution (competitor A)/The emphasis here is on the ranks and not the individual scores.
**B1** For a correct explanation to support the use of Spearman
(1 mark)
## 1(d)
Both show positive correlation, but the judges agree more on the beam (since 0.952 is closer to 1)
**B1** For a correct comparison of the correlation coefficients
(1 mark)
**Total: 10 marks**\begin{enumerate}
\item In a gymnastics competition, two judges scored each of 8 competitors on the vault.
\end{enumerate}
\begin{center}
\begin{tabular}{ | l | c | c | c | c | c | c | c | c | }
\hline
Competitor & A & B & C & D & E & F & G & H \\
\hline
J udge 1's scores & 4.6 & 9.1 & 8.4 & 8.8 & 9.0 & 9.5 & 9.2 & 9.4 \\
\hline
J udge 2's scores & 7.8 & 8.8 & 8.6 & 8.5 & 9.1 & 9.6 & 9.0 & 9.3 \\
\hline
\end{tabular}
\end{center}
(a) Calculate Spearman's rank correlation coefficient for these data.\\
(b) Stating your hypotheses clearly, test at the $1 \%$ level of significance, whether or not the two judges are generally in agreement.\\
(c) Give a reason to support the use of Spearman's rank correlation coefficient in this case.
The judges also scored the competitors on the beam.\\
Spearman's rank correlation coefficient for their ranks on the beam was found to be 0.952\\
(d) Compare the judges' ranks on the vault with their ranks on the beam.
\hfill \mbox{\textit{Edexcel FS2 AS Q1 [10]}}