Question 4:
4 | (a) | E.g. ratings are arbitrary, or population not bivariate
normal, or r measures only linear correlation | B1
[1] | 2.4 | Not “data are ratings not scores” unless explained further. Not “population
may not be normal”, nor just “looking for agreement not correlation”
(b) | I 5 4 3 2 1
II 4 5 2 3 1
d2 = 4
6d2
r = 1− = 0.8
s
5(52−1) | B1
B1
M1
A1
[4] | 1.1
1.1
1.2
1.1 | Or with rankings reversed (2 1 4 3 5)
4 stated or implied
Correct formula used, with reasonable attempt at d2 using rankings
0.8 or 4/5 only
(c) | H :  = 0, H :  > 0, where  is the population rank
0 s 1 s s
correlation coefficient between the rankings given by
the two magazines, or H : no correlation between
0
population rankings, H : positive correlation
1
0.8 < 0.9 so do not reject H .
0
Insufficient evidence of agreement between
magazines’ opinions. | B2
B1ft
B1ft
[4] | 1.1
2.5
1.1
2.2b | One error, e.g. two-tailed or  not defined, or verbal: B1
s
If verbal, must include clearly one-sided H for B2
1
Allow B1 for H :  = 0, H :  > 0. Same marks also for using r or r
0 1 s
For B2 must include either context or “population” (or both).
Allow any of correlation, association, agreement.
Compare with 0.9 and do not reject, FT on their r if M1 gained in (b).
s
FT on CV 1.0 if hypotheses two-tailed. Allow “Accept H ”, etc
1
Contextualised, not too assertive, FT as above. Not “evidence of no
agreement”, but allow from CV 1.0. Needs hypotheses right way round
(d) | Magazine III 2 1 4 3 5 | B1ft
[1] | 3.1b | Reverse of rankings of II used in part (b) (= 6 – their rankings of II)
NB: “4 5 2 3 1” could come from ranking high-to-low.
I | 5 | 4 | 3 | 2 | 1
II | 4 | 5 | 2 | 3 | 1
Magazine III | 2 | 1 | 4 | 3 | 5
A | Takes into account magnitudes of scores (wrong) | B0
B | Takes into account differences in ranks (wrong) | B0
C | Not enough data to use PMCC | B0
D | One magazine may have a stricter standard and Spearman would eliminate this (scaling would not affect PMCC) | B0
E | Spearman’s Rank will not be as much affected by uncertainties in measurements/anomalous results (too vague?) | B0
F | Eliminates the magnitude of the scores (too vague) | B0
G | Testing association rather than a linear relationship (generally allow any answer that says SRCC doesn’t need linearity) | B1
H | Looking for agreement between opinions rather than between numerical values, so association not correlation | B1
I | The numbers are just opinions | B1
J | H : no correlation between magazine’s ratings, H : positive correlation
0 1 | B2
K | H : no correlation,  = 0, H : positive correlation,  > 0 (neither the verbal nor the symbolic statement scores B2)
0 s 1 s | B1
L | H : r = 0, H : r > 0, where r is the correlation coefficient between the rankings given by the magazines
0 1 | B2
M | H : no agreement between population rankings, H : there is agreement (2-tailed so B1B0)
0 1
0.8 < 1.0 so do not reject H . (FT on 2-tailed)
0
Insufficient evidence of no agreement between magazines’ opinions. (FT) | B1B0
B1
B1
N | H : no positive agreement between population rankings, H : positive agreement (1-tailed so B1B1 – allow this H )
0 1 0
0.8 < 1.0 so do not reject H . (NO FT on 1-tailed if 0.9 not used)
0
Insufficient evidence of no agreement between magazines’ opinions. (NO FT) | B1B1
B0
B0
O | H : no agreement between population rankings, H : there is agreement (2-tailed so B1B0)
0 1
0.8 < 0.9 so do not reject H . (allow, even though inconsistent)
0
Significance evidence of agreement between magazines’ opinions. (can’t assert that H is correct)
0 | B1B0
B1
B0