SOCI 212 – STATISTICS ASSIGNMENT 4 CONCORDIA UNIVERSITY
Part 1
1. Since gamma is a PRE measure, it tells us
A. the improvement in predicting the order of pairs of cases by taking the
independent variable (X) into account
2. A researcher tested the relationship between occupational prestige and level of
approval of a proposal to ban handguns in the province and found a gamma of
-0.17. This means that
A. as prestige goes up, support for the ban goes down
3. Ordinal level scales measuring religiosity and personal happiness range from 1 to
5. Which measure of association would be the most appropriate to assess the
relationship between these two variables?
C. Gamma
4. A study of the effects of fluoride in the water supply on the level of calcium
deficiency in women found a Spearman’s rho of +0.30. Our PRE for this
relationship is
D. 9 %
Part 2
A researcher is interested in identifying the relationship between GPA as an
indicator of academic performance and average number of hours devoted to
studying per week.
a) Based on the results presented in the table above and assuming that at least one
variable is measured at the ORDINAL (CONTINUOUS) level, identify the measure of
association that should be used to assess the relationship between academic
performance and number of hours of study per week.
b) Spearmen’s rho (rs)
, c) Calculate the measure of association identified in question a.
Case Hours of Rank Performance Rank D D2
studying
A 60 (1) 1 4.2 1 0 0
B 57 (2) 2 3.7 5 3 9
C 48 (3) 3 4.0 2 -1 1
D 45 (4) 4 3.5 8.5 4.5 20.25
E 40 (5) 5 3.2 14.5 9.5 90.25
F 38 (6) 6 3.9 3 -3 9
G 35 (7) 7.5 3.3 11 3.5 12.25
H 35 (8) 7.5 3.2 14.5 7 49
I 34 (9) 9 3.1 17.5 8.5 72.25
J 32 (10) 10 3.6 6.5 -3.5 12.25
K 30 (11) 11 3.2 14.5 3.5 12.25
L 29 (12) 12 3.8 4 -8 64
M 28 (13) 13 3.5 8.5 -4.5 20.25
N 27 (14) 14.5 3.2 14.5 0 0
O 27 (15) 14.5 3.3 11 -3.5 12.25
P 20 (16) 16 3.6 6.5 -9.5 90.25
Q 19 (17) 17 3.3 11 -6 36
R 18 (18) 18 3.1 17.5 -0.5 0.25
S 15 (19) 19 2.6 19 0 0
T 13 (20) 20 1.9 20 0 0
Total 0 510.5
Numerator (6 D2) 3063
.Denominator, N=20 (N(N2-1) 7980
Numerator / denominator 0.38
Calculation samples:
Spearmen’s rho :
6∑ D2
rs =1− D ¿ RankDV −Rank IV
N ( N2−1) 2
D(B)=5−2=3 D2 =3 =9
(B )
6 ∑ D2=3060
N ( N2−1)=20 ( 202−1)=20( 400−1)=7980
Part 1
1. Since gamma is a PRE measure, it tells us
A. the improvement in predicting the order of pairs of cases by taking the
independent variable (X) into account
2. A researcher tested the relationship between occupational prestige and level of
approval of a proposal to ban handguns in the province and found a gamma of
-0.17. This means that
A. as prestige goes up, support for the ban goes down
3. Ordinal level scales measuring religiosity and personal happiness range from 1 to
5. Which measure of association would be the most appropriate to assess the
relationship between these two variables?
C. Gamma
4. A study of the effects of fluoride in the water supply on the level of calcium
deficiency in women found a Spearman’s rho of +0.30. Our PRE for this
relationship is
D. 9 %
Part 2
A researcher is interested in identifying the relationship between GPA as an
indicator of academic performance and average number of hours devoted to
studying per week.
a) Based on the results presented in the table above and assuming that at least one
variable is measured at the ORDINAL (CONTINUOUS) level, identify the measure of
association that should be used to assess the relationship between academic
performance and number of hours of study per week.
b) Spearmen’s rho (rs)
, c) Calculate the measure of association identified in question a.
Case Hours of Rank Performance Rank D D2
studying
A 60 (1) 1 4.2 1 0 0
B 57 (2) 2 3.7 5 3 9
C 48 (3) 3 4.0 2 -1 1
D 45 (4) 4 3.5 8.5 4.5 20.25
E 40 (5) 5 3.2 14.5 9.5 90.25
F 38 (6) 6 3.9 3 -3 9
G 35 (7) 7.5 3.3 11 3.5 12.25
H 35 (8) 7.5 3.2 14.5 7 49
I 34 (9) 9 3.1 17.5 8.5 72.25
J 32 (10) 10 3.6 6.5 -3.5 12.25
K 30 (11) 11 3.2 14.5 3.5 12.25
L 29 (12) 12 3.8 4 -8 64
M 28 (13) 13 3.5 8.5 -4.5 20.25
N 27 (14) 14.5 3.2 14.5 0 0
O 27 (15) 14.5 3.3 11 -3.5 12.25
P 20 (16) 16 3.6 6.5 -9.5 90.25
Q 19 (17) 17 3.3 11 -6 36
R 18 (18) 18 3.1 17.5 -0.5 0.25
S 15 (19) 19 2.6 19 0 0
T 13 (20) 20 1.9 20 0 0
Total 0 510.5
Numerator (6 D2) 3063
.Denominator, N=20 (N(N2-1) 7980
Numerator / denominator 0.38
Calculation samples:
Spearmen’s rho :
6∑ D2
rs =1− D ¿ RankDV −Rank IV
N ( N2−1) 2
D(B)=5−2=3 D2 =3 =9
(B )
6 ∑ D2=3060
N ( N2−1)=20 ( 202−1)=20( 400−1)=7980
