Spearman’s Rho
6
Another non-parametric test
Different from anything you’ve done yet
SPEARMAN’S RHO
25.11.13
GOLDSMITHS |PS51008C: DESIGN AND ANALYSIS OF PSYCHOLOGICAL
INVESTIGATIONS
Dr Keon West
Spearman’s Rho
Spearman’s Rho
7
8
Test
Investigate
IV
(Cat /
Cont)
DV
(Cat /
Cont)
Within/
Between
Formula
critical
Test
Chi-square test Chi-square test MannWhitney U
Differences Categorical Either
(ppts.)
Between
ΣR n(n+1)/2
<
Investigate
IV
(Cat /
Cont)
DV
(Cat /
Cont)
Within/
Between
Differences Categorical Categorical Between
Formula
Σ(0 - E)2/E
critical
>
MannWhitney U
Wilcoxon
SignedRank
Wilcoxon
SignedRank
Spearman’s Correlation
Rho
Continuous Continuous Within
/Ordinal
/Ordinal
ρ=
1–
[6(Σd2)/ n(n2-1)] >
Spearman’s
Rho
Spearman’s Rho
Spearman’s Rho
9
10
Test
Investigate
IV
(Cat /
Cont)
DV
(Cat /
Cont)
Within/
Between
Chi-square test Differences Categorical Categorical Between
Σ(0 - E)2/E
MannWhitney U
Differences Categorical Either
(ppts.)
ΣR n(n+1)/2
Test
Investigate
>
Chi-square test Differences Categorical Categorical Between
Σ(0 - E)2/E
>
<
MannWhitney U
Differences Categorical Either
(ppts.)
Between
ΣR n(n+1)/2
<
Wilcoxon
SignedRank
Between
Formula
critical
Differences Categorical Either
(condition)
Within
ΣR
<
Wilcoxon
SignedRank
Spearman’s Correlation
Rho
Continuous Continuous Within
/Ordinal
/Ordinal
ρ=
1–
[6(Σd2)/ n(n2-1)] >
Spearman’s
Rho
IV
(Cat /
Cont)
DV
(Cat /
Cont)
Within/
Between
Formula
critical
ρ=
1–
[6(Σd2)/ n(n2-1)] 1
11/20/13
Spearman’s Rho
Spearman’s Rho
11
12
Test
Investigate
Chi-square test Differences Categorical Categorical Between
Σ(0 - E)2/E
DV
(Cat /
Cont)
Within/
Between
MannWhitney U
Differences Categorical Either
(ppts.)
Between
ΣR n(n+1)/2
<
Wilcoxon
SignedRank
Differences Categorical Either
(condition)
Within
ΣR
<
ρ=
1–
[6(Σd2)/ n(n2-1)] >
Continuous Continuous Within
/Ordinal
/Ordinal
Formula
>
Spearman’s Correlation
Rho
IV
(Cat /
Cont)
critical
Used to investigate continuous or ordinal independent variables dependent variables:
Continuous:
Ordinal
Continuous:
Age,
height . . .
Ordinal
Year
in uni, place in a race . . .
Spearman’s Rho
Spearman’s Rho
Grade at end of term
14
Grade at end of term
13
Lectures attended
# of relationships per term
Spearman’s Rho
Spearman’s Rho
15
16
Correlations range between -1 and +1
?
2
11/20/13
Spearman’s Rho
Spearman’s Rho
18
Grade at end of term
How do we condense this into one number?
How do we condense this into one number?
Grade at end of term
17
Compare the ranks of grades to the ranks of the lectures Hours studying
Hours studying
Spearman’s Rho
Spearman’s Rho
20
Grade at end of term
How do we condense this into one number?
Compare the ranks of grades to the ranks of the lectures How do we condense this into one number?
Grade at end of term
19
ρ= 1–
Keeping track of the number of students
Hours studying
6(Σd2)
_________
n (n2 - 1)
Hours studying
Spearman’s Rho
Spearman’s Rho
21
22
Student
Hours
Studying
Position in Class
Emma
60
Paula
88
Temi
Studying
Rank
Class
Rank
Difference d2 between ranks
Student
Hours
Studying
Position in Class
Studying
Rank
6
Emma
60
6
Paula
88
3
1
65
5
Temi
65
5
5
Farzana
70
4
Farzana
70
4
3
Shredder
33
7
Shredder
33
7
7