11/20/13

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