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Descriptive Statistics - Spearman Rank Order Correlation

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[Rank Order Correlation] [Non Corrected] [Corrected] [t Test] [z Test]

Data

Example Data Set ()

Computations 1

Note: a "mean rank" is assigned if 2 or more data values are equal (e.g. Student C and L both have a score of 25 corresponding to a mean rank of 5.5 = (5+6)/2)

Student Variable x Variable y
Score Rank Score Rank di di
A 30 11.0 70 10.5 +0.5 0.25
B 30 11.0 70 10.5 +0.5 0.25
C 25 5.5 68 7.5 -2.0 4.00
D 27 7.5 63 5.0 +2.5 6.25
E 23 3.0 52 2.5 +0.5 0.25
F 21 1.0 50 1.0 +0.0 0.00
G 27 7.5 68 7.5 +0.0 0.00
H 23 3.0 59 4.0 -1.0 1.00
I 23 3.0 52 2.5 +0.5 0.25
J 30 11.0 70 10.5 +0.5 0.25
K 28 9.0 70 10.5 -1.5 2.25
L 25 5.5 64 6.0 -0.5 0.25
15.00

Computations 2 : Rank Order Correlation - Not corrected

Descriptive Statistics - Spearman Rank Order Correlation

Computations 3 : Rank Order Correlation - Corrected

Computations 4 : t-Test Statistic

Computations 5 : z-Test Statistic

Output: Numerical

+-----------------------------------+
 SPEARMAN RANK ORDER CORRELATION 1 
+-----------------------------------+

RESULTS RANK ORDER CORRELATION

Correlation not Corrected :       .947552
                Corrected :       .945461

t-Test Statistic    Value :      9.178631
       Degrees of Freedom :     10
              Probability :       .000002


D-Square Value Calculated :     15.000000
                 Expected :    286.000000
       Standard Deviation :     86.232245

z-Test Statistic    Value :     -3.142676
              Probability :       .999163

Number of Observations    :     12

+-----------------------------------+
 SPEARMAN RANK ORDER CORRELATION 2 
+-----------------------------------+

LS RESULTS FOR RANKED DATA

Regression         Intercept :       .376812
                       Slope :       .942029

Coefficient of   Correlation :       .945461
Coefficient of Determination :       .893896

() Cohen, L. and Holliday, M.

Statistics for the Social Scientists

Harper & Row, London, 1982, p. 155.

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