Descriptive Statistics

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	d_i	d_i²
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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