|
1. "Correlation analysis deals with
the association between two or more variables." -
Simpson & Kafka.
2. "Correlation analysis attempts to determine
the 'degree of relationship' between variables." -
Ya Lun Chou.
3. "Correlation is an analysis of the covariation
between two or more variables." -
A.M. Tuttle.
Karl Pearson's coefficient of correlation
| |
|
[n å
xy - (å x X
å y)]
|
| r = |
|
|
| |
|
{[n å
x2 - (å
x)2] X [n å
y2 - (å
y)2]}
|
Where:
x = variable 1
y = variable 2
n = number of pair of scores
r = coefficient of linear correlation
Q. 1. Calculate the correlation coefficient
for the following data: (June
2002)
| x
|
8 |
12 |
15 |
20 |
24 |
27 |
32 |
| y
|
30 |
24 |
36 |
44 |
56 |
64 |
72 |
Solution.
| x |
y |
x2
|
y2
|
x X y |
|
8 |
30 |
64
|
900
|
240
|
|
12 |
24 |
144
|
576
|
288
|
|
15 |
36 |
225
|
1296
|
540
|
|
20 |
44 |
400
|
1936
|
880
|
|
24 |
56 |
576
|
3136
|
1344
|
|
27 |
64 |
729
|
4096
|
1728
|
|
32 |
72 |
1024
|
5184
|
2304
|
|
å x = 138
|
å y = 326
|
å
x2 = 3162 |
å
y2 = 17124 |
å
xy = 7324 |
Here, n = 7
| |
|
[n å
xy - (å x X
å y)]
|
| r = |
|
|
| |
|
{[n å
x2 - (å
x)2] X [n å
y2 - (å
y)2]}
|
| |
|
[(7 X 7324) - (138 X 326)]
|
| or r = |
|
|
| |
|
{[(7 X 3162) - (138)2]
X [(7 X 17124) - (326)2]}
|
or r = 0.969
| Note: Coefficient of correlation
lies between +1 and -1. |
|
