Concurrent Deviation
The method of studying the correlation is the simplest of all methods. The only thing that is needed under this method is to find out the direction of change of X variable and Y variable. The formula for the concurrent deviation is shown below:
RC = ± √[± (2 c-)/ n]
Where RC stands for coefficient of correlation by the concurrent method; C stands for the number of concurrent deviations or the number of positive signs obtained after multiplying Dx with Dy.
N = number of pairs of compared observations.
Steps:
1) At first find out the direction of change of x variable as compared with the first value whether the second value is increasing or decreasing or is constant. If it is increasing put a + sign (plus); and if it is decreasing put a - sign (minus) & if it is constant put zero. In the same way as compared to second value, find out whether the third value is increasing, decreasing or constant. Repeat the similar process for other values. Represent this column by Dx.
2) In the similar manner as discussed above find out the direction of change of y variable and represent this column by Dy.
3) Multiply the Dx with Dy and determine the value of C. the number of positive sign
4) Now apply the above formula
RC = ± √[± (2 c-)/ n]
Illustration: Find the coefficient of concurrent deviation from the following
|
X
|
60
|
55
|
50
|
56
|
30
|
70
|
40
|
35
|
80
|
80
|
75
|
|
Y
|
65
|
40
|
35
|
75
|
63
|
80
|
35
|
20
|
80
|
60
|
60
|
Solution
Calculation of correlation by concurrent deviation method
|
X
|
Dx
|
Y
|
Dy
|
DxDy
|
|
60
|
|
65
|
|
+
|
|
55
|
-
|
470
|
-
|
+
|
|
50
|
-
|
35
|
-
|
+
|
|
56
|
+
|
75
|
+
|
+
|
|
30
|
-
|
63
|
-
|
+
|
|
70
|
+
|
80
|
+
|
+
|
|
40
|
-
|
35
|
-
|
+
|
|
35
|
-
|
20
|
-
|
+
|
|
80
|
+
|
80
|
+
|
+
|
|
80
|
0
|
60
|
0
|
0
|
|
75
|
-
|
60
|
0
|
0
|
|
|
|
|
|
C = 8
|
Rc = ± √(± 2 C-n)/n = ± √(± 2 x 8-10 /10) = √(6/10) = 0.774