Topic: Correlation Analysis

1

• Session 3
• Topic Correlation Analysis
• Faculty Ms Prathima Bhat K
• Department of Management Studies
• Acharya Institute of Technology
• Bangalore 90
• Contact prathimabhatk_at_gmail.com
• 9242187131

2

• In two sets of variables X Y with 50
• observations each, following data was observed
  AM of X is 10 SD of X is 3 AM of Y is 6 SD of
  Y is 2 coefficient of correlation is 0.3.
  However after subsequent verification one pair
  (10,6) was weeded out. What is the change in the
  correlation coefficient with the remaining 49
  pairs of values?

3
PROBABLE ERROR
After computing correlation coefficient, the next
step is to find the extent to which it is
dependable. Probable Error is a old measure of
testing the reliability of the observed values.
PE (r) SE (r) 0.6745
r lt PE (r) r is not at all significant r gt 6
PE (r) r is significant other cases nothing
can be concluded with certainty.
4
r 0.7804
5
r
nS dx.dy - Sdx. Sdy
vnSdx2 (Sdx)2. nS dy2 -(Sdy)2
r
10141 (2)2
v10140 (-2)2 . 10176 (2)2
r 0.90
6
PE (r) SE (r) 0.6745
PE (r) 0.0600 0.6745
SE (r) 0.0600
SE (r) 0.0405
0.9 gt 6 PE (r) i.e.,0.2432 r is highly
significant
7
IMPORTANT FORMULAS
8
Bivariate Frequency Distribution
9
-3
-14
-6
5
-14
-12
16
-20
10
(No Transcript)
11
(No Transcript)
12
-12
-4
-5
-3
-4
-4
-6
13
40(-38) 96 v(4047)-(9)2 v(4050)-(6)2
r -0.8373
14
ALGEBRAIC METHOD (RANK CORRELATION METHOD)
When ranks are not repeated
When ranks are repeated
15
r 0.7804
l 0.51
16
r 0.7804
l 0.82
17
r 0.7804
l 0.7333
18
ALGEBRAIC METHOD (CONCURRENT DEVIATIONS)
19
r -1
r 0.7804