Page 178 - DMGT404 RESEARCH_METHODOLOGY

Research Methodology

Notes Solution:

Student Reading (X) Spelling (Y) X –  x Y –  y (X – x) (Y –  y)
1 3 11 – 2.5 0.7 – 1.75
2 7 1 1.5 – 9.3 – 13.95
3 2 19 – 3.5 8.7 – 30.45
4 9 5 3.5 – 5.3 – 18.55
5 8 17 2.5 6.7 16.75
6 4 3 – 1.5 – 7.3 10.95
7 1 15 – 4.5 4.7 – 21.15
8 10 9 4.5 – 1.3 – 5.85
9 6 15 0.5 4.7 2.35
10 5 8 – 0.5 – 2.3 1.15
Sum 55 103 0.0 0.0 – 60.5
Mean 5.5 10.3
Standard 2.872 5.832
Deviation

Using the correlation formula;
S (X - m )(Y - m )
r = x y
Ns s y
x

- 60.5 - 60.5
= = = - 0.36
(10)(2.872)(5.832) 167.495
However, in real practice, we use the computational or raw score formula for the correlation
coefficient:

N XY - ( X )( Y )
S
S
S
r =
N X - ( X ) 2 N Y - ( Y ) 2
S
S
S
S
2
2
Where:
(i) N is the number of subjects
(ii) SXY is the sum of each subject X score times the Y score,
(iii) SX is the sum of the X scores
(iv) SY is the sum of the Y scores
2
(v) SX is the sum of the squared X scores
2
(vi) SY is the sum of the squared Y scores,
Correlation between Reading and Spelling for the data given in example using Computational
Formula:
S
S
S
N XY - ( X )( Y )
r =
N X - ( X ) 2 N Y - ( Y ) 2
S
S
S
S
2
2
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