A)
Computation of Pearson Product-Moment Correlation Coefficient
The
scores obtained by a group of 10 children on two tests, viz., spelling and
comprehension are given below :
| Name |
Spelling Test (X) |
Comprehension test (Y) |
|
Shanti |
31 |
7 |
|
Elango |
28 |
18 |
|
Ponnaruvi |
38 |
12 |
|
Mangaiyar |
22 |
6 |
|
Janaki |
24 |
8 |
|
Mahendra |
26 |
5 |
|
Nagajothi |
31 |
14 |
|
Arungalai |
31 |
10 |
|
Arumbu |
37 |
13 |
|
Meena |
30 |
17 |
| Name |
X |
Y |
x |
y |
x2 |
y2 |
xy |
|
1 |
31 |
7 |
+1 |
-4 |
1 |
16 |
4 |
|
2 |
28 |
18 |
-2 |
+7 |
4 |
49 |
-14 |
|
3 |
38 |
12 |
+8 |
+1 |
64 |
1 |
8 |
|
4 |
22 |
6 |
-8 |
-5 |
64 |
25 |
40 |
|
5 |
24 |
8 |
-6 |
-3 |
36 |
9 |
18 |
|
6 |
26 |
5 |
-4 |
-6 |
16 |
36 |
24 |
|
7 |
31 |
14 |
+1 |
+3 |
1 |
9 |
3 |
|
8 |
33 |
10 |
+3 |
-1 |
9 |
1 |
-3 |
|
9 |
37 |
13 |
+7 |
+2 |
49 |
4 |
14 |
|
10 |
30 |
17 |
0 |
+6 |
0 |
36 |
0 |
|
å M |
300 30 |
110 11 |
0 |
0 |
244 |
186 |
86 |
σx
= 244/10
= 24.40 =
4.94
σy
= 186/10
= 18.60 =
4.31
åxy 86 86
rxy = ------------ = ------------------------ = ------------ = .40
N σx σy (10)(4.94)(4.31) 212.91
\ The Pearson product-moment correlation coefficient is
i.e., rxy = 0.40
B)
Computation of Rank Order Correlation Coefficient
Two tests were
administered to a group of 12 teacher-trainees. The scores obtained by them
are given below :
| Name |
Maximum 40 |
Maximum 40 |
|
|
40 39 38 37 36 35 34 32 31 30 29 27 |
38 40 35 37 39 31 28 34 27 30 33 29 |
Subsequently the scores obtained by them in both the tests are correlated by using the Rank order Correlation Method.
| Name |
Ranks obtained |
Difference (D) |
D2 | |
|
Test-I |
Test-II | |||
|
1 2 3 4 5 6 7 8 9 10 11 12 |
1 2 3 4 5 6 7 8 9 10 11 12 |
3 1 5 4 2 8 11 6 12 9 7 10 |
2 1 2 0 3 2 4 2 3 1 4 2 |
4 1 4 0 9 4 16 4 9 1 16 4 |
|
|
ådi2 = 72 | |||
The correlation between the ranks of the trainees is calculated through the following formula :
P
= 1 -
6ådi2___
n-(n2-1)
= 1 - 6 x 72__ = 1 - 432__ = 1716 - 432
12 (144-1) 1716 1716
= 1284_ = 0.74825 = 0.75
1716
From
the value obtained (P), it can be interpreted that the correlation of ranks between
the two tests are appreciable.