Developmental psychology.pdf

526 Psychology and Society
Figure 19.14
Computation of Rank-Order
Correlation. The first step is to
convert all scores to ranks. Then the
difference (D) is determined between
the two ranks in each case- Squaring
is used for weighing purposes, and
the sum of these squares is divided
by an expression of N, representing
the number of pairs of scores
involved. Also a constant, 6, is
included, and the result is subtracted
from 1. The formula becomes:
6 (sum D 2 )
rho = 1 - •
N (N 2 - 1)
As can be seen by inspection of
the formula, when the differences (D)
are zero, the numerator becomes
zero and therefore the whole fraction
is zero, leaving nothing except
+1.00, a perfect correlation. As the
differences increase, the correlation
decreases.
Fingers
Right index
Left index
Right middle
Left middle
Right ring
Left ring
Right little
Left little
Sum D 2 = 48
6(Sum D 2 )
rhn 1 (\(\
rho = 1.00 -
rho = .43
Ability
161
143
134
121
101
99
115
106
N(N 2 - 1)
6(48)
8(63)
.57
Scores
Workload
1,490
1,535
640
1,492
996
658
296
803
Ability
1
2
3
4
7
8
5
6
Ranks
Workload
3
1
7
2
4
6
8
5
D
2
1
4
2
3
2
3
1
D 2
4
1
16
4
9
4
9
1
48
When these ranks are compared, it is noted that the ranking for finger ability
is different from that for finger workload. The difference between these rankings is the
critical issue in this method of determining the correlation.
The difference between ranks is then squared, summed, and entered into a
formula, which yields a coefficient of +0.43. This value also shows a moderate relationship
between finger ability and workload (Figure 19.14).
Interpretating the Coefficient In understanding the significance of this value, we
notice first that the correlation is positive, meaning that high scores on one variable
are associated with high scores on the other; low scores on one variable are associated
with low scores on the other. But we also notice that the size of the coefficient is only
moderate. Considering the extremely wide usage of the standard keyboard in today's
world, this relationship of +0.43 is not as high as one might hope. There are instances
in which more capable fingers are doing less work than less capable ones. The middle
finger on the right hand is third in ability, yet it has the next-to-lowest workload of all
eight fingers.
This correlation, or any other, does not indicate that one variable causes the
other. It does not mean that finger ability causes workload or vice versa. Sometimes a
third factor is involved, such as Scholes's preference when he assembled the keyboard.
Among children, weight and memory are positively correlated, but one would not conclude
that gaining weight improves a child's memory. Both conditions increase with a
third variable, age. The influence of age becomes evident when we correlate weight
and memory in children of the same age, for then the relationship is negligible.
Furthermore, a correlation does not indicate percentage. A coefficient of +0.43
indicates considerably less than 43 percent interdependence between these two variables.
It merely shows the degree to which two variables increase and decrease together
in magnitude.