nship is as follows:

=================================================================
|ARITH- | | | | | |
|METIC | x | x^2 |Spelling | y | y^2 | x.y
--+-------+----+-----------+---------+----+-------------+--------
| | | | | | | - +
A | 2 | -2 | 4 | 12 | +4 | 16 | -8 +6
B | 1 | -3 | 9 | 8 | 0 | | 0 +4
C | 4 | 0 | | 2 | -6 | 36 | 0 +4
D | 5 | +1 | 1 | 14 | +6 | 36 | -6
E | 3 | -1 | 1 | 4 | -4 | 16 | -14 +14
F | 7 | +3 | 9 | 6 | -2 | 4 |
G | 6 | +2 | 4 | 10 | +2 | 4 |
| ____| | | ___ | | |
| |28 | |Sum x^2=28 | 7|56 | | Sum y^2=112 | x.y=0
| AV.=4 | | | AV.=8 | | |
===================================================================

(Sum x.y) 0
r = ---------------------------- = ------------------- = 0.
(sqrt(Sum x^2)sqrt(Sum y^2)) (sqrt(28)sqrt(112))

In a similar manner, when the relationship is largely positive as would
be indicated by a displacement of each score in the series by one step
from the arrangement which gives a +1 coefficient, the coefficient will
approach unity in value.

===============================================================
ARITHMETIC| x | x^2 |SPELLING| y | y^2 |
---+------+----+-----------+--------+----+------------+--------
A |1 | -3 |9 |4 | -4 | 16 |+ 12
B |2 | -2 |4 |2 | -6 | 36 |+ 12
C |3 | -1 |1 |8 | 0 | |+ 4
D |4 | 0 | |6 | -2 | 4 |+ 4
E |5 | +1 |1 |12 | +4 | 16 |+ 18
F |6 | +2 |4 |10 | +2 | 4 |Sx.y=50
G |7 | +3 |9 |14 | +6 | 36 |
|Av. =4| |Sum x^2 =28|Av. = 8 | |Sum y^2= 112|
===============================================================

Sum x.y +50
r= -------------------------- = ---- = +.89.
sqrt(Sum x^2)sqrt(Sum y^2) 56

Other illustrations might be given to show how