Sum = is the sign commonly used to indicate the algebraic sum (_i.e._ the difference between the sum of the minus quantities and the plus quantities). _x · y _= products of deviation in one trait multiplied by deviation in the other trait with appropriate sign. Applying the formula we find: =================================================================== |ARITH-| | | SPEL- | | | | |METIC | x | x^2 | LING | y | y^2 | x·y | --+------+---+------------+-------+---+-------------+-------------+ A | 1|-3 | 9| 2|-6 | 36| +18| B | 2|-2 | 4| 4|-4 | 16| +8| C | 3|-1 | 1| 6|-2 | 4| +2| D | 4| 0 | 0| 8| 0 | | | E | 5|+1 | 1| 10|+2 | 4| +2| F | 6|+2 | 4| 12|+4 | 16| +8| G | 7|+3 | 9| 14|+6 | 36| +18| | ___| | __| ___| | ___| __| | 7 |28| |Sum x^2 = 28| 7 |56| |Sum y^2 = 112|Sum x·y = +56| |Av. =4| | |Av. =8 | | | | =================================================================== Sum x · y +56 +56 r = ---------------------------- = --------------------- = ---- = +1 (sqrt(Sum x^2)(sqrt(Sum y^2) (sqrt(28))(sqrt(112)) 56 If instead of achievement in one field being positively related (going together) in the highest possible degree, these individuals show the opposite type of relationship, _i.e.,_ the maximum negative relationship (this might be expressed as opposition--a place above the average in one achievement going with a correspondingly great deviation below the average in the other achievement), then our coefficient becomes -1. Applying the formula: