For paired measurements, such as individual weight and height, sum of products of z scores, divided by number of individuals, makes a number {correlation coefficient}| between -1 and +1. Correlation coefficient R measures relations between two variables: R^2 = SSR/SST = 1 - SSE/SST, where SSR is residual sum of squares, SST is term sum of squares, and SSE is error sum of squares.
z scores
Sum from i = 1 to i = N of z1(i) * z2(i) / N, where z is z score and N is population size.
means
Sum from i = 1 to i = N of (n1(i) * n2(i) / N - x1 * x2) / (s1 * s2), where n is value, x is mean, s is standard deviation, and N is population size.
values
(N * (sum from i = 1 to i = N of n1(i) * n2(i)) - (sum from i = 1 to i = N of n1(i)) * (sum from i = 1 to i = N of n2(i))) / ((N * (sum from i = 1 to i = N of (n1(i))^2) - (sum from i = 1 to i = N of n1(i)) * (sum from i = 1 to i = N of n1(i)))^0.5) * ((N * (sum from i = 1 to i = N of (n2(i))^2) - (sum from i = 1 to i = N of n2(i)) * (sum from i = 1 to i = N of n2(i)))^0.5).
Mathematical Sciences>Statistics>Correlation
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Date Modified: 2022.0224