I have two data setw A and B.
A=10 readings of output, and avg of data with sigmaA standard Dev
B = 10 reading of an other results and avg with sigmaB standard dve
i want = + ( average of each ) with sigmaC stadard dev
how to calculate sigmaC,?
so simple.
Var (C) = Var (A+B) = Var (A) + Var (B) + 2 Cov (A, B)
Therefore
(sigmaC)2 = (sigmaA)2 + (sigmaB)2 + 2 Cov (A, B)
(sigmaC)2 = (sigmaA)2 + (sigmaB)2 + 2 Sum { (Ai - avg A)(Bj - avg B) } / 9
Therefore
sigmaC = square root [(sigmaC)2]
= square root [(sigmaA)2 + (sigmaB)2 + 2 Sum { (Ai - avg A)(Bj - avg B) } / 9]
Hello Sikander,
The variance of a sum is:
Var(A + B) = Var(A) + Var(B) + 2*Cov(A,B)
or, equivalently:
Var(A + B) = Var(A) + Var(B) + 2*r(A,B)*SD(A)*SD(B)
where r(A,B) is the Pearson correlation of the paired scores across cases, and SD indicates standard deviation.
Note the addition sign ("+") is used for the covariance term, not the minus sign. If you were computing the variance of a difference (e.g., A - B), then Abolfazl Ghoodjani 's answer would be correct.
Good luck with your work.
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