adding weighted deviations

Discussion in 'Scientific Statistics Math' started by Dal Mon, Nov 11, 2010.

  1. Dal Mon

    Dal Mon Guest

    I have two independent distributions with

    stdev1 = 3.5
    stdev2 = 4.1

    To get the combined std dev it's usually just

    sqrt(stdev1 ^ 2 + stdev2 ^ 2)

    But let's say I want to incorporate weight

    weight1 = .95
    weight2 = .05

    Is it simply sqrt(weight1 * (stdev1 ^ 2) + weight2 * ( stdev2 ^ 2)) ?
    Dal Mon, Nov 11, 2010
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  2. Dal Mon

    Rich Ulrich Guest

    You want to be more specific with your operations here,
    and use different terminology.

    I don't think I would use the phrase, "combined SD" for
    anything except for the value of the SD after pooling
    two samples. (That's a different formula, and also requires
    the Ns and the means.)

    The sum of the variances is what you get as the variance
    of the sum of two uncorrelated scores. Is that what you
    have in mind?
    var (A + B) = var(A) + var(B).
    Also, keep in mind that SD(b*A) = b* SD(A) implies that
    var (b*A) = (b^2)* var(A).
    I can't tell you that you are necessarily wrong because I don't
    know what you mean by "incorporate weight."

    But that is wrong if you are looking for the
    variance of Total= 0.95*X1 + 0.05*X2 .
    Rich Ulrich, Nov 12, 2010
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