Calculating sums of squaresmain topic
Calculating sums of squaresSums of Squares (SS) and standard deviations are closely related - standard deviations are just sums of squares divided by the appropriate degrees of freedom. Consider the following formulas and notation:
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SS Total = SS Within + SS Between |
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SS Total is the sum of all squared deviations of individual observations from the overall process mean. |
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SS Total = |
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SS Within is the sum of all squared deviations of individual observations from their subgroup means. |
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SS Within = |
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SS Between is the sum of squared deviations of subgroup means from the overall process mean. |
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SS Between = |
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where:
Xik
= kth data
of the ith
subgroup
mi = mean
of ith subgroup
mLT =
overall process mean
Thus, SS Within is purely a function of the inherent variation of the process, while SS Between is a function of the natural variation in subgroup means as well as changes in subgroup means caused by shifts and drifts in the process mean.
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