Six Sigma Green Belt Certification Practice Exam

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When performing a one-way ANOVA, how is the treatment sum of squares calculated?

  1. By finding the difference between the total degrees of freedom and the treatment degrees of freedom

  2. By finding the sum of the squared deviations of each observation within a treatment from the treatment average

  3. By finding the sum of the squared deviations of each treatment average from the grand average

  4. By finding the difference between the crude sum of squares and the correction factor

The correct answer is: By finding the sum of the squared deviations of each treatment average from the grand average

The treatment sum of squares in a one-way ANOVA is calculated by finding the sum of the squared deviations of each treatment average from the grand average. This measure helps to quantify how much the treatment means vary from the overall mean of all the data combined. When the treatment means differ significantly from the grand mean, it indicates that changes in the treatment levels are likely having an effect on the response variable. In this calculation, each treatment average is subtracted from the grand average, and the result is squared to eliminate any negative values. Multiplying each squared deviation by the number of observations in that treatment gives the overall treatment sum of squares. This is crucial because it allows ANOVA to evaluate whether the between-treatment variability is greater than the within-treatment variability. The other choices present different concepts related to ANOVA, such as the degrees of freedom or within-treatment variability, but they do not correctly define the treatment sum of squares as it specifically relates to the average differences among the treatment groups compared to the overall mean.

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