Explaining the Total Degrees of Freedom for Six Sigma Practitioners

# Explaining the Total Degrees of Freedom for Six Sigma Practitioners

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Explaining the Total Degrees of Freedom for Six Sigma Practitioners Tags: E. George Woodley | degrees of freedom statistics | Six Sigma practitioners | degrees of freedom | analysis of variance | Six Sigma | statistical analysis | Methodologies, Statistical Analysis, and Tools We, as statisticians, Six Sigma Belts and quality practitioners have utilized the term degrees of freedom as a part of our hypothesis testing, such as the t-test for comparison of two means and ANOVA (Analysis of Variance), as well as confidence intervals, to mention a few references. I can recall from the many classes I have taught from Six Sigma Green Belts to Six Sigma Master Black Belts inclusive, that students have had a bit of a problem grasping the whole idea of the degrees of freedom , especially when we describe the concept of the standard deviation: …the average distance of the data from the MEAN… 1 By now, Six Sigma practitioners should have a comfort level with concepts like the MEAN ; which is calculated by taking the sum of all the observations, and dividing by the number of observations ( n ). The total degrees of freedom are then represented as ( n-1 ). Defining Degrees of Freedom One method for describing the degrees of freedom , as per William Gosset, has been stated as, “The general idea: given that n pieces of data x 1 , x 2 , … x n , you use one ‘degree of freedom’ when you compute μ, leaving n-1 independent pieces of information.” 2 This was reflected in the approach summarized by one of my former professors. He stated that

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