The values would reflect the actual observations of a given data set. A definition that can also be representative of the concept of the degrees of freedom can be summarized as "equal to the number of independent pieces of information concerning the variance."3 For a random sample from a population, the number of degrees of freedom is equal to the sample size minus 1.Ī numerical example of this approach might illustrate this. This may seem very elementary, but from my own experiences, degrees of freedom have not been the easiest of concepts to comprehend-especially for the novice Six Sigma belt. Since we assume populations are infinite and cannot be easily accessed to generate parameters, we rely on samples to generate statistical inferences that provide estimates of the original population, provided the sampling techniques are both random and representative another discussion for later. He stated that the degrees of freedom represented the total number of observations minus the number of population parameters that are being estimated by a specific statistical test. This was reflected in the approach summarized by one of my former professors. 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 x1, x2, … xn, you use one ‘degree of freedom’ when you compute μ, leaving n-1 independent pieces of information."2 The total degrees of freedom are then represented as ( n-1). 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).
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.
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