Friday, August 2, 2013

Degrees of Freedom


By Julie Rahm

In statistics, the number of “degrees of freedom” is the number of values in the final calculation of a statistic that are free to vary. The number of independent ways by which a dynamic system can move without violating any constraint imposed on it, is called “degree of freedom”. In other words, the degree of freedom can be defined as the minimum number of independent coordinates which can specify the position of the system completely. Or, stated another way.
Estimates of statistical parameters can be based upon different amounts of information or data. The number of independent pieces of information that go into the estimate of a parameter is called the “degrees of freedom”. Restated, the degrees of freedom of an estimate of a parameter is equal to the number of independent scores that go into the estimate minus the number of parameters used as intermediate steps in the estimation of the parameter itself. (I know. A visual would be helpful!) Degrees of freedom are required to find a confidence interval or test a hypothesis about the average using a t-distribution for a given sample size. Of course we would use a t-distribution if the population is normally distributed, the standard deviation of the population is unknown and the sample size is less than thirty. Got that? Let me use an example.
Three children have three different cards, a one, five and ten. The first two children draw one card each. The last child to draw has no choice and will get the card that remains. In this example, there are two degrees of freedom. Another good example is the average of ten numbers. If the average of ten numbers is a specified value, one can pick the first nine numbers at random. The first nine can be any value. But, the last number can only be one value in order to bring the given average back to the specified value. In this example, there are nine degrees of freedom. So, I tell you about the degrees of freedom in order to tell you this metaphor.
We all make many choices every day of our lives. Some choices are mundane. But, other choices are hugely significant. For example, your choice in clothing today is probably not very significant in the long term. But, your choice in a spouse is significant. Choosing not to attend college is another significant choice. With these significant strategic type choices, you are using up your degrees of freedom. A succession of poor choices will limit your potential. Poor choices manifest low degrees of freedom. Do not cast your die prematurely. Be thoughtful with your choices. Sadly, I coach many clients who have chosen poorly. The list is extensive. But, most involve a series of choices that culminate in a predicament. So, my message this week is choose wisely to preserve the freedom of choice in your life.
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