What Is Degrees of Freedom-ECO6416

What Is Degrees of Freedom-ECO6416 - What Is "Degrees...

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What Is “Degrees of Freedom"? Recall that in estimating the population's variance, we used (n-1) rather than n, in the denominator. The factor (n-1) is called “degrees of freedom." Estimation of the Population Variance: Variance in a population is defined as the average of squared deviations from the population mean. If we draw a random sample of n cases from a population where the mean is known, we can estimate the population variance in an intuitive way. We sum the deviations of scores from the population mean and divide this sum by n. This estimate is based on n independent pieces of information, and we have n degrees of freedom. Each of the n observations, including the last one, is unconstrained ('free' to vary). When we do not know the population's mean, we can still estimate the population variance; but, now we compute deviations around the sample mean. This introduces an important constraint because the sum of the deviations around the sample mean is known to be zero. If we know the value for the first (n-1) deviations, the last one is known. There are only n-1 independent pieces of information in this estimate of variance. If you study a system with n parameters x i , i =1. .., n, you can represent it in an n-dimension space. Any point of this space shall represent a potential state of your system. If your n parameters could vary independently, then your system would be fully described in a n- dimension hyper-volume (for n over 3). Now, imagine you have one constraint between the
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What Is Degrees of Freedom-ECO6416 - What Is "Degrees...

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