What, exactly, are degrees of freedom?There is actually a very simple explanation that leads to a slightly better understanding of what goes on in statistics. It goes something like this…Let’s take a look at the equation for standard deviation:You should notice that, in this equation, we subtract the average from each observation of X. But, there is a problem with simply average these deviations because if we simply add all values of X- we would get 0. That is why we need to square each of these deviations, and then take the square root.Here’s where degrees of freedom comes in: if we know that simply adding all deviations together gets ananswer of zero, then we don’t need to know the last observation. We know the average and we know that all X- must equal zero. Therefore, if we have 10 observations and have measured X- for 9 of those observations, we need not know the last observation because the last observation must make the sum of all X- equal to zero.Observations X-1 -4.52 -3.53 -2.54 -1.55 -0.56 0.57 1.58 2.59 3.5??? ???Average = 5.5In this example, the last observation is ten because the average is 5.5 and the last observation must havea value of X- that makes the second column equal to zero.Any time something like this happens in statistics, we lose degrees of freedom which is why we use n-1 degrees of freedom for the calculation of standard
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