I am trying to learn the basics:) Could anybody explain why a degree of freedom is required (used) while calculating a statistic from a sample. While dealing with population, we don’t use degree of freedom to calculate a parameter. Don’t you think the application of degree of freedom distort the statistical value calculated from a sample? Thanks kochunni
Degree of freedom is just one of the parameters of a distribution. There is nothing special about it compare to other distribution parameters. Frankly speaking your question doesn’t make any sense if you know the meaning of degree of freedom.
The way to think about degrees of freedom is that degrees of freedom is about how much information you have in estimating the variability. Each observation gives you 1 d.f. but if you have to estimate the center of the data you lose one for estimating one thing. If you estimate two things you lose two df’s. Etc… For example, a) n degrees of freedom: I estimate variance in my problem using Sum(X(i) - Mu)^2 b) n - 1 df: I estimate variance in my problem using Sum(X(i) - X-bar)^2 c) n - 2 df: I estimate variance in my problem using Sum(Y(i) - a + b*X(i))^2 (where I’ve used the data to estimate a and b)