The process of estimating the mean affects our degrees of freedom as shown below. Instead, we have to first estimate the population mean (\(\mu\)) with the sample mean (\(M\)). The estimates would not be independent if after sampling one Martian, we decided to choose its brother as our second Martian.Īs you are probably thinking, it is pretty rare that we know the population mean when we are estimating the variance. The two estimates are independent because they are based on two independently and randomly selected Martians. Since this estimate is based on two independent pieces of information, it has two degrees of freedom. We could then average our two estimates (\(4\) and \(1\)) to obtain an estimate of \(2.5\). If we sampled another Martian and obtained a height of \(5\), then we could compute a second estimate of the variance, \((5-6)^2 = 1\). This estimate is based on a single piece of information and therefore has \(1\ df\). Therefore, based on this sample of one, we would estimate that the population variance is \(4\). This single squared deviation from the mean, \((8-6)^2 = 4\), is an estimate of the mean squared deviation for all Martians. We can compute the squared deviation of our value of \(8\) from the population mean of \(6\) to find a single squared deviation from the mean. Recall that the variance is defined as the mean squared deviation of the values from their population mean. We randomly sample one Martian and find that its height is \(8\). The degrees of freedom (\(df\)) of an estimate is the number of independent pieces of information on which the estimate is based.Īs an example, let's say that we know that the mean height of Martians is \(6\) and wish to estimate the variance of their heights. For example, an estimate of the variance based on a sample size of \(100\) is based on more information than an estimate of the variance based on a sample size of \(5\). Some estimates are based on more information than others.
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |