Which term refers to the amount of information free to vary when estimating a statistical parameter?

Which term refers to the amount of information free to vary when estimating a statistical parameter?

• A. Degrees of freedom
• B. Standard error
• C. Sample size
• D. Population size

Answer: (A)

Degrees of freedom describe how many pieces of information in the data can vary independently after you've fixed certain quantities when estimating a parameter. When you estimate a statistic from n observations, some information is consumed by the estimation itself (for example, the mean is being set), so only a portion can vary freely. A common way this shows up is that, for estimating the variance around a sample mean, you have n minus 1 independent pieces of variation, because once the mean is fixed, the deviations are not all free to vary independently. This concept carries into many analyses: the degrees of freedom often equal the number of observations minus the number of parameters estimated (such as the mean, regression coefficients, etc.). That remaining freedom influences the shape of sampling distributions and the calculation of standard errors and test statistics. The other terms don’t describe this idea. The standard error is a measure of how much a statistic would vary across samples, not a count of independent pieces of information. Sample size is the number of observations you have, and population size is the total number of units in the population.

Degrees of freedom describe how many pieces of information in the data can vary independently after you've fixed certain quantities when estimating a parameter. When you estimate a statistic from n observations, some information is consumed by the estimation itself (for example, the mean is being set), so only a portion can vary freely. A common way this shows up is that, for estimating the variance around a sample mean, you have n minus 1 independent pieces of variation, because once the mean is fixed, the deviations are not all free to vary independently. This concept carries into many analyses: the degrees of freedom often equal the number of observations minus the number of parameters estimated (such as the mean, regression coefficients, etc.). That remaining freedom influences the shape of sampling distributions and the calculation of standard errors and test statistics.

The other terms don’t describe this idea. The standard error is a measure of how much a statistic would vary across samples, not a count of independent pieces of information. Sample size is the number of observations you have, and population size is the total number of units in the population.