Task 3: Key Concepts about Calculating Degrees of Freedom

Due to the complex sample design of NHANES, estimates computed from the data are more variable than the sample size would suggest.  Therefore, as reviewed in Task 1, it is important to always calculate the variance, or standard error, that reflects the sampling design for any estimate obtained from these data.

The variance of an estimate calculated from NHANES data is related to the number of PSUs.  Because the number of PSUs is relatively small in NHANES, hypothesis tests and confidence intervals should based on a t-distribution rather than the more commonly used z-distribution.  The t-distribution is directly dependent on the number of degrees of freedom, as the number of degrees of freedom is used to choose the critical value on which the t-distribution is based.

Degrees of freedom are calculated by subtracting the number of strata from the number of PSUs, as shown in the equation below.  Therefore, a 2-year survey cycle generally has 15 degrees of freedom, which is calculated by subtracting 15 strata from 30 PSU.  However, when data are analyzed on a subgroup of sample persons, all of whom may not be represented in all strata and PSUs (e.g. Mexican Americans), the degrees of freedom provided in the output may differ. For example, SAS Survey procedures, such as PROC SURVEYMEANS, compute the degrees of freedom as the number of PSUs in the non-empty strata minus the number of non-empty strata. This means that if your data have empty strata (i.e. no persons in the population for either PSU), the number of degrees of freedom will increase. This is incorrect and SAS is currently working on correcting this problem.  In the meantime, you can use SAS macros that have been developed to get around this issue.  Please see the Continuous NHANES tutorial for more information. 

Equation for Degrees of Freedom

The degrees of freedom are inversely proportional to relative standard of error and proportional to the reliability of an estimated standard error.  As the number of degrees of freedom increases, the relative standard error decreases and the reliability of the estimate increases.  The NHANES guidelines recommended a relative standard error of at most 30%. This corresponds to at least 22 degrees of freedom. 

IMPORTANT NOTE

For more information on degrees of freedom, please visit “Module 12: Variance Estimation” of the Continuous NHANES Tutorial.