Typically, a sufficiently large probability sample will have point estimates that are approximately normally distributed. The end points of the confidence interval, then, are a function of the estimate (), its standard error (), and a percentile of the normal distribution with zero mean and unit variance, referred to as the standard normal deviate (z score), and are given by:
The continuous NHANES sample is a multistage, area probability sample. The number of independent pieces of information, or degrees of freedom, depends upon the number of PSUs rather than on the number of sample persons. Sample persons within a given PSU are not independent. Therefore, a t-statistic with degrees of freedom equal to the difference between the number of PSUs and the number of strata containing observations is used instead of a z-statistic, which would otherwise be used in a large sample. The endpoints for a confidence interval for the continuous NHANES are given by:
Sample weights and other design effects (e.g. strata, PSUs) must be incorporated when calculating an estimate and its standard error (see “Module 5: Overview of NHANES Survey Design and Weighting” for more information). Taylor Series Linearization is one example of a design-based method. The design variables needed to obtain estimates of standard errors through this method are provided on the demographic files for the continuous NHANES (see below for an example of a program).
Confidence intervals, as constructed above, are based on one possible sample from a finite population. Many possible samples of the same size can be obtained using the same procedures and measurements. For each of these samples, a confidence interval can be constructed. For a 95% CI, 95% percent of these intervals would then contain the true value of the population parameter.
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