Adapting Cochran’s sample-size rule to an estimate from a complex sample

Music City Center 

Given the mean of a simple random sample without replacement, Cochran claimed that calculating a two-sided 95% confidence interval for the population mean using a standard normal-distribution table is often reasonable when the sample size is 25 times the square of the skewness coefficient of the population. We adapt a variant of this crude rule to a two-sided confidence interval for a parameter estimated from a complex probability sample. We conjecture that the standard two-sided 95% confidence interval for an estimated parameter is usually reasonable when the absolute value of the skewness coefficient of the nearly unbiased parameter estimate is less than 0.2. Conversely, it is not reasonable to use the standard two-sided 95% confidence interval for an estimated parameter when the absolute value of the skewness coefficient of its estimate is greater than 0.2. This warning is particularly germane for estimated proportions and differences between proportions. When applying out conjecture, an estimate's skewness coefficient will rarely be known. Instead, it will usually need to be estimated, often in an ad hoc manner.

Effective sample size

Third central moment

Confidence interval

Skewness coefficient

Clopper-Pearson confidence interval 

Survey Research Methods Section