These variations significantly affect the precision of sample estimates. Estimates derived from any sample are subject to sampling variability, which is usually measured as the standard error. The standard error of a sample statistic estimates the variation of that statistic across many similar samples drawn from the same population. Approximately two-thirds of random samples will produce estimates within one standard error of the full population, and approximately 95 percent of samples produce estimates within two standard errors.
Standard errors depend on both sample size and sample design.
The most interesting census information describes individual characteristics, such as age, race, sex, income, education, and so on. The number of independent observations in each census file is the number of households or dwellings, not the number of individuals. Some individual characteristics, such as ancestry, are highly correlated within households. For example, if one household member is Chinese, the odds are high that other household members are also Chinese. Suppose we wish to estimate the standard error for the proportion of the population of Chinese ancestry.