The Growth of Metropolitan Suburbs

ence of a pair of these estimates valid confidence intervals (and tests of hypotheses) can also be constructed. Beyond these, however, mathematical formulas are lacking for the analytical treatment of data arising from complex samples. For the research scientist who wants to apply analytical treatment this article presents seven procedures for arriving at an approximate answer. These procedures are offered as preferable alternatives to the present common practice of relying on standard formulas based on the s.r.s. (independence) assumption. Of these alternatives three amount to evasions of the worst problems by designing simpler samples. The other four attempt approximations of analytical statistics for complex samples.