Standard Errors for Indexes From Complex Samples

Methods of computing standard errors were developed and applied for several statistics of importance in economic and social surveys. These statistics are based on ratio means r = y/x; x is often the variable sample size of complex samples. Some statistics involve weighted sums σWjrj, others concern the relatives R1 = r1/r0 = (y1/x1)/(y0/x0), the ratio of current (1) to base (0) mean. From these relatives the indexes are constructed, and changes, I2 – I1, in the index. We develop computing formulas and helpful approximations for standard errors of these statistics, and apply them to a series of data from our Center's Surveys of Consumer Attitudes & Expectations. A large group of empirical results yield evidence on the behavior of these statistics, with wide implications for the design of surveys to measure economic and social indicators.