Final Report (PDF, 2132K) - Measure DHS

APPENDIX BSAMPLING ERRORSThe results from sample surveys are affected by two types of errors: nonsampling error andsampling error. The former is due to mistakes in implementing field activities, such as failing to locateand interview the correct household, errors in asking questions, data entry errors, etc. While numeroussteps were taken to minimize this sort of error in the ODHS, nonsampling errors are impossible to avoidentirely, and are difficult to evaluate statistically.Sampling errors, on the other hand, can be evaluated statistically. The sample of women selectedin the ODHS is only one of many samples of the same size that could have been drawn from thepopulation using the same design. Each sample would have yielded slightly different results from thesample actually selected. The variability observed among all possible samples constitutes sampling error,which can be estimated from survey results (though not measured exactly).Sampling error is usually measured in terms of the "standard error" (SE) of a particular statistic(mean, percentage, etc.), which is the square root of the variance of the statistic across all possiblesamples of identical size and design. The standard error can be used to calculate confidence intervalswithin which one can be reasonably sure the true value of the variable fails. For example, for any givenstatistic calculated from a sample survey, the value of that same statistic as measured in 95 percent of allpossible samples of identical size and design will fall within a range of plus or minus two times thestandard error of that statistic.If simple random sampling had been used to select women for the ODHS, it would have beenpossible to use straightforward formulas for calculating sampling errors. However, the ODHS sampledesign used two stages and clusters of households, and it was necessary to use more complex formulas.Therefore, the computer package CLUSTERS, developed for the World Fertility Survey, was used tocompute sampling errors.CLUSTERS treats any percentage or average as a ratio estimate, r = y/x, where both x and y areconsidered to be random variables. The variance of r is computed using the formula given below with thestandard error being the square root of the variance:l_f H [mh (mhvar (r) -- Z Z z~h~x2 h=l mh-1 i=l m~z2h)linwhich, zh~ = Yhl - rxh±, and z h = Yh - rxh,where hra~Yh~Xhifrepresents the stratum and varies from 1 to H,is the total number of PSUs selected in the h-th stratum,is the sum of the values of variable y in PSU i in the h-th stratum,is the sum of the number of cases (women) in PSU i in the h-th stratum, andis the overall sampling fraction, which is so small that CLUSTERS ignores it.87