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Appendix C Estimates of Sampling Errorsfor the Serbia SampleThe sample of respondents selected in the Serbia MultipleIndicator Cluster Survey is only one of the samples thatcould have been selected from the same population, usingthe same design and size. Each of these samples wouldyield results that differ somewhat from the results of theactual sample selected. Sampling errors are a measureof the variability between the estimates from all possiblesamples. The extent of variability is not known exactly,but can be estimated statistically from the survey data.The following sampling error measures are presentedin this appendix for each of the selected indicators:• Standard error (se): Sampling errors are usuallymeasured in terms of standard errors for particularindicators (means, proportions etc). Standard error isthe square root of the variance of the estimate. TheTaylor linearization method is used for the estimationof standard errors.• Coefficient of variation (se/r)) is the ratio of thestandard error to the value of the indicator, and is ameasure of the relative sampling error.• Design effect (deffdeff) ) is the ratio of the actual varianceof an indicator, under the sampling method usedin the survey, to the variance calculated under theassumption of simple random sampling. The squareroot of the design effect (deft)) is used to show theefficiency of the sample design in relation to theprecision. A deft value of 1.0 indicates that the sampledesign is as efficient as a simple random sample,while a deft value above 1.0 indicates the increase inthe standard error due to the use of a more complexsample design.• Confidence limits are calculated to show the intervalwithin which the true value for the population can bereasonably assumed to fall, with a specified level ofconfidence. For any given statistic calculated from thesurvey, the value of that statistic will fall within a rangeof plus or minus two times the standard error (r r + 2seor r – 2se) ) of the statistic in 95 percent of all possiblesamples of identical size and design.For the calculation of sampling errors from MICS data,SPSS Version 18 Complex Samples module has beenused. The results are shown in the tables that follow.In addition to the sampling error measures describedabove, the tables also include weighted and unweightedcounts of denominators for each indicator. The weightedcounts are based on the normalized weights, so theweighted count at the national level is equal to theunweighted count. Given that the average relative weightis 1, in comparing the weighted count for each domainto the corresponding unweighted count, it is possible todetermine whether the weights for the domain are aboveor below average. A relative weight higher than 1 meansthat the domain was over-sampled in relative terms.Sampling errors are calculated for indicators of primaryinterest, for the national level, for the regions, and for urbanand rural areas. Five of the selected indicators are basedon household members, 18 are based on women, 8 arebased on men and 12 are based on children under 5. Allindicators presented here are in the form of proportions.Table SE.1 shows the list of indicators for which samplingerrors are calculated, including the base population(denominator) for each indicator. Tables SE.2 to SE.8 showthe calculated sampling errors for selected domains.266MULTIPLE INDICATOR CLUSTER SURVEY 2010