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Appendix A: Technical Notes

Accuracy of Estimates

The accuracy of any statistic is determined by the joint effects of nonsampling and sampling errors. Both types of error affect the estimates presented in this report. Several sources can contribute to nonsampling errors. For example, members of the population of interest are inadvertently excluded from the sampling frame; sampled members refuse to answer some of the survey questions (item nonresponse) or all of the survey questions (questionnaire nonresponse); mistakes are made during data editing, coding, or entry; the responses that respondents provide differ from the “true” responses; or measurement instruments such as tests or questionnaires fail to measure the characteristics they are intended to measure. Although nonsampling errors due to questionnaire and item nonresponse can be reduced somewhat by the adjustment of sample weights and imputation procedures, correcting nonsampling errors or gauging the effects of these errors is usually difficult.

Sampling errors occur because observations are made on samples rather than on entire populations. Surveys of population universes are not subject to sampling errors. Estimates based on a sample will differ somewhat from those that would have been obtained by a complete census of the relevant population using the same survey instruments, instructions, and procedures. The standard error of a statistic is a measure of the variation due to sampling; it indicates the precision of the statistic obtained in a particular sample. In addition, the standard errors for two sample statistics can be used to estimate the precision of the difference between the two statistics and to help determine whether the difference based on the sample is large enough so that it represents the population difference.

Most of the data used in this report were obtained from complex sampling designs rather than a simple random design. The features of complex sampling require different techniques to calculate standard errors than are used for data collected using a simple random sampling. Therefore, calculation of standard errors requires procedures that are markedly different from the ones used when the data are from a simple random sample. The Taylor series approximation technique or the balanced repeated replication (BRR) method was used to estimate most of the statistics and their standard errors in this report.

Standard error calculation for data from the School Crime Supplement was based on the Taylor series approximation method using PSU and strata variables available from each dataset. For statistics based on all years of NCVS data, standard errors were derived from a formula developed by the U.S. Census Bureau, which consists of three generalized variance function (gvf) constant parameters that represent the curve fitted to the individual standard errors calculated using the Balanced Repeated Replication (BRR) technique.

The coefficient of variation (CV) represents the ratio of the standard error to the mean. As an attribute of a distribution, the CV is an important measure of the reliability and accuracy of an estimate. With the exception of Indicator 2, the CV was calculated for all estimates in this report, and in cases where the CV was between 30 and 50 percent the estimates were noted with an “!” symbol (interpret data with caution). In Indicator 2, the “!” symbol cautions the reader that estimates marked indicate that the reported statistic was based on fewer than 10 cases or the CV was greater than 50 percent. With the exception of Indicator 2, in cases where the CV was 50 percent or greater, the estimate was determined not to meet reporting standards and was suppressed.