BJS: Bureau of Justice Statistics

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Bureau of Justice Statistics (BJS)
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What is statistical significance?

When national estimates are derived from a sample, as with the NCVS, caution must be used when comparing one estimate to another estimate or when comparing estimates over time. Although one estimate may be larger than another, estimates based on a sample have some degree of sampling error. The sampling error of an estimate depends on several factors, including the amount of variation in the responses and the size of the sample. When the sampling error around an estimate is taken into account, the estimates that appear different may not be statistically different.

One measure of the sampling error associated with an estimate is the standard error. The standard error can vary from one estimate to the next. Generally, an estimate with a small standard error provides a more reliable approximation of the true value than an estimate with a large standard error. Estimates with relatively large standard errors are associated with less precision and reliability and should be interpreted with caution.

Data users can use the estimates and the standard errors of the estimates provided in NCVS reports to generate a confidence interval around the estimate as a measure of the margin of error. A confidence interval around the estimate can be generated by multiplying the standard errors by ±1.96 (the t-score of a normal, two-tailed distribution that excludes 2.5% at either end of the distribution). Therefore, the 95% confidence interval around an estimate is the estimate ± (the standard error X 1.96). In others words, if different samples using the same procedures were taken from the U.S. population, 95% of the time the estimate would fall within that confidence interval. See the NCVS Methodology for an example.

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