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To assist users in ascertaining the reliability of the Modeled Wage Estimates, BLS provides relative standard errors for MWE data. Relative standard errors (expressed as a percentage of cost) are a measure of precision (reliability) of estimates. Relative standard errors are not available for the 2021 and 2022 year estimates. Due to implementation of modeled-based estimates (MB3) used by the Occupational Employment and Wage Statistics (OEWS), the BLS is currently developing an approach to calculate the relative standard errors. For more information see the Monthly Labor Review article, Model-based estimates for the Occupational Employment Statistics program and the Technical Notes for May 2021 OEWS Estimates.

Standard errors relate to differences that occur from sampling errors, but not from nonsampling errors. Sampling errors are differences between the results computed from a sample of observations and those computed from all observations in the population. In the case of MWE, the population of an estimate is an occupation in the civilian sector.

Nonsampling errors are not measured. One type of nonsampling error is survey nonresponse, when sample members are unwilling or unable to participate in the survey. Other nonsampling errors include inaccurate or incorrectly entered data, and processing errors. BLS quality assurance programs contain procedures for reducing nonsampling errors. These procedures include data collection reinterviews, observed interviews, and systematic reviews of collected data. Finally, field economists (data collectors) undergo extensive training to maintain high data collection standards.

BLS provides measures of reliability for all of its National Compensation Survey (NCS) programs: standard errors for the Employment Cost Index (ECI) and the Employee Benefits estimates, and relative standard errors (reported as a percentage of the estimate value) for estimates in the Employer Costs for Employee Compensation (ECEC) and the Modeled Wage Estimates.

Modeled Wage Estimates are reported as dollar amounts. For dollar amounts, a standard error reported in the same unit provides less information than a relative standard error. There is no inherent value of knowing the dollar amount of a standard error – which is an abstraction – without knowing how it is proportional to the estimate.

Standard errors can be used to measure the precision with which an estimate from a particular sample approximates the expected result (value) of all possible samples (population). The chances are about 68 out of 100 that an estimate from the survey differs from a population result by less than the standard error. The chances are about 90 out of 100 that this difference would be within 1.645 standard errors.

The standard errors can be used to define a range or level of confidence (confidence interval) around an estimate. BLS uses a 90 percent confidence level. If all possible samples were selected and an estimate of a value and its sampling error were computed for each, then (for approximately 90 percent of the samples) the intervals from 1.645 standard errors below the estimate to 1.645 standard errors above the estimate would include the "true" average value. In Example 1 below, the 90 percent confidence interval for an average hourly wage estimate of $26.87 with a relative standard error of 11.6 percent is $26.87 plus or minus $5.13 (1.645 standard errors times $3.12) or $21.74 to $32.00.

Note: examples are for illustrative purposes only and are not intended to represent current data.

Comparative statements appearing in Modeled Wage Estimates publications are statistically significant at the 90 percent level of confidence, unless otherwise indicated. This means that for differences cited, the estimated difference is greater than 1.645 times the standard error of the difference. If you wish to calculate a 95 percent confidence interval, replace the critical value of 1.645 with 1.96. For a 99 percent confidence interval, use 2.575 as the critical value. Footnotes appear next to estimates with relative standard errors greater than 30 percent. In such cases, differences in estimates that may appear to be important at first glance may fail statistical significance tests. (See example 2 below.)

**Example 1: building an interval**

Average hourly wage for part-time civilian workers in business and financial occupations, New York-Newark-Jersey City, NY-NJ-PA = $26.87

Relative standard error = 11.6% of $26.87 ≅ $3.12

90% confidence interval = $26.87 +/- (1.645 x $3.12) ≅ [$21.74, $32.00]

Thus, there is a 90% chance that the population value is between $21.74 and $32.00.

Example 2 shows that it may be difficult to draw conclusions about differences between two estimates without considering the relative standard error.

**Example 2: comparing intervals**

Average hourly wage for full-time aerospace engineers in California = $60.66

Relative standard error = 0.8%

90% confidence interval = $60.66+/- (1.645 x .008 x $60.66) ≅ [$59.86, $61.46]

Average hourly wage for full-time aerospace engineers in Maryland= $69.18

Relative standard error = 10.2%

90% confidence interval = $69.18 +/- (1.645 x .102 x $69.18) ≅ [$57.57, $87.79]

Values from $59.86 to $61.46 fall within the 90% confidence intervals for full-time aerospace engineers in both areas. Thus, at the relevant level of precision, all values within the range of $59.86 to $61.46 are plausible values for either area. That is, the comparative statement that the average hourly wage for full-time aerospace engineers in Maryland is larger than the average hourly wage for full-time aerospace engineers in California does not pass the statistical significance test.

For a more detailed explanation of the variance estimation methodology, see the article Estimating variances for modeled wage estimates (Guciardo, March 2020). Data users may also refer to the section **Calculating estimate reliability** in the NCS Handbook of Methods: Calculation.

**Last Modified Date:** September 5, 2023