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Employment Cost Trends
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Relative standard errors for the Employer Costs for Employee Compensation

BLS provides relative standard errors for Employer Costs for Employee Compensation (ECEC) estimates. Relative standard errors (expressed as a percentage of cost) are a measure of precision (reliability) of estimates. See the HTML or PDF relative standard errors tables for current quarter news releases; private industry supplementary tables are available in TXT or PDF.


Sources of error

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 the ECEC, the population of an estimate is an industry or occupation in the civilian, private, or state and local government sector. Estimates derived from different samples selected using the same sample design may differ from each other.

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.

Standard errors and relative standard errors

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 ECEC and the Modeled Wage Estimates.

ECI and Employee Benefits estimates are themselves relative values: percent changes and index values for ECI, and percentage shares for EBS. If an ECI series is estimated to increase by 1.0 percent over a time period and the standard error is 0.2 percent, then this implies a relative standard error of 0.2/1.0, or 20 percent. Reporting an error of 20 percent for an estimate of 1.0 percent would be confusing because the standard error and the estimate it refers to are in the same units. However, the error is one-fifth the amount of the estimate, not twenty times the estimate. NCS would report the standard error (0.2 percent) instead, for clarity.

Modeled Wage Estimates are reported as dollar amounts. ECEC estimates are reported as dollar amounts or, for components of total compensation, as a percentage of total compensation. 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. Relative standard errors are also available for ECEC percentages of total compensation.

Using relative standard errors

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 a total compensation estimate of $37.03 with a relative standard error of 1.3 percent is $37.03 plus or minus $0.79 (1.645 standard errors times $0.48) or $36.24 to $37.82.

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

Comparative statements appearing in ECEC 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

Total compensation for civilian workers = $37.03
     Relative standard error = 1.3% of $37.03 = $0.48
     90% confidence interval = $37.03 +/- (1.645 x $0.48) = [$36.24, $37.82]

Thus, there is a 90% chance that the population value is between $36.24 and $37.82.

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

Retirement and savings costs for professional and business services workers = $0.17
     Relative standard error = 39.0%
     90% confidence interval = $0.17+/- (1.645 x .39 x $0.17) = [$0.06, $0.28]

Retirement and savings costs for education and health services workers = $0.08
     Relative standard error = 24.7%
     90% confidence interval = $0.08 +/- (1.645 x .247 x $0.08) = [$0.05, $0.11]

Values from $0.06 to $0.11 fall within the 90% confidence intervals for both industries. Thus, at the relevant level of precision, all values within the range of $0.06 to $0.11 are plausible values for either industry. That is, the comparative statement that retirement and savings costs for professional and business services workers is larger than costs for those in education and health services workers does not pass the statistical significance test.

More information

For a more detailed explanation of relative standard errors, see the section Calculating estimate reliability in the NCS Handbook of Methods: Calculation and the article Measuring Trends in the Structure and Levels of Employer Costs for Employee Compensation. For a detailed explanation of how to use standard error data to analyze differences in year-to-year changes, see Analyzing Year-to-Year Changes in Employer Costs for Employee Compensation.

 

Last Modified Date: June 18, 2020