## FAQs About Estimated Measures of Sampling Variability

**Originally Released:** January 19, 2017

**Updated:** January 26, 2017

### Did EIA change the way estimates of stocks and net changes are calculated as a result of incorporating estimated measures of sampling variability in the *Weekly Natural Gas Storage Report* (WNGSR) releases?

The methodology for calculating estimates of stocks and net changes in the WNGSR has not changed. See Methodology for EIA Weekly Underground Natural Gas Storage Estimates for more information about the WNGSR estimation methodology.

### Why has EIA incorporated estimated measures of sampling variability in WNGSR releases?

As a Principal Federal Economic Indicator, WNGSR is required to meet the Office of Management and Budget requirement for dissemination of error estimates so that information is publicly available on the statistical properties of the published estimates. In the publicly available three-year performance evaluations on WNGSR, EIA has been including estimated measures of sampling variability for the weeks that most closely correspond to the ends of the calendar months. Including estimated measures of sampling variability in the WNGSR release provides data users with more information on a weekly basis regarding the statistical properties of the estimates published in the WNGSR.

### What is sampling error?

Sampling error is one component of total survey error, and measures of sampling error may be estimated based on the sample selected for WNGSR. See *Types of Possible Survey Errors in Estimates Published in the Weekly Natural Gas Storage Report* for more information on the types of possible errors in estimates published in the WNGSR.

Sampling error is the error caused by observing a sample instead of the entire survey frame. Statistics based on the sample (such as totals, means, and medians) generally differ from statistics on the entire frame because the sample includes only a subset of the frame. For example, if EIA measures the weekly underground storage inventory estimate for the East region from a sample of natural gas storage operators, the total stocks estimated from the sample may not be the same as the overall total stocks from the full frame of natural gas storage operators in the East region.

### What is the standard error?

The standard error (SE), which EIA measures in the same units as its corresponding survey estimate (billion cubic feet), is a measure of the sampling variability of the estimate based on all possible samples that could have been selected using the chosen sample design.

### What is the coefficient of variation?

The coefficient of variation (CV), which may also be referred to as the *relative standard error*, is the standard error expressed as a fraction of the estimate and is displayed as a percentage.

### How does EIA compute estimated measures of sampling variability?

Simple estimators have standard equations for measuring sampling errors. However, because the WNGSR estimator is complex, as described in the WNGSR estimation methodology, there is no standard formula to compute measures of sampling error. EIA computes estimates of standard errors for both the published estimates of weekly working gas storage levels and the weekly net changes in working gas storage levels using the bootstrap method, which is also described in the WNGSR estimation methodology.

### Does EIA publish estimated measures of sampling variability for estimates of the implied flows published in WNGSR releases?

No, EIA publishes estimated measures of sampling variability only for estimates of stocks and net changes by region and for the Lower 48 states.

### Why can an estimated measure of sampling variability change from one WNGSR release to the next?

Factors that may affect an estimated measure of sampling variability include increased variability in the weekly data reported on the EIA-912, changes to the group of operators known to be in the target population, the introduction of a new WNGSR sample, and increased variability in the monthly data reported on the EIA-191 that are used to impute data for operators that are not in the WNGSR sample.

### How can the estimated measures of sampling variability published in the WNGSR be used to provide information on the statistical properties of the estimates published in the WNGSR?

The published estimate of the standard error or coefficient of variation in the WNGSR can be used to compute a confidence interval centered about the corresponding published estimate with a desired level of confidence. The WNGSR estimation methodology provides information on how to calculate confidence intervals for levels and net changes that may be used to conduct individual two-sided tests of significance. For example, for a published estimate of weekly net change, if a given confidence interval does not contain zero, then it may be concluded at the specified level of significance that the actual weekly net change is different from zero. Otherwise, there is not sufficient statistical evidence to conclude at the specified level of significance that the actual weekly net change is different from zero.

### The estimates of natural gas stocks that EIA publishes in the WNGSR can be summed across the five regions to produce the stock estimate for the Lower 48 states. Why canâ€™t the standard errors and coefficients of variation be similarly summed across the regions to produce the standard error and coefficient of variation for the Lower 48 states?

Similar to the stock estimates, the squared values of the standard errors can be summed across the five regions because independent samples were selected by region. However, this mathematical property does not hold for the standard errors.

### Why are the coefficients of variation for natural gas stock estimates typically larger for salt facilities than for nonsalt facilities?

For a stock estimate, EIA estimates its coefficient of variation by dividing the estimate of its standard error by the estimate. Although the standard errors for estimates of stocks are typically only slightly smaller for salt facilities than for nonsalt facilities, the estimates of stocks are typically much smaller for salt facilities than for nonsalt facilities. As a result, the coefficients of variation for estimates of stocks are typically larger for salt facilities than for nonsalt facilities.

### Why are the coefficients of variation for natural gas stock estimates smaller for the Lower 48 states than for the regions, but the standard errors for the Lower 48 states are higher than for the regions?

For a stock estimate, EIA estimates its coefficient of variation by dividing the estimate of its standard error by the estimate. Because the stock estimate for the Lower 48 states is larger than for any one region, the denominator in the calculation is larger, resulting in a smaller coefficient of variation. However, the standard error for the estimate of weekly net change for the Lower 48 states is higher than for the regions because we compute it by summing the squared values of the standard errors by region and then taking the square root.

### What happens when there is a revision to working gas?

The revision policy for WNGSR estimates is unaffected by the inclusion of estimated measures of sampling variability in the WNGSR publication. When EIA publishes a revision, we use data currently available at the time of the WNGSR release to compute the estimated measures of sampling variability, including any updates that EIA made for the prior week. Also consistent with the current established policy, the historical database of estimated measures of sampling variability will be updated weekly and will contain the most current set of estimates available. EIA may revise these historical estimated measures of sampling variability when we revise the historical working gas levels.

Mathematically, revisions cannot affect the standard errors on the current published net change, except in the instance of a revision triggering an out-of-cycle release. In this case, EIA will perform an out-of-cycle WNGSR release following established policy and recalculate the coefficient of variation and standard error estimates for the week. Conditions that require an out-of-cycle WNGSR release, described in the WNGSR Revision Policy, have never occurred since the implementation of the out-of-cycle revision policy in 2005.

For additional information contact Jose Villar at jose.villar@eia.gov or (202) 586-9613.