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Technical Notes

The Science and Engineering Indicators (SEI) State Indicators data tool contains trend data for most indicators. These data are available for download within the data tool and from the State Indicators Export Data page.

1. Standard Errors

The State Indicators uses a large number of sources to compile different types of data, which can be categorized as follows:

  • Data based on censuses. These are complete population counts; therefore, there is no standard error associated with the estimate. When standard errors are applicable, they are available by selecting the “Download Indicator standard error” at the downloads button under Export.
  • Data based on samples. Standard errors for estimates, where available, are provided by the source. Data from sources such as The National Assessment of Educational Progress (NAEP), American Community Survey (ACS), and Survey of Doctorate Recipients (SDR) are based on samples of target populations. Estimated standard errors are provided where available but may be incomplete for some data sets; for example, standard errors are not available prior to 2007 for the Occupational Employment Statistics (OES) survey. The business research and development data set has associated standard errors for its values, but some historical values of standard errors are not available due to updates to the estimates but not to the standard errors.
  • Data based on statistical models. Standard errors cannot be provided for some estimates due to the estimating techniques of the data source (for example, gross domestic product (GDP) data and Census-based population estimates).
  • Data derived directly from the source data set. For data series where the standard error information for the source data is available, approximation formulas for combining sampling errors were used. Because the source data used to derive these estimates are from different independent samples, there is no covariance term included in the formulas.

Standard error tables are provided for download except for where the standard errors are not applicable (“na”) or not available (“NA”).

The following formulas were used to estimate standard errors for derived data series.

Sums and differences

Where available for aggregate estimates, such as the total for the United States, sampling errors were collected for the aggregate estimate as provided by the source.

In a few cases, aggregate estimates were calculated from individual parts of the aggregate, and therefore, sampling errors also had to be calculated based on the individual parts of the aggregate. The same formula was also used for computing the standard error for the difference of two estimates. It was assumed that the covariance between the individual parts was negligible.

This formula was used, where applicable, for such roll-ups as national values.

The standard error of the sum or difference of two estimates is the square root of the sum of the variances of the two estimates. The variance of an estimate is the squared standard error of the estimate.


This formula was used to calculate the standard errors of the ratios (assuming X and Y are uncorrelated, using the first order Taylor series expansion, which is an approximate but widely used and accepted approach).

The standard error of the ratio of two estimates is the product of the ratio (of the two estimates) and the square root of the sum of the relative variance of the numerator and the relative variance of the denominator. The relative variance of an estimate is the variance of the estimate divided by the squared estimate.

Relative standard error

Errors for some estimates are only available as the relative standard error (RSE) or percent relative standard error (PRSE).

The percent relative standard error of an estimate is the standard error of the estimate divided by the estimate expressed as a percentage.

Therefore, to transform the PRSE to standard error, the following equation was used:

The standard error is the product of the estimate and the percent relative standard error.

2. Constant Dollar Data

The State Indicators presents data as current dollars. To facilitate comparisons over time, the data tool also has an option for presentation of the information as constant dollars in the table and chart views. The data tool uses constant 2012 dollars based on the gross domestic product (GDP), as prepared by the Bureau of Economic Analysis. The constant dollar adjustment is available in the State Indicators for all financial indicators, except for ratio or percentage indicators where both numerator and denominator are expressed in dollar units.

Table S-A provides the GDP price deflators used in the State Indicators. These price indices are for the national GDP and are not adjusted for states. The State Indicators tables that are available for download present information as current dollars only. The data in Table S-A can be used to replicate the constant dollar information in the State Indicators. It may also be applied to the standard error tables, as applicable.

3. Statistical Testing

As noted in the overview, indicators based on estimates have associated standard errors, and therefore, small differences in numbers may not be statistically significant.

4. Knowledge- and Technology-Intensive (KTI) Industry Employment

This tool and the Production and Trade of Knowledge- and Technology-Intensive Industries report defines knowledge- and technology-intensive (KTI) industry employment as those occupations with the highest research and development (R&D) intensities based on a taxonomy of economic activities developed by the Organization for Economic Co-operation and Development (OECD). They consist of nine manufacturing industries—chemicals and chemical products; pharmaceuticals; computer, electronic, and optical products; electrical equipment; other machinery and equipment; motor vehicles, trailers, and semi-trailers; air and spacecraft and related machinery; railroad, military vehicles and other transport equipment; medical and dental instruments—and three services industries—information technology (IT) and other information services; software publishing; and scientific research and development.

Each industry is defined by a four-digit code that is based on the North American Industry Classification System (NAICS). The KTI data reflect the 2012 NAICS codes. For more detailed information on the KTI industries and methodological approach see Indicators 2022 report, “[2022] Production and Trade of Knowledge- and Technology-Intensive Industries Technical Appendix.”

As part of the calculation of KTI employment in the Indicators 2022 report (Indicators 2022 “[2022] Production and Trade of Knowledge-and Technology-Intensive Industries), employment information from the 2017 Economic Census was used to prorate estimated employment based on the PUMS for modified NAICS industries partially assigned to multiple International Standard Industrial Classification (ISIC Revision 4) industries. This creates internationally comparable data. Caution should be exercised when making international comparisons because international data is compiled from multiple national sources and are prone to varying issues of quality and reliability. The partial employment rates for modified NAICS industries 3335 and 332MZ are shown in Table SAKTI-3 of the KTI Technical Appendix based on the 2017 Economic Census. These partial employment rates were used for the estimation of KTI employment for data years after 2017. Table S-B shows the partial employment rates of modified NAICS industries 3335 and 332MZ based on the 2012 Economic Census (for data years 2013 through 2017) and the 2017 Economic Census (for data years after 2017).

5. States Included on the Histogram Display

To aid in visualizations, outliers are not displayed on histograms. Here we define an “outlier” as a data point that falls outside the median plus or minus three times the interquartile range of the most recent year of the data series.

Table S-A

Calendar-year price deflators: 1990–2021

YearGDP price deflator (chained) 2012 dollars

GDP = gross domestic product.

NOTE: The base year (= 1.0000) used for the constant dollar calculations is 2012, consistent with the current Bureau of Economic Analysis and Office of Management and Budget convention.

SOURCES: Bureau of Economic Analysis, National Economic Accounts, Gross Domestic Product, accessed 8 March 2022.

Science and Engineering Indicators

Table S-B

Modified NAICS CodePartial Rate of Employment Estimated from 2012 Economic CensusPartial Rate of Employment Estimated from 2017 Economic Census
NAICS 33350.7536021030.760893075
NAICS 332MZ0.1203094640.119286701

SOURCES: US Census Bureau, 2012 Economic Census, accessed 8 May 2022. US Census Bureau, 2017 Economic Census, accessed 2 May 2022.

Science and Engineering Indicators