Policy for Storing and Reporting Significant Figures for Chemical Data

In Reply Refer To:                                      February 14, 2002
Mail Stop 412

Office of Water Quality Technical Memorandum 2002.11

Subject:   Policy for Storing and Reporting Significant Figures for
Chemical Data

This memo establishes the policy of the Office of Water Quality (OWQ) for
storing and reporting the appropriate number of significant figures for
chemical data in the U.S. Geological Survey's National Water Information
System (NWIS) and describes the systematic implementation of this policy.
Concepts presented in this memo were developed over the past year by
members of the Phoenix Water-Quality User Group, and by staff from OWQ, the
Branch of Quality Systems (BQS), and the National Water Quality Laboratory

Questions about the established policy and the concepts presented in this
memo should be directed to Pete Rogerson (rogerson@usgs.gov) or Stephen
Sorenson (sorenson@usgs.gov) in OWQ.

Background and Purpose:

All water-quality data have an associated uncertainty resulting from
variability in sample collection, preparation, and analysis.  This memo
addresses only the uncertainties associated with laboratory sample
preparation and analysis. Data should be stored in and reported from NWIS
at a level of significance that accurately reflects these uncertainties.
Too many digits imply a higher level of precision than is justified by a
particular analytical method.  Too few digits potentially eliminate real
information about the actual measured constituent concentration that may be
critical for interpretation.  Current guidance (Novak, 1985, and Hansen,
1991) for reporting significant figures in USGS data reports and other
publications recommends that when "presenting numerical data, give only
those digits that convey actual information.  The last digit should
represent the uncertainty in the data."

There is no universally recognized means for determining the location of
this uncertain digit and the OWQ has not had a defined policy.  This memo
establishes the practice that will be implemented by the OWQ to derive the
significant figures for analytical values by determining the variability of
the method using laboratory replicate samples distributed over a range of
constituent concentrations.  These determinations of variability will then
be used to estimate the precision of individual results over the full
analytical range of the method.


The convention for reporting rounded analytical values in NWIS is to
include all digits known with certainty, plus one digit that is uncertain.
The uncertain digit will be called the least significant digit (LSD) in
this document.  Determination of the LSD will follow the guidance outlined
by the American Society for Testing and Materials (1993).

Laboratories will report data to the NWIS database to the least significant
digit plus one additional digit (LSD+1).  One additional uncertain digit is
recommended because there is potentially useful information in this added
data that will contribute to the ability to statistically evaluate large
data sets.
Standard USGS publication policy is to report all numbers rounded to the
LSD.  Standard rounding procedures in NWIS will be written to properly
round results to the LSD, but additional retrieval options will be
available for users to retrieve data at the LSD+1 level for use in
statistical and interpretive analyses.

Measurement of variability in analytical methods and the designation of
significant figures for each measured constituent is the responsibility of
each laboratory providing data to NWIS.    The number of significant
figures to be reported for a particular laboratory analysis by a particular
method will be based on measurement variability for multiple points in the
concentration range.  The performance of analytical methods will continue
to be monitored by the individual laboratories to determine if the initial
variability determined for the method is representative of longer-term
variability.  Each laboratory must define the rationale and operational
procedures they will use to report significant figures.  A review of these
procedures will become part of periodic reviews of each laboratory by the
BQS, as implementation of this policy is achieved.


It will take time to implement the substantial changes outlined in this
memo. Structural changes and changes in reporting conventions will be
required for NWIS and upgrades will need to be made to laboratory software.
The OWQ and BQS will initially pilot this change with the NWQL and the
Ocala Water Quality and Research Laboratory (OWQRL).  Following successful
implementation, the plan will be applied to field water-quality
determinations and at other water-quality production laboratories.

Currently the NWIS database does not have the capability to store the
necessary information to fully implement this policy, and will not have
this capability until the 4_2 release currently scheduled for FY 2002.  The
Phoenix Water-Quality User Group, OWQ, and BQS will continue to work with
the NWQL and OWQRL to develop and test procedures needed for this new
policy.  Until this policy is fully implemented, data publication and
rounding will continue to be done by the default rounding rules provided
through the NWIS parameter code dictionary.

The guidance provided in this memo does not fit all water-quality data that
the USGS uses in its investigations.  Some procedures, such as
radiochemical determinations, isotope analyses, and counts of organisms in
biological samples may not allow for the determination of variability or
may produce results that are expressed in units of measurement that are not
consistent with this policy.  The OWQ and others will be working toward
more consistent and scientifically defensible ways to determine how to best
present and store these types of data as experience is gained with this
process.  Regardless of how the LSD is determined, it is critical that
every data user decide whether the number of significant figures provided
is appropriate for the intended use of the data.


American Society for Testing and Materials, 1993, Standard practice for
   using significant digits in test data to determine conformance to
   specifications: Section 7.4, Reporting Test Results:  Annual Book of
   ASTM Standards, Volume 14.02, pp. 19-22.

Hansen, W.R., 1991, Suggestions to authors of the reports of the United
   States Geological Survey, (7th ed.) pp. 119-121.

Novak, C.E., 1985, Preparation of water-resources data reports: U.S.
   Geological Survey Open File Report 85-480, 331 p.

                                             Stephen K. Sorenson /s/
                                             Acting Chief, Office of Water

This memorandum does not supersede any other Office of Water Quality
Technical Memorandum.

Distribution:  All WRD Employees

Stephen K. Sorenson
Acting Chief, Office of Water Quality
U.S. Geological Survey
412 National Center
Reston, VA  20192