What kind of method can be used to manage censored laboratory data (such as: water quality data like nitrate, phosphorus, silica, etc)? I mean sometimes we get data below the accuracy of the measurement (
From a statistical viewpoint it is the best is to record both, the "nondetect" value (e.g. < 0.01) and the original measurement, even if it is below the detection limit (and even if it is negative!), see:
Analytical Methods Committee (2001) Measurement of near zero concentration: recording and reporting results that fall below the detection limit. The Analyst 126, 256-259.
See also: Analytical Methods Committee (2001) What should be done with results below the detection limit? Mentioning the unmentionable. Royal Society of Chemistry, amc technical brief. http://www.rsc.org/images/results-below-detection-limit-technical-brief-5_tcm18-214854.pdf
If there is no chance to get the original value, it is not that easy, but you may try to estimate the distribution of these values. The R package NADA (Nondetects And Data Analysis for environmental data) from the USGS supports this:
http://cran.r-project.org/package=NADA
The background can be found in a related book: Helsel, D. (2004) Nondetects and Data Analysis: Statistics for Censored Environmental Data (Statistics in Practice). Wiley-Interscience, 268pp.
Finally, an overview about the methods was presented by the book and package authors at the useR! conference in Dortmund 2004, the slides are still online: http://www.statistik.uni-dortmund.de/useR-2008/slides/Helsel+Lee.pdf
Helsel also has a newer book "Statistics for Censored Environmental Data Using Minitab(R) and R" (2012) which provides a good summary of different ways to record and include censored data in statistical analyses.
USGS has a publication that would be helpful in answering your question.
Techniques of Water-Resource Investigations of the USGS Book 4 Hydrologic Analysis and interpretations. Chapter A3 Statistical Methods in Water Resources.
Chapter 13 in the above publication should answer your questions "Methods for Data Below the Reporting Limit." Direct link to Chapter 13 is below. https://pubs.usgs.gov/twri/twri4a3/pdf/chapter13.pdf