General Statistical Methods
- NIST information on Uncertainty of Measurements: The site relates primarily to uncertainty considerations that apply to NIST measurements but includes basic information of general interest, such as how to calculate the standard deviation, how to propagate errors, extended uncertainty and confidence levels, and Type A and Type B uncertainties.
- NIST/SEMATECH Engineering Statistics Handbook: This online version of the handbook covers a rather wide spectrum of concepts related to statistical inference and uncertainty important in the measurement and analysis processes.
Online Statistical Calculators
- VassarStats. The site includes statistical calculators applicable to numerous distributions, probabilities (including conditional probabilities associated with Bayes theorem), calculators for regression analysis (the data-import option seems to work best for the linear regression; you may still enter x,y data pairs manually, but leave exactly one space after the x entry before the y entry, and do not put a return after the last data entry), and much more.
- Counter and Scaler MDC/MDA Calculations. The online calculator evaluates critical levels and lower limits of detection in a fashion that is basically consistent with the recommendations of Lloyd Currie. The values are appropriate for an instrument (such as a digital scaler) that outputs digital counts as opposed to an analog meter output. This calculator is part of the Rad Pro Calculator site managed by Ray McGinnis.
- Scanning MDC Calculator. This on-line utility calculates scan MDCs for select contaminant radionuclides in soil for 1-second scaler counts with NaI detectors based on probabilistic MCNPX modeling of detection efficiency along with related modifications to the MARSSIM method (see resource links below for supporting technical information). Environmental Remediation Group
- Statistics Tables. Parameters and probabilities for normal, student t-, and chi-square distributions.
Downloadable Statistical Software
ProUCL version 5.1.002 (5.1) is the latest update of the ProUCL statistical software package for analysis of environmental data sets with and without nondetect (ND) observations. ProUCL version 5.1 is a comprehensive statistical software package with statistical methods and graphical tools to address many environmental sampling and statistical issues. ProUCL Factsheet.
- ProbPlot 3.0. This software prepares probability plots from data that may be input from spreadsheets or by other routes. It is intended to assist in interpreting the consistency of data with Gaussian model assumptions and incorporates statistical tests to aid in acceptance/rejection decision making. ProbPlot is part of the Rad Pro Calculator site managed by Ray McGinnis. ProbPlot (originally called CumPlot) was developped by Bob Tuttle, Brian Oliver and Ray McGinnis.
- Instrument Counting Statistics. Downloadeable MS Excel spreadsheet. Scanning and static instrument statistics are calculated for a variety of different alpha, beta and gamma detectors, including uncertainties, critical level, detection limit, lower limit of detection, minimum detectable activity.
Equations used are taken from,
- Introduction to Health Physics, Herman Cember, Third Edition
- Introduction to Health Phics, Thomas E. Johnson, Fifth Edition
- NUREG-1575, Multi-Agency Radiation Survey and Site Investiation Mannual (MARSSIM), August 2000
- NUREG-1507, Minimum Detectable Concentrations with Typical Radiation Survey Instruments for Various Contaminants and Field Conditions. June 1998
- Wilcoxon Rank Sum Hypothesis Test. MS Excel spreadsheet template for testing if a survey area exceeds a reference background area by more that the derived concentration guideline limit (DCGL). Uses procedures described in,
- NUREG-1505, A Nonparametric Statistical Methodology for the Design and Analysis of Final Status Decommissioning Surveys. June 1998
- MARSSIM Table I.11. MS Excel spreadsheet template for calculating the sum of reference ranks in the Wilcoxon Rank Sum test. Uses cell formulae in MARSSIM Table I.11, as illustrated in MARSSIM Table 8.6.
- Multi-isotope Wilcoxon Rank Sum Test. MS Excel template for the multi-isotope WRS test with non-zero DCGLs. Ignors potential ties since the sum of fractions of concentrations divided by DCGLs is unlikely to generate ties. Facilitates choosing a posteriori DCGLs that meet a priori survey unit data.
- Propagation of Uncertainties. Downloadable MS Excel spreadsheet to proagate uncertainties using square root of sum of squares for addition, subtraction, multiplication, division and average.
- Statistical Equivalency Test. Downloadable MS Excel spreadsheet to test the statistical equivalency of two measurements with uncertainties.
- Uranium Isotopic Ratios. Downloadable MS Excel spreadsheet to test if uranium isotopic measurements indicate natural, depleted or enriched uranium.
Some health physicists are experts in statistics. Perhaps the better known are Carl Gogolak and Dan Strom. Several papers and presentations by these two gurus are shown below.
- Why You Can't Measure Zero. This document is provided to present some additional discussion on the subject of measurement criteria based on non-detectability. In particular, not detectable does not mean zero radioactivity concentration. To understand this, we need to examine the concept of minimum detectable concentration. This involves the Data Quality Objectives process and limiting decision error rates. Carl Gogolak. July 2001.
- False Alarms, True alarms, and statistics: Correct Usage of Decision Level and Minimum Detectable Amount. We frequently detect activity that is less than the minimum detectable activity! This occurs because the "minimum detectable activity" is misnamed, not because we are doing something impossible or nonsensical. The random nature of radioactive decay leads to erratic count rates when the total number of radioactive transitions detected is not very large (<100), a situation complicated by the need to subtract some value of "background" from the observation of the sample. Dan Strom. July 15, 1998.
- Statistical Inference in Environmental Radioactivity Measurements. Statistical criteria for decision-making in environmental cleanup. Dan Strom. November 18, 2003.
- Uncertainty in Inferences We Make from Radiation Measurements: Counting Statistics and Other Uncertainties. Dan Strom. July 11, 2004.
- Is Anything There? Evaluation of Statistical Decision Rules for Radioactivity Counting Experiments. Dan Strom. August 30, 2005.
- Everything Is Lognormal ... or Is It? Occupational and environmental radiation monitoring data are usually lognormally-distributed. Dan Strom. July 10, 2007.
- Effect of Using True Variability for Baseline Cancer Rates. Most of us are familiar with the concept of calculating the average (mean or expectation value) and the standard deviation of a set of data. But what is done if there is only one data point? One approximation is to use the Poisson distribution which approximates the normal distribution for large numbers. The mean of a single data point, x, is x. And the standard deviation of the single data point, x, is the square root of x, √x. This approximation should only be used if there is only one estimate or measurement (theoretical method). If there is a set of measured values, then conventional parametric statistics should be used to calculate a mean and standard deviation of the distribution (empirical method). Unfortunately, this requirement is often overlooked in community health studies where census tract data is compared to county data. The theoretical method is usually used to calculate county (baseline) parametric statistics. The empirical method should be used, since the larger variability of all individual county census tracts is known.