(With Application to Radiological Measurements)

Statistics is the cornerstone in the interpretation of radiological measurements.  A single measurement has an associated error, critical level (a.k.a. decision level), and detection level (a.k.a. lower limit of detection or minimum detectable activity).  Groups of measurements have means, standard deviations, upper confidence levels, upper tolerance levels, upper simultaneus levels, and many other parametric measures. Multiple groups of measurements can be compared by many methods to determine equivalency or non-equivalency using hypothesis testing.  It is easy to see how statistics gets a bad rap ... because it is complicated, so few people really understand it, and it is easy to unintentionally or intentionally misinterpret data !!!

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. 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,

  • 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.

Counting Statistics

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.

Cancer Statistics

  • 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.