Counting Errors and Statistics - RCT Training

Vocabulary practice flashcards covering counting errors, statistics, Gaussian distribution, chi-squared testing, quality control documentation, operating limits, and counter efficiency from the RCT and RCT Supervisor Training Guide.

Sample Variance

The amount of scatter of data points around the mean; it describes how much the data "varies" from the mean.

Standard Deviation (ANSI N13.30-1989D)

The estimated dispersion of a set of measurements. In a normal distribution, it is mathematically defined as the square root of the variance and is represented by $\sigma$ ("sigma").

Population Standard Deviation ($\sigma$)

The biased standard deviation of a population, defined mathematically as $\sigma = \sqrt{\frac{\sum (x_i - \bar{x})^2}{n}}$, where $x_i$ represents sample counts for each data point, $\bar{x}$ is the mean, and $n$ is the number of data points.

Sample Standard Deviation ($s$)

The unbiased standard deviation of a population commonly used in practice, calculated by the formula $s = \sqrt{\frac{\sum (x_i - \bar{x})^2}{n - 1}}$.

Gaussian Distribution Counting Threshold

A counting distribution representative of a counting function with a mean observable success $>20$, in which mathematical probabilities are defined across standard deviation intervals.

Gaussian Empirical Probabilities ($\pm 1\sigma$, $\pm 2\sigma$, $\pm 3\sigma$)

In a Gaussian distribution, $68.2\%$ of observed successes fall within $\pm 1$ standard deviation of the mean, $95.4\%$ fall within $\pm 2$ standard deviations, and $99.97\%$ fall within $\pm 3$ standard deviations.

Random Process in Radiation Protection

The decay of a radioactive sample, where the area under the statistical curve represents the probability of success.

Pre-Operational Source Checks (Calibration)

A routine evaluation of a counting system wherein a radioactive source with known activity is counted twenty times for one minute each to calculate the mean, standard deviation, system efficiency, and chi-squared test.

Chi-Squared Test ($X^2$)

A statistical "goodness-of-fit" test used to determine the precision of a counting system by assessing how well observed counting data fits a Poisson distribution curve.

Precision

A measure of exactly how a result is determined without regard to its accuracy; it measures the reproducibility of a result, or how often a result/success can be repeated.

Chi-Squared Value Formula (Equation 5)

The equation used to calculate the sample chi-square value: $X^2 = \frac{\sum (x_i - \bar{x})^2}{\bar{x}}$, where $x_i$ is the sample count for each data point and $\bar{x}$ is the mean.

Acceptable Chi-Square Range (Air Quality Control Criteria)

For fixed counting systems performing $20$ one-minute counts at a $95\%$ desired confidence level, the satisfactory range for $p = 10\%$ through $p = 90\%$ is $12$ to $27$.

Quality Control (QC) Charts

Charts prepared using calibration source counting data to track system performance while in use, displaying center lines for the mean as well as lines at $\pm 1$, $\pm 2$, and $\pm 3$ standard deviations.

Alpha/Beta Counter Performance Record

A specific documentation form completed after calibration and performance testing, maintained daily while the counter is in use, and stored near the counter for reference to background trends, minimum detectable activity, and counter efficiency.

Warning Limits

System operating limits set at $\pm 2$ standard deviations ($\pm 2\sigma$) from the mean; counts falling outside these limits suggest that something may be wrong.

Control Limits

System operating limits set at $\pm 3$ standard deviations ($\pm 3\sigma$) from the mean; values falling outside indicate unacceptable counter performance, serving as the standard for acceptable performance.

Indicators of Systematic Error

Non-random patterns appearing on quality control charts, such as multiple points outside $2\sigma$, repetitive points outside $1\sigma$, multiple consecutive points on the same side of the mean, or multiple consecutive points going steadily up or down.

Counter Efficiency (Yield)

The fraction of the total number of radiations emitted by a radioactive source that is intercepted, registered, and detected by a detector.