Interpretation of errors in counting experiments

Abstract Digital experiments, such as the measurement of radioactivity, are usually characterized by random errors which follow the Binomial or Poisson distribution. Three types of difficulty which commonly arise in the statistical treatment of such experiments include a) failure to recognize that the uncertainty in the physical quantity of interest may be governed by a compound probability distribution, particularly when dealing with shortlived radioactivity; b) the improper use of the chi-squared statistic when making standard error estimates in weighted least-squares calculations; c) selecting the correct number of degrees of freedom and choosing between the X2 dispersion test and the goodness-of-fit test for grouped data.