Calculation of confidence intervals for a finite population size

For any estimate of response, confidence intervals are important as they help quantify a plausible range of values for the population response. However, there may be instances in clinical research when the population size is finite, but we wish to take a sample from the population and make inference from this sample. Instances where you can have a fixed population size include when undertaking a clinical audit of patient records or in a clinical trial a researcher could be checking for transcription errors against patient notes. In this paper, we describe how confidence interval calculations can be calculated for a finite population. These confidence intervals are narrower than confidence intervals from population samples. For the extreme case of when a 100% sample from the population is taken, there is no error and the calculation is the population response. The methods in the paper are described using a case study from clinical data management.