Statistical variability of biomedical data: Part 1. The influence of serial correlation on mean value estimates

Many biomedical variables are subject to large short-term fluctuations; so, measurements of the variable requires statistical improvement. Such variables also commonly exhibit longitudinal correlation due to systematic variations contributed by underlying biological mechanisms and sometimes constituting most of the variability. This correlation structure interferes with the operation of statistical procedures, such as longitudinal averaging to improve resolution of the mean value, and manipulations designed to provide objective comparative assessments of data samples. A convenient approach to evaluating and overcoming these problems can be made through the degrees of freedom concept. It is shown how the degrees of freedom content of the sample of serially correlated data is related to the correlation structure of the variable and how this affects variability of the mean in different sized samples. The approach is confirmed both by simulation and by empirical studies on several biomedical variables: various intra-arterial and left ventricular blood-pressure measurements, heart rate, and nystagmus inter-beat intervals in the stimulated electro-oculogram. The implications for measurement are discussed, specifically in respect of sampling protocols to improve resolution to a specified extent (for which a microprocessor instrument has been designed), as well as in determining the inherent longitudinal resolution of a data sequence and the effective precision displayed by the observations.