A statistical approach to histology is outlined starting from the notion that the field of histology is morphological, and that its data are provided by the exercise of a skill. These data give rise by a variety of operations to certain scales of measurement. Particular attention is drawn to the use of the ordinal scale in histology.
The concept of randomness has been utilized in several ways. Volume can be estimated by microscopic random sampling, and relative numbers of cells or nuclei can be determined by enumeration in representative tissue sections, provided systematic bias is allowed for. The observation that particular cells or events appear to occur at particular sites in a tissue may have to be tested against the alternative hypothesis that the spatial distribution is random. There are certain fallacies which may enter into the use of the appropriate tests for randomness and non-randomness.
The statistical concept of a random variable underlies probabilistic models of cellular proliferation in tissues that are growing exponentially. Stochastic models of the steady state have not been constructed for cell populations.
Models of tissues in a steady state can be constructed in terms of specific hypotheses concerning the component cells, i.e. as regards the distribution of age or intermitotic time. These models give little information about individual cells unless the equilibrium is perturbed and the restoration of equilibrium of the models compared with empirical data.