Small random samples of biochemical and biological data are often representative of complex distribution functions and are difficult to analyze in detail by conventional means. The common approaches reduce the data to a few representative parameters (such as their moments) or combine the data into a histogram plot. Both approaches reduce the information content of the data. By fitting the empirical cumulative distribution function itself with models of integrated probability distributions, the information content of the raw data can be fully utilized. This approach, distribution analysis by nonlinear fitting of integrated probabilities, allows analysis of normally distributed samples, truncated data sets, and multimodal distributions with a single, powerful data processing procedure. D 1990 Academic Press, Inc.
Typically, analysis of the variation in small random samples of experimental data in biochemistry and biology is limited to calculation of a few descriptive parameters and application of simple statistical tests. The errors in the data are often assumed to be normally distributed (except for counting data which are generally assumed to follow a Poisson distribution). They are processed to obtain a mean value and its standard deviation and statistical tests are subsequently applied to these numbers on the assumption that they represent parameters for a normally distributed sample. More rigorous analysis might include calculation of higher order moments (the mean and standard deviation are the 0th order moment and the square root of the 1st reduced moment, respectively) and examination of these values to see if they actually fit within the range of values for a normal distribution. However with a small sample, the calculated values of the moments, particularly the higher order moments, will vary considerably from the 0003.x97/90