THERE ARE A NUMBER OF REASONS FOR THE USE OF STATISTICAL METHODS IN THE ANALYSIS OF DATA, ONE OF THESE IS RANDOMNESS; E.G., IN THE USE OF AN ANALYSIS OF TECNIQUE THERE WILL USUALLY BE VARIATIONS AND OVERLAP IN THE DISTRIBUTIONS DUE TO SOURCES OF ERROR IN THE TECHNIQUE, THE OBSERVATION, OR THE METHOD OF MEASUREMENT. SOURCES OF ERROR MAY INVOLVE VARIABILITY OF THE EXPERIMENTAL MATERIAL, UNCONTROLLED CONDITIONS, OR MEASUREMENT ERROR. DISTRIBUTION FUNCTIONS PROVIDE A MODEL OF HOW SOMETHING BEHAVES. GOODNESS OF FIT TESTS ARE BASED ON THE TRUE (HYPOTHESIZED) DISTRIBUTION FUNCTION AND THE SAMPLE CUMULATIVE DISTRIBUTION FUNCTION, AND INCLUDE AMONG OTHERS THE CHI-SQUARED TEST. RESEARCH EXEMPLIFYING THE USE OF STATISTICAL METHODS IN CRIMINALISTICS IS PRESENTED. THESE INCLUDE LEVEL OF CONFIDENCE PREDICTIONS FOR BREATH ANALYZERS, BIVARIATE DISCRIMINATION FOR GUNSHOT RESIDUE DETECTION, AND MULTIVARIATE DISCRIMINATION IN PROFILE MATCHING OF TRACE ELEMENT ANALYSES OR THE OUTPUT OF A SPEECH FREQUENCY ANALYZER BY USING THE CHI-SQUARED VARIABLE. STATISTICAL CHARTS AND GRAPHS ARE INCLUDED. (JAP)