Basic elements of probability theory, including simple examples based on the roll of a pair of dice, are used to demonstrate the general application of this technique to any area subject to statistical analysis. Probability, sampling distributions, sampling, common theoretical distributions, and the logic of hypothesis testing are discussed. Interpretations of tests of significance are presented in the contexts of simple random sampling and of populations and nonprobability samples. The relationship between significance testing and the construction of confidence intervals is explored. Important assumptions and assumptions which can be ignored in interpreting selected techniques are given. The paper also provides technical and philosophical criticisms of the use of tests of significance in social science research. It is concluded that such tests should be used with caution, although many social scientists believe that the tests are valuable. Figures, tables, notes, and 27 references are included. For other monographs in this series, see NCJ 72008 and 72011-14.