ABSTRACT
Chi-square and distribution-free tests are used in science and engineering. Chi-square is a statistical test commonly used to compare observed data with data students would expect to obtain according to a specific hypothesis. Distribution-free methods do not rely on assumptions that the data are drawn from a given probability distribution. Non-parametric methods are widely used for studying populations that take on a ranked order. The chapter describes a Chi-square value for a given distribution, test hypotheses on fitting data to theoretical distribution using the Chi-square distribution. It utilizes the sign test for two samples, the Wilcoxon signed-rank test for two samples and the Mann–Whitney test for two samples. For theoretical distributions such as the binomial, Poisson and normal distributions, expected frequencies can be calculated.
