ABSTRACT
The binomial distribution and its normal approximation provide a test of significance for hypotheses about dichotomous data. It is an appropriate test to use when observations can be classified into one of two possible categories such as “yes-no,” or “male-female,” or “correct-incorrect.” When data can be classified in more than two categories, the binomial no longer provides a test of significance. For example, a response might be classified as occurring “always,” “often,” “sometimes,” or “never.” In that situation, when the population is composed of more than two classes of events, it would appear reasonable to employ the multinomial distribution to determine the probability of obtaining particular kinds of samples. This is theoretically possible but the calculations required quickly become prohibitive. Consequently, we use a distribution that approximates the multinomial (and the binomial) distribution. This distribution, and the test of significance named for it, is called Chi Square (χ2).
