ABSTRACT

At the end of this chapter, you should be able to:

• calculate a Chi-square value for a given distribution • test hypotheses on fitting data to theoretical distribution using the Chi-square distribution • recognise distribution-free test • use the sign test for two samples • use the Wilcoxon signed-rank test for two samples • use the Mann-Whitney test for two samples

The significance tests introduced in Chapter 65 rely very largely on the normal distribution. For large sample numbers where z-values are used, the mean of the samples and the standard error of the means of the samples are assumed to be normally distributed (central limit theorem). For small sample numbers where t-values are used, the population from which samples are taken should be approximately normally distributed for the t-values to be meaningful. Chi-square tests (pronounced K Y and denoted by the Greek letter χ), which are introduced in this chapter, do not rely on the population or a sampling statistic such as the mean or standard

error of the means being normally distributed. Significance tests based on z-and t-values are concerned with the parameters of a distribution, such as the mean and the standard deviation, whereas Chi-square tests are concerned with the individual members of a set and are associated with non-parametric tests.