ABSTRACT
This chapter explains why the chi-square distribution can be used to approximate the sampling distribution when comparing observed frequencies with expected frequencies. It discusses the use of the chi-square distribution in environmental and agricultural research. The chapter provides statistical tests of hypotheses for goodness-of-fit tests, test of differences among proportions, tests of independence, and tests of homogeneity. It calculates the expected frequencies for these tests, and determines the degrees of freedom (d.f.) for each. Chi-square analysis is used to test hypotheses about the significance of the differences that may exist between three or more sample percentages. In environmental and agricultural research we often replicate experiments several times to make sure that error is minimized in experimentation. When the data from several replications are available for analysis, the chi-square test of homogeneity is used to pool the data over all replications.
