11.3 The Chi-Square Test of Homogeneity

cell

one element of a table, which corresponds to a specific row and column - table cells can hold counts, percentages, measurements on other variables, or several values

expected counts for homogeneity

the distribution of counts into groups as would be expected if each group were distributed in the same way across the given categories

chi-square test of homogeneity

a test comparing the distribution of counts for two or more groups on the same categorical variable - the degrees of freedom are equal to (# of rows - 1) * (# of columns - 1), where the number of rows is the number of categories and the number of columns is the number of groups being compared

chi-square model

these are skewed to the right, parameterized by their degrees of freedom, becoming less skewed with increasing degrees of freedom

counted data condition

the condition that the values in each cell of a table must be counts for the categories for a categorical variable - these methods cannot be applied to proportions, percentages, or measurements, just because they happen to be organized in a table

chi-square statistic

the chi-square statistic can be used to test whether the observed counts match the counts we expect according to some model - the formula is χ² = ∑_{all cells} (Obs-Exp)² / Exp

chi-square component

the components of a chi-square calculation are found for each cell of the table - (Obs - Exp)² / Exp

expected cell frequency condition

the expected counts should be greater than 5 in each cell