11.4 The Chi-Square Test of Independence

expected cell frequency condition

the expected counts should be greater than 5 in each cell

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

contingency table

a two-way table that classifies individuals according to two categorical variables

chi-square test of independence

a test for determining whether two categorical variables are independent by examining the distribution of counts classified by two categories at the same time - the degrees of freedom are equal to (# of rows - 1)(# of columns - 1) where the number of rows and the number of columns are the number of categories in each of the two categories

expected counts of independence

the distribution of counts into groups as would be expected if the first category were distributed in the same way across the second category - this calculation is the same as the expected counts for a test of homogeneity

chi-square model

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

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

two-way table

each cell inside shows counts of individuals - one way classifies a sample according to a categorical variable, and the other way can classify different groups of individuals according to the same variable or classify the same individuals according to a different categorical variable

chi-square statistic

can be used to test whether the observed counts match the counts we expect according to some model - the equation 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 using (Obs-Exp)² / Exp