11.5 Which Chi-Square Test?

expected cell frequency condition

the expected counts should be greater than 5 in each cell

chi-square test for 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)

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)

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

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 test of goodness-of-fit

a test comparing the distribution of counts across categories to a given distribution - the degrees of freedom is equal to (# of cells - 1)

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

expected counts

the distribution of counts into groups as would be expected if they were distributed as completely perfectly