11.4 The Chi-Square Test of Independence

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10 Terms

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expected cell frequency condition

the expected counts should be greater than 5 in each cell

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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

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contingency table

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

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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

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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

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chi-square model

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

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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

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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

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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

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chi-square component

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