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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