Chi-Squared Tests
Chi Squared Tests
Goodness of Fit
Use when 1 variable, many categories, 1 sample
Hypothesis
\(h_0:p_1=p_2=p_n...\) or \(p_1=..., p_2=..., p_n=...\)
\(h_a:\) At least \(n\) proportions are wrong
Conditions
- Expected count \((E) \ge 5\)
- Random or representative
Equations
\[
\large
\chi^2=\Sigma{\frac{(O-E)^2}{E}}
\]
Independence
Use when 2 variables and 1 sample
Hypothesis
\(h_0:\) Variable 1 and variable two are independent
\(h_a:\) Variable 1 and variable two are dependent
Conditions
Random or representative, and expected count \((E) \ge 5\)
Equations
\[
E=\frac{(\text{row})(\text{column})}{\text{grand total}}
\]
Homogeneity
Descriptors
Use when 1 variable, many categories, and multiple samples
Hypothesis
\(h_0:\) Category proportions are the same across each population
\(h_a:\) Category proportions are not the same across each population