Independence and Homogeneity¶

Test for Independence¶

Contingency table: 2-way table

Conditions for Independence Test¶

• Random sample
• Independent values
  • Sample with replacement
  • or \(n < 0.1N\)
• Large counts condition
  • Expected values \(\geq 5\)
  • or \(\geq 80\%\) of expected values \(> 5\) and all are \(\geq 1\)

Calculate Independence Test¶

• \(Expected\ value\) = \(Probability\ in\ row \times Probability\ in\ column \times Total\ number\ in\ the\ sample\) = \(\dfrac{Row\ total \times Column\ total}{Total\ number\ in\ the\ sample}\)
• \(dof = (N_{row} -1)(N_{col} -1)\)