The for independence is a powerful tool for analyzing relationships between . It helps determine if there's a significant association between two variables by comparing to if the variables were independent.
This test is crucial for understanding patterns in data, especially in business contexts. By constructing , calculating the , and interpreting results, we can uncover valuable insights about customer preferences, market trends, and other important categorical relationships.
Chi-Square Test for Independence
Appropriateness of chi-square test
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Used when analyzing relationship between two categorical variables (nominal or ordinal)
Nominal has no inherent order (gender, color, product category)
Ordinal has natural order but no fixed interval (education level, satisfaction rating, income bracket)
Assesses significant association between variables
(H0): Variables are independent, no association
(H1): Variables are dependent, association exists
Requires data from single population with each subject classified on both variables simultaneously
Cannot combine data from separate populations or different time periods
Construction of contingency tables
Contingency table is matrix displaying frequency distribution of variables
Rows represent categories of one variable (age groups)
Columns represent categories of other variable (preferred product)
Each cell contains observed frequency (count) for combination of categories
Calculate expected frequency for each cell assuming null hypothesis is true