A simple test of association for contingency tables with multiple column responses

Area of Science:

• Statistics
• Biometrics
• Survey Data Analysis

Background:

• Standard chi-squared tests are inadequate for two-way tables with multi-response categorical variables.
• Existing bootstrap procedures offer valid association tests but are computationally intensive and unfamiliar to many.
• The need for accessible and efficient statistical methods in analyzing complex categorical data is evident.

Purpose of the Study:

• To develop a simplified statistical test for association in two-way tables with multi-response categorical variables.
• To adapt methods for complex survey data analysis to address limitations of existing tests.
• To provide a computationally less involved alternative to bootstrap tests for this specific data structure.

Main Methods:

• Utilized the Rao and Scott (1981) methods for analyzing complex survey data.
• Developed a corrected chi-squared statistic based on these survey data analysis techniques.
• Applied the corrected statistic to test for associations in two-way tables with one multi-response categorical variable.

Main Results:

• The proposed corrected chi-squared statistic offers a simpler approach compared to bootstrap methods.
• The new method provides a valid alternative for testing associations in the specified data scenarios.
• This approach aims to enhance the practical applicability of statistical tests for researchers.

Conclusions:

• A computationally simpler and accessible corrected chi-squared test is presented for association in two-way tables with multi-response categorical variables.
• The study successfully adapted complex survey data analysis techniques for a more practical statistical test.
• This method offers a valuable tool for practitioners dealing with multi-response categorical data, enhancing statistical analysis efficiency.