An extension of the Wilcoxon Rank-Sum test for complex sample survey data

Area of Science:

• Statistics
• Survey Methodology

Background:

• Complex survey designs often involve unequal probabilities of selection, stratification, and clustering.
• These design features are crucial for generalizability but complicate standard statistical analyses.
• The Wilcoxon rank sum test is a common tool for bivariate ordinal data analysis, but lacks a direct extension for complex survey data.

Purpose of the Study:

• To develop an extension of the Wilcoxon rank sum test suitable for complex survey data.
• To provide a method for analyzing ordinal variables in complex surveys that accounts for design features.
• To offer a statistical approach that generalizes bivariate ordinal analysis to complex survey settings.

Main Methods:

• Formulated a proportional odds cumulative logistic regression model for ordinal outcomes in complex survey data.
• Utilized an estimating equations score statistic for the null hypothesis of no group effect.
• Leveraged the equivalence between the Wilcoxon rank sum test and score tests in simple random sampling as a foundation.

Main Results:

• The proposed method provides a statistically sound extension of the Wilcoxon rank sum test for complex survey data.
• The approach effectively incorporates survey design features like unequal probabilities, stratification, and clustering into the analysis.
• Demonstrated application of the method using national health care survey data.

Conclusions:

• The developed proportional odds model and score test offer a robust extension of the Wilcoxon test for complex survey analysis.
• This method allows for reliable comparison of ordinal variables while accounting for intricate survey designs.
• The approach is applicable to various complex surveys, including those assessing health care utilization and insurance coverage.