Constructing efficient strata boundaries in stratified sampling using survey cost.

Area of Science:

• Statistics
• Survey Methodology
• Econometrics

Background:

• Stratified sampling designs aim for precise population parameter estimation.
• Optimal strata boundaries (OSB) and sample sizes (OSS) are crucial for maximizing precision.
• Existing OSB/OSS methods may not remain optimal under fixed total sample size or budget constraints.

Purpose of the Study:

• To propose a methodology for computing OSB and OSS considering per-unit stratum measurement costs or probability density functions.
• To address the challenge of maintaining optimal stratification under fixed survey budgets.
• To improve the accuracy of population parameter estimates in stratified surveys.

Main Methods:

• Developed a novel methodology for calculating OSB and OSS incorporating cost information.
• Employed design-based stratification using the HILDA Survey dataset (Wave 18).
• Estimated the mean of Gamma-distributed annual total disposable income in Australia.
• Provided numerical illustrations with exponential and right-triangular distributions.

Main Results:

• The proposed method for computing OSB and OSS is effective even with fixed total sample sizes and known costs.
• Empirical application using HILDA data demonstrated the method's utility for policy-relevant variables like income.
• The technique was implemented in the updated stratifyR package for practical application.

Conclusions:

• The suggested method provides satisfactory results, offering improved or comparable efficiency to existing techniques.
• This approach enhances the accuracy of population parameter estimates in stratified surveys.
• The methodology is robust across different continuous variable distributions and practical survey constraints.