多階層取樣單位異質性對科學調查之母體推論研究

Abstract

本研究以Bootstrap重複取樣程序，評估分層隨機取樣（stratified random sampling）及規模等比率取樣（probability proportional to size），對於調查研究的母體推論影響。調查研究的資料常包含多層次的結構，而分析必須搭配適當的取樣權重，才能正確推論母體特性（蔡良庭、楊志堅，2008）。權重的計算又隨不同取樣設計而計算方式不同，但此權重計算的差異對於母體特性的推論，卻最常被忽略，也需更進一步驗證。本研究以數值模擬方法並搭配臺灣社會變遷調查的實徵資料分析，探討不同權重的計算對於母體推論的影響。結果顯示，若忽略了取樣單位間的樣本數差異，採用分層隨機取樣設計時，取樣數愈多，母群體特性的推論愈不精確。規模等比率的取樣設計及權重計算能提供更精準的母體推論。In this study, the Str. RS (stratified random sampling) and PPS (probability proportional to size) sampling procedures were used to evaluate the heterogeneity of multi-level primary sampling units on population inference in social science research. When a social science survey has complexly designed sampling frames, the Str. RS and PPS are often applied. However, the effects of different sampling weights within these two methods on the inference of population characteristics are often neglected. A numerical simulation study and a real data analysis on Taiwan Social Change Survey data with a further extension confirmatory factor analysis model based on Yang and Tsai (2008) were proposed in this study. Independent variables manipulated in this study include the sampling designs, data type (continuous or categorical), sampling size, and heterogeneity of PSU. The results suggest the PPS sampling design can provide a more precise parameter estimate of CFA models in a complexly designed sampling frame survey, whether the data type is continuous or categorical. We summarize the findings and recommend the PPS multistage procedure based on the bootstrap method that can be used in practical social science survey applications.