Generalized Mean Estimators for Sensitive and Non-Sensitive Variables in the Presence of Measurement Errors.

Abstract

In survey research, accurate collection and recording of information is very critical. The researcher must deal with many potential problems. First the response rate may be poor due to various reasons such as poorly prepared survey instrument, poor execution of survey, survey questions being very personal in nature, and untrained field workers. Some of these issues lead to measurement errors which are the most common form of non-sampling errors. More formally, these errors are defined as the difference between the true value of a variable and its recorded value. It is for this reason these errors are also known as observational errors.

Measurement errors have been studied by various authors with Cochran (1963) drawing early attention to these errors. While mean estimation for nonsensitive variables has been studied extensively in the presence of measurement errors, no attempt has been made to study mean estimation for sensitive variables in the presence of measurement errors. By sensitive variable, we mean a variable for which there is a natural tendency on the part of survey respondent to either refuse to answer or to give a socially desirable answer as opposed to correct answer. Randomized Response Technique (RRT) introduced originally by Warner (1965), and later refined by many researchers, is a great tool to deal with the problem of social desirability bias in surveys involving sensitive questions. The main focus of this thesis is on introducing a generalized mean estimator for non-sensitive as well as sensitive quantitative variables in the presence of measurement errors, and on studying the impact of measurement errors on mean estimation.

In Chapter 1, we have provided a brief discussion about measurement errors, sensitive variables, and various versions of the Randomized Response Techniques (RRT). Furthermore, measurement errors under simple random sampling and stratified random sampling have been illustrated. Greater details on these two important topics, measurement errors and randomized response methodology, are provided as part of literature review in Chapter 2. In Chapter 3, we have reviewed some existing mean estimators for non-sensitive and sensitive study variables in the presence of measurement errors under both sampling designs.

The major contributions of this thesis start from Chapter 4. In this chapter, a generalized mean estimator for a non-sensitive study variable under simple random sampling design has been proposed to examine the impact of measurement errors on mean estimation. Some special cases for generalized mean estimator have also been discussed. In Chapter 5, we continue the study undertaken in Chapter 4 but in the context of the stratified random sampling design. Chapters 6 and 7 are very important chapters where we have examined the impact of measurement errors on mean estimation of a sensitive study variable under the simple random sampling design and the stratified random sampling design respectively. We have used extensive simulations and numerical examples to validate our theoretical findings. Finally some concluding remarks with some possible future directions are mentioned in Chapter 8.