Degree Type


Date of Award


Degree Name

Doctor of Philosophy




An estimator of the population distribution function that can be used with the complex sampling designs found in survey sampling is given. This estimator is used to define a quantile estimator and an estimator of the interquartile range that are based on the survey design. A design-consistent superpopulation model is assumed, and large sample properties of estimators constructed from single-stage stratified cluster samples are presented. Extensions to other complex designs are discussed. Based on these results, large-sample procedures for constructing confidence sets for quantiles and the interquartile range are given. Design-based variance estimators for both the quantile estimator and the interquartile range are derived form these procedures;The proposed estimation procedures have been incorporated into PC CARP, a computer program which analyzes data from one-stage or two-stage stratified cluster samples. Computational procedures used to esimate the distribution function, quantiles, the interquartile range, and other associated statistics are briefly described;Three Monte Carlo simulation studies were performed to evaluate the performance of this implementation of the proposed estimation procedures. For the populations and sample sizes included in the studies, sample quantiles of order 0.25, 0.50, and 0.75 displayed near zero bias. Comparison of observed variances of the quantile estimators to the average of variance estimators across simulated samples showed that the proposed variance estimator is acceptable. In all cases, the obtained coverage probabilities for confidence intervals were near the nominal level of 95 percent.



Digital Repository @ Iowa State University,

Copyright Owner

Carol Ann Francisco



Proquest ID


File Format


File Size

196 pages