ORCID

0000-0001-8937-5148 (Wickrama Senevirathne), 0000-0002-7211-2752 (Dutta)

College

College of Sciences

Department

Mathematics & Statistics

Graduate Level

Doctoral

Graduate Program/Concentration

Computational and Applied Mathematics

Publication Date

2023

DOI

10.25883/fxev-bv52

Abstract

Clustered data are frequently observed in various domains of scientific and social studies. In a typical clustered data, units within a cluster are correlated while units between different clusters are independent. An example of such clustered data can be found in dental studies where individuals are treated as clusters and the teeth in an individual are the units within a cluster. While analyzing such clustered data, it has been observed that the number of units present in a cluster can be informative in terms of being associated with the outcome from that cluster. Specifically, when the aim is to compare the outcomes from two different groups of units (e.g., upper teeth vs. lower teeth) in a clustered data, then the number of units belonging to a group in a typical cluster, i.e., an intra-cluster group size, can be informative about the outcome from that group in that cluster. Although such clustered data analysis has recently gained importance, there does not exist any formal statistical method for testing the hypothesis that a particular clustered data has informative intra-cluster group sizes (IICGS). However, ignoring the existence of this IICGS during group-based outcome comparisons in a clustered data can result in a biased inference. In this research, we focus on developing a statistical hypothesis testing mechanism that can test a claim of IICGS in a clustered data setting. We use Kolmogorov-Smirnov test-type nonparametric test statistic and a bootstrap hypothesis testing procedure to develop our testing method. Through a variety of simulated data, we demonstrate that our proposed statistical testing method maintains the nominal type-I error rate and has substantial power in identifying IICGS in a clustered data.

Keywords

Bootstrapping, Clustered data, Correlated data, Hypothesis testing, Informative intra-cluster group size, Resampling

Disciplines

Statistical Methodology

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A Bootstrap Test for Informative Intra-Cluster Group Sizes in Clustered Data


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