Date of Award

Spring 5-10-2019

Degree Type


Degree Name

Master of Public Health (MPH)


Public Health

First Advisor

Brian Barger, Ph.D.

Second Advisor

Rebecca Wells, Ph.D.


Complex surveys such as the National Survey of Children’s Health (NSCH) are used to inform public policy and make important decisions. Often researchers using complex survey data may wish to study relationships in subgroups of the data set, but subgrouping can lead to unstable variance estimates. Unstable variance estimates lead to large confidence intervals and reduced likelihood of statistically significant results. This study explored the genesis of unstable variance by unpacking subgroups and investigating relationships between (a) subgroup size and variance estimates and (b) small strata and variance estimates.

Demographic (N= 36), health condition (N= 27), and combinations of both health condition and demographic (N= 90) categories found in the 2016 NSCH were used to form 156 subgroups within the survey. A simple logistic model, = β1*sex, was built for each subgroup and the lengths of confidence intervals for β1 were recorded. The relationships between (a) subgroup size and variance estimates and (b) count of small strata (strata with less than three observations) and confidence interval length were analyzed visually and in linear regression.

Two models, for unweighted and weighted analysis, were built for the relationships between subgroup size and confidence interval lengths in the functional form = a/bxn and first derivatives of the functions confirmed visual analysis that the rate of change stabilized at subgroup sizes greater than 450. No model was found to adequately describe the relationship between small strata and confidence interval length.

Subgroups sized larger than 450 and subgroups with no small strata produced stable variance estimates. The variance estimate increased exponentially as the subgroup size decreased from 450. The variance estimates increased rapidly as the small strata increased from zero.

These results may help researchers predict if unstable variance estimates are likely to be produced when planning a study using 2016 NSCH. Furthermore, they underscore that policy decisions informed by the NSCH should be made with care.

Available for download on Wednesday, May 06, 2020