In this paper, we consider the estimation of intracluster correlation for ordinal data. We focus on pure-tone audiometry hearing threshold data, where thresholds are measured in 5 decibel increments. We estimate the intracluster correlation for tests from iPhone-based hearing assessment applications as a measure of test/retest reliability. We present a method to estimate the intracluster correlation using mixed effects cumulative logistic and probit models, which assume the outcome data are ordinal. This contrasts with using a mixed effects linear model which assumes that the outcome data are continuous. In simulation studies, we show that using a mixed effects linear model to estimate the intracluster correlation for ordinal data results in a negative finite sample bias, while using mixed effects cumulative logistic or probit models reduces this bias. The estimated intracluster correlation for the iPhone-based hearing assessment application is higher when using the mixed effects cumulative logistic and probit models compared to using a mixed effects linear model. When data are ordinal, using mixed effects cumulative logistic or probit models reduces the bias of intracluster correlation estimates relative to using a mixed effects linear model.