For the cases of normally- and binomially-distributed outcome variables, methods are presented for analyzing ophthalmologic data to which a person may have contributed two eyes worth of information, the values from the two eyes being highly correlated. A frequently-used method of analysis, where each eye is treated as an independent random variable, is shown to be invalid in the presence of intraclass correlation: it yields true p-values two to six times as large as nominal p-values when realistic assumptions are made about the degree of correlation between eyes. These results may be applicable to other medical specialties, such as otolaryngology, where highly-correlated replicate observations are obtained from individuals.