Random Groups-Smoothing in Equipercentile Equating

As described in Chapter 2, sample statistics are used to estimate equating relationships. For mean and linear equating, the use of sample means and standard deviations in place of the parameters typically leads to adequate equating precision, even when the sample size is fairly small. However, when sample percentiles and percentile ranks are used to estimate equi-percentile relationships, equating often is not sufficiently precise for practical purposes because of sampling error.