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Formulas for the standard error of equating (SEE) for a new equating technique, the kernel method, are developed in detail for three equating designs –two random groups, external anchor‐test and internal anchor‐test. The kernel method includes both linear and equipercentile methods as special cases. The SEEs developed in this paper make crucial use of log‐linear models to presmooth (i.e. estimate) score distributions. The resulting SEEs reflect the method of estimation, the equating design and the final shape of the resulting equating function. An example is given that compares the SEEs for several applications of the kernel method.

Introduction and Background.

For a national survey of reading ability among young adults using a multistage, stratified probability sample, generalized variance functions (GVF) were estimated. That is, an attempt was made to express the estimated variance of a statistic as a function of that statistic and other characteristics of the variable of interest. With GVFs estimated from a development sample of variables, predictions of sampling variance were made for other variables in a confirmation sample and comparisons made with conventional jackknife estimates. Conclusions were drawn about the feasibility of use of GVFs, with emphasis on the margin of additional error that is introduced.