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The standard error of moving average smoothed equipercentile equating

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Abstract

A very important aspect of virtually any kind of systematic investigation is to be able to identify whether two entities are different, and, almost equivalently, whether they are the same. We need to be sure that measurements made at different time in different places by different experimenters are equivalent. To do this in the social sciences, the procedure of equating is necessary to be able to compare measurements made using different instruments. Small sample sizes can lead to apparent jaggedness in the formulae for equating two quantities, and some kind of smoothing procedure is frequently necessary when dealing with relatively small samples. A large-sample formula is developed for the standard error of moving average smoothed equipercentile equating on a single sample. An example is given of the application in equating two versions of a reading test, and the results are verified using a bootstrap procedure. The large sample formula gives a result that is close to the bootstrap procedure, except at very sparse frequencies.

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  1. NFER, The Mere, Upton Park, Slough, Berkshire, SL1 2DQ, UK

    Dougal Hutchison

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  1. Dougal Hutchison
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Correspondence to Dougal Hutchison.

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Hutchison, D. The standard error of moving average smoothed equipercentile equating. Qual Quant 44, 783–791 (2010). https://doi.org/10.1007/s11135-009-9231-1

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  • DOI: https://doi.org/10.1007/s11135-009-9231-1

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