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This chapter provides a general overview of equating and briefly considers important concepts. The concept of equating is described, as is why it is needed, and how to distinguish it from other related processes. Equating properties and designs are considered in detail, because these concepts provide the organizing themes for addressing the statistical methods treated in subsequent chapters. Some...
As was stressed in Chapter 1, the same specifications property is an essential property of equating, which means that the forms to be equated must be built to the same content and statistical specifications. We also stressed that the symmetry property is essential for any equating relationship. The focus of the present chapter is on methods that are designed to achieve the observed score 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 equipercentile relationships, equating...
Chapter 1 introduced the common-item nonequivalent groups design. For this design, two groups of examinees from different populations are each administered different test forms that have a set of items in common This design often is used when only one form of a test can be administered on a given test date. As discussed in Chapter 1, the set of common items should be as similar as possible to the...
Equipercentile equating methods have been developed for the common-item nonequivalent groups design. These methods are similar to the equipercentile methods for random groups described in Chapter 2. Equipercentile methods with nonequivalent groups consider the distributions of total score and scores on the common items, rather than only the means, standard deviations, and covariances that were considered...
Item response theory (IRT) methods are used in many testing applications, and the use of IRT has been reinforced by many book-length treatments (e.g., Baker, 1992a; Hambleton and Swaminathan, 1985; Hambleton et al., 1991; Lord, 1980; van der Linden and Hambleton, 1997; Wright and Stone, 1979). Applications of IRT include test development, item banking, differential item functioning, adaptive testing,...
Two general sources of error in estimating equating relationships are present whenever equating is conducted using data from an equating study: random error and systematic error. Random equating error is present when the scores of examinees who are considered to be samples from a population or populations of examinees are used to estimate equating relationships. When only random equating error is...
Many of the practical issues that are involved in conducting equating are described in this chapter. We describe major issues and provide references that consider these issues in more depth. The early portions of this chapter focus on equating dichotomously scored paper-and-pencil tests. In later portions, the focus broadens to include practical issues in other contexts, including computerized testing...
As discussed briefly in Chapter 1, scaling is the process of associating numbers or other ordered indicators with the performance of examinees. These numbers and ordered indicators are intended to reflect increasing levels of achievement or ability. The process of scaling results in a score scale. The scores that are used to reflect examinee performance are referred to as scale scores. The term primary score scale...
Equating adjusts for differences in difficulty, not differences in content. That statement on page 3 is one of the most important sentences in the introductory chapter of this book. To a large extent this chapter considers situations in which statistical adjustments are made to scores for tests that differ in content and/or difficulty, and usually both. In some cases, these differences are...
In Chapter 1, we summarized the concepts of equating, scaling, and linking In subsequent chapters, these concepts were further developed and elaborated. In Chapter 11 we focus on some current and future challenges in each of these areas.
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