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Several techniques have been developed for creating continuous smooth distributions of test norms. This paper describes two studies that explore the behavior of cubic splines in order to determine their appropriateness for use in test norming. The first study uses data from the Curriculum Referenced Tests of Mastery (CRTM) and employs two smoothing techniques in determining distributions of percentile ranks (PR). Method 1 calculated PR values from cumulative frequency counts of raw scores values and then smoothed them to create a continuous distribution. Method 2 smoothed the raw frequencies to create the continuous distribution. The second study was designed to generate a theoretical population, sample repeatedly from it, and smooth the results in a comparative study of the two procedures. Both studies showed that spline smoothing techniques are a convenient and economical procedure for analytically smoothing test score distributions and generally give good results. The second study found that, of the methods, method 2 produced better results and was more robust with regard to the choice of smoothing parameter. Both methods were easy, efficient and economical to use. Statistical tables of standard deviations and means are included. (EGS)

Data from three subtests (language, mathematics, and social) scales of the Head Start Measures Battery (HSMB) were analyzed using principal components analysis (PCA) and non-metric multidimensional scaling (MDS). The HSMB measures preschool development in language, mathematics, nature and science, perception, reading, and social development. The sample included 1,000 children (36-60 months old) who participated in the Head Start Program and received all language, mathematics, and social routing items in fall of 1985. Loadings on the first factor were high, and eigenvalues obtained from the PCA suggested that one (or possibly two) dimensions were present in the data. Loadings of rotated principal components suggested that at least three factors corresponding to the subtests were present. The structure was clarified by MDS plots, showing that items were located in distinct sectors corresponding to their subtest. However, items having the highest IRT discrimination parameters were clustered toward the center, suggesting that the measures have a strong common factor and unique variance related to each subtest. Practically, this justifies both a common scale for all subtests when an overall measure of achievement is needed and individual subtest scaling when information on particular skills is required. Agreement between PCA and MDS can be used to reinforce the validity of the principal components model. Seven tables and four figures are provided. (SLD)

In order to determine the effectiveness of multidimensional scaling (MDS) in recovering the dimensionality of a set of dichotomously-scored items, data were simulated in one, two, and three dimensions for a variety of correlations with the underlying latent trait. Similarity matrices were constructed from these data using three margin-sensitive and three margin-free coefficients and used as input to MDS. Stress (S1), S1 by dimension plots, and plots of the scaled items were examined to determine the effect of varying the magnitude and pattern of correlations. The results suggested that items with similar patterns of correlations tend to cluster together, that distance from the center of a cluster is a function of the amount of random error in the item, and that as the number of latent traits underlying the data increases, the dimensionality of the representational space increases. Cluster analysis using MDS coordinates is suggested to isolate homogeneous sets of items, whereas consideration of the S1 coefficient is recommended to determine the number of latent traits in the data. (Author)