A mastery test is frequently described as follows: an examinee responds to n dichotomously scored test items. Depending upon the examinee's observed (number correct) score, a mastery decision is made and the examinee is advanced to the next level of instruction. Otherwise, a nonmastery decision is made and the examinee is given remedial work. This…

Three separate papers are included in this report. The first describes a two-stage procedure for choosing from among several instructional programs the one which maximizes the probability of passing the test. The second gives the exact sample sizes required to determine whether a squared multiple correlation coefficient is above or below a known…

A model permitting construction of algorithms for the polynomial conjoint analysis of similarities is presented. This model, which is based on concepts used in nonmetric scaling, permits one to obtain the best approximate solution. The concepts used to construct nonmetric scaling algorithms are reviewed. Finally, examples of algorithmic models for…

When analysis of variance is used, statistically significant differences may or may not be of practical significance to educators. A large part of the problem is due to the fact that a "zero difference" null hypothesis can always be rejected statistically if the sample size is large enough. If, however, a method based on the noncentral F…

This booklet, part of a series of four which provide problems in probability and statistics for the secondary school level, is aimed at aiding the student in developing models as structure for data and in learning how to change models to fit real-life problems. Twelve different problem situations arising from biology, business, English, physical…

This paper presents an index of goodness-of-fit for comparing m models over n trials. The index allows for differentiated weighting of the trials as to their importance in the comparison of the models. Several possible weighting schemes are suggested and the conditions on the weights which assure asymptotic normality of the index distribution are…

An asymptotic theory is developed for a new time series model introduced in TM 502 289. An algorithm for computing estimates of the parameters of this time series model is given, and it is shown that these estimators are asymptotically efficient in that they have the same asymptotic distribution as the maximum likelihood estimators. (Author/RC)

Queuing theory is explored by considering a simple example and by simulation with a computer. Sample BASIC computer programs are included. (DT)

An alternative to the uniform probability distribution model for ordinal data is considered. Implications for statistics and for test theory are discussed. (JKS)

A short course in probability and statistics for administrators and managers is described. Topics covered in one of the lecture sessions are discussed. (DT)

A sophomore-level course in applications of mathematics was designed to introduce students to the diversity of situations in which mathematical models are used. The course precedes the study of the calculus, and is composed of a sequence of modules. A problem-solving approach is used. (SD)

Reports on a test of the applicability of the theory of General Scalability to documents in terms of transitivity, substitutability, and independence. Implications for the construction of test collections in information retrieval research are examined. (24 references) (EAM)

The effect of large, within-examinee item difficulty variability on estimates of the proportion of consistent classification of examinees into mastery categories was studied over 2 test administrations for 100 simulated examinees. The proportion of consistent classifications was adequately estimated using the technique proposed by M. Subkoviak…