Search

Decision-theoretic testing is used to explore whether students can improve their realism, i.e. congruence between reported and true probabilities. Randomized sets of math problems were presented at computer terminals to 49 seventh graders from two classes (high/low achievers) over a period of three weeks. The subject assigned values to each of four alternatives for each problem. Two groups worked individually, one with realism feedback. A third group, also with feedback, worked in teams of size three. Only the individual-study feedback groups in the low class improved on Posttest I. On Posttest II, with harder items and peer interaction, nearly all subjects overvalued information. Deviation from realism consistently increased with task difficulty and the direction of deviation was nearly always toward overconfidence. (Author)

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 distribution is used, trivial differences cannot attain statistical significance. The (non-zero) null hypothesis is now rejected at the alpha level when the observed F exceeds the noncentral F cutoff point where the noncentrality parameter delta (sub0) is determined by the minimum practical difference set by the researcher. (Author)

The Statistical Concepts Package (STAT-CONCEPT) is a coordinated collection of interactive computer programs and printed materials designed to enrich graduate instruction in educational statistics. Probability, descriptive statistics, sampling distributions, and power are four of the thirteen topics included. By doing the computational labor and providing a responsive enrivornment, the computer frees the student to explore statistical concepts in a "what happens if ...," laboratory-type, investigative atmosphere. This paper discusses the rationale, content, and student-program interaction of the STAT-CONCEPT package. Technical aspects as well as the package's usage during the past two years are also discussed. (Author)

This study examines the correspondence between a representation of subject-matter structure and a representation of the cognitive structure in students as a result of instruction. Eighty-seven eighth-grade students were assigned randomly to experimental and control treatments. The experimental students (N = 43) studied from a programmed text on probability developed by the School Mathematics Study Group (SMSG). The control group (N - 44) studied from a programmed text on factors and prime numbers. Digraphs, graphs and task analysis were used to map out the content structure. A word association test (WA) was used to measure the existing cognitive structure. The WA test, an achievement test and an attitude measure were given before, after and at a delayed post-experiment time. The results indicate that: (1) eighth-grade students were unfamiliar with the concepts of probability; (2) instruction in probability changed subjects' cognitive structure concerning concepts in probability; (3) the experimental group learned a significant portion of the structure of probability as a matter of instruction while the control group learned almost nothing; and (4) this learning of structure was retained until the retention-test time. (JP)

An empirical sampling study investigated six procedures for testing differences between means in the presence of unequal n's and variances. Support was obtained for previous research which found t robust to heterogeneous variances only when n's are equal and of moderate size. The procedure which emerged as providing the best control over Type I errors while maintaining satisfactory power in all test conditions was the Behrens-Fisher v statistic with Welch's solution for degrees of freedom (df). The general recommendations when the population variances are unknown are: (1) when n's are the same and equal to or greater than 20 it is permissible to use the t statistic with df = 2n - 2, but when n is less than 20 use v with Welch's solution for df; (2) when n's are unequal use the v statistic with the Welch adjustment for df. (Author)

College students attempted to learn the concept of binomial probability from four-lesson teaching booklets. The booklets were of two forms, one emphasizing calculation with a formula and the other stressing the meanings of component variables. Also some subjects studied only one or two parts of the booklets while others completed the booklets before taking a transfer posttest. Results indicate a consistent treatment-by-posttest interaction pattern. The subjects using the calculating-with-a-formula approach excelled on near-transfer while the other group excelled on far-transfer. (Author/LS)

The problem of test bias has been a growing concern in recent years. Of the several available methods for determining test bias, probably the most effective means involves collecting criterion information. This data collection process often provides a considerable barrier to the researcher, especially for the small test user and for someone who needs an immediate solution to a test bias question. This paper presents a method for identifying and analyzing the nature of test bias. This method is intended as only a preliminary analysis prior to, or concurrently to, a criterion data collection process. (Author)

A major difficulty in predictions of school enrollments is the failure of the forecaster to express adequately his degree of certainty in his estimates. To alleviate this problem, a method was developed by which a forecaster could prepare probability distributions of enrollment predictions. A basic method of enrollment prediction was chosen and modified to accommodate probabilistic input and output. The method required separate estimates for such variables as migration, retention, and transfer; and it was modified to require three estimates (high, low, and most likely) for each variable. A Monte Carlo computer simulation program was written to combine these various estimates into probability distributions of enrollment prediction. (Appendix A, pages 150-161, may reproduce poorly.) (Author/RA)

Description of the characteristics and mechanics of the Delphi technique of identifying the likelihood of occurrence of specified future events precedes suggested uses for the technique in research, planning, and teaching. The procedure involves obtaining individual predictions, aggregating results, presenting results to the individuals, and having individuals evaluate predictions. A RAND Corporation study to predict major developments in population growth, probability and prevention of war, future weapon systems, automation, space progress and scientific breakthrough illustrates the mechanics of the technique. The potential of the procedure for resource forecasting, application of the technique to establish city planning goals, and a discussion of a modified version of the procedure as used in teaching a graduate course in research methodology indicate the possible value of the Delphi technique in incorporating variables in research and in attempting to identify priorities at various spatial scales of planning. (Author/SHM)

Part of an international study of the nature and extent of childhood mortality in geographically, socioeconomically and culturally disparate populations, this report focuses on (1) an investigation into all deaths of children under 5 years of age, and (2) a probability sample of live children within the same northern California area during an 18-month period. For the Mortality Component, data are provided on mortality rates, description of the population, birth history of the deceased infants and children, prenatal care, circumstances of death, causes of death, and Sudden Infant Death. In the Probability Sample of Live Children, emphasis is on descriptions of both mothers of children under 5 years of age and children under 5 years of age. Major recommendations are offered for state and local health departments assuming responsibility for the stimulation, planning, and conduct of community-wide research on prenatal, infant, and childhood mortality on an individual case basis; and for international collaborative studies. Specific suggestions are made regarding data recording methods, health care delivery systems, methods of care for high-risk newborns, studies of Sudden Infant Death, childhood accidents, maternal education, and immunization programs. (LH)

This survey attempted to obtain data on the probability of improving student achievement when a new instructional program is implemented in an elementary school. The purpose of estimating the variable probability of improving student achievement was for use in the specification of a decision model whose purpose is to rank educational goals in terms of priority for curriculum change. To estimate the variable, questionnaires were designed to obtain the opinions of professional researchers and educators regarding the expected improvement in student performance for 40 goal areas and six different school types. The results indicated statistically significant differences among goal areas, but not among school types. However, the differences were so small as to suggest that the questionnaires were inadequately structured to reflect sensitivity to differences between goal areas and school types. (Author/DN)

In this paper, a new item analysis index, e, is derived as a function of difficulty and discrimination to represent item efficiency. Item discrimination in this paper is not independent of item difficulty, and it is demonstrated algebraically that the maximum discriminating power of an item may be determined from its difficulty. Item efficiency is defined as the ratio of observed discrimination to maximum discrimination. The e-index will range from zero to unity and will provide additional information for item analyses. Its probability interpretations may provide an attractive psychometric criterion for the retention or rejection of items. (Author)

One approach to the problem of analyzing classroom interaction by use of a Markoff chain is presented. The two sections of the paper present (1) a discusion of Hoel's test of order of a Markoff chain, and a Likelihood Ratio Criterion (LRC) for a two-dependent Markoff chain is given, and (2) a discussion of possible adjustments of Darwin's LRC with which to analyze data on a one-dependent chain assumption. The results of Hoel's test of order of a Markoff chain showed that a two-dependent (Order two) model is a better fit to interaction data than the one-dependent model (Order one). Tables and graphs present the statistical data. (DB)

This booklet contains suggestions for developing six of the twenty topics recommended for students in Secondary Forms III and IV in the schools of Victoria, Australia. These suggestions are intended for students for whom the standard course is unsuitable because of subject time allotments, ability levels, or vocational or educational needs. The six topics are Hire Purchase; Income Tax; Topology; Curve Stitching; Probability; and Relations, Loci and Graphs. Objectives of the modified course, and a bibliography of reference materials, are also included. (MM)

The materials in these units are designed especially for the low achiever student in junior high school mathematics. These materials are intended to be a source of new ideas for teachers who are trying to encourage interest, enthusiasm, and participation from low achieving students in mathematics. The four units in this collection contain mathematical materials involving area measurement, graphing, probability, and an introduction to flow charting. This work was prepared under an ESEA Title III contract. (RP)

In this report, the author suggests changes in the treatment of overhead costs by hypothesizing that "the effectiveness of standard costing in planning and controlling overhead costs can be increased through the use of probability theory and associated statistical techniques." To test the hypothesis, the author (1) presents an overview of the problem, (2) reviews probability theory, (3) discusses the selection of the proper empirical probability distribution to be used in the study, (4) uses the normal distribution to develop a cost control chart for dollar costs of manufacturing supplies, and (5) discusses the use of simple linear and multilinear regression and correlation analysis for budgeting overhead costs. (Author)

"Environmental measures" in the forms of probability inductions are conceptualized to express the relationship between environmental conditions (temperature, illumination, etc.) and human satisfaction levels for comfort and utility. An "evaluation" method is hypothesized as a way to gather the data needed to make environmental measure probability inductions. Evaluations gather counts and measures of objects and environments needed for human activities. Human satisfaction levels are then defined through questionnaires and indepth probes of cultural meanings, and correlated to the counts and measures. Environmental measure probability inductions are made from these correlations. Preliminary to making evaluation field studies, assumptions are made about environmental parameters, quantifying user activities, the validity of user opinions, the dimensions of cultural meanings, and the manipulation of data. Five "realities" are isolated for evaluation comparisons: objects, environments, standards, records, and opinions. (Some pages in Appendix C may reproduce poorly.) (Author)

The problem of comparing proportions when some data are missing is investigated, and determination is made of what statistical techniques are appropriate under each of several probability models describing the observations likely to be missing. Monte Carlo methods were used to investigate the properties of standard estimators under each of the missing data models. Applying standard techniques which ignore the occurrence of missing observations may yield misleading conclusions. Some tests and estimators are fairly robust to the model for missing data, but others may be seriously affected. If the model for missing observations is complex, the sample information may be insufficient for adequate data analysis. This report is useful since the problem of missing data is recurrent in educational research and may present serious difficulties even for simple problems. (Author/LH)

Selection of items for analogy tests according to the Rasch item probability of "goodness of fit" to the model is compared with three commonly used item selection criteria: item discrimination, item difficulty, and item-ability correlation. Word, picture, symbol and number analogies in multiple choice format were administered to several hundred college students. Analysis showed that Rasch item probabilities of .05 and .01 are more lenient (in terms of proportion of items rejected) criteria than commonly used criteria (item difficulty of between .10 and .80, item discrimination of .20, item-ability correlation of .20). Results also showed only a moderate amount of overlap among the four criteria, with the Rasch item probability and item discrimination being the most similar, and item difficulty and item-ability correlates being the most dissimilar. (Author)

The area investigated in the present study is the comparison of the permutation t-test with Student's t-test and the Mann-Whitney U-test. The comparison was made for small samples for three distributions, including a normal distribution, a uniform distribution, and a skewed distribution. The properties of each test compared were the probability of a Type I error and the power against a location-shift alternative hypothesis. The present research indicates that the permutation t-test is an acceptable statistical procedure for the two-sample problem for the normal and uniform populations and suggests that it might be more desirable than the traditional Student's t-test when sample sizes are proportional to the means and the parent population is nonnormal and asymmetric. Further research is needed before a more definite statement can be made about the permutation t-test when sampling from nonnormal populations. (Author)

A number of hypotheses derived from sociological theory and from previous research concerning the potential collaboration of citizens of the United States and Mexico were tested. Included in the samples were 1,528 interviews from the United States general public; 306 interviews from rural persons residing in places of 2,500 or less in Michigan; 105 interviews with Spanish-speaking informants in the states of Arizona, California, Colorado, New Mexico, and Texas; 1,126 interviews with informants in urban Mexico; and 288 from rural Mexico, or from villages and towns of between 100 and 2,500 population. The findings are discussed under the following chapter titles: "Factors of Knowledge and Mass Communication,""Actual Behavioral Linkages,""Attitudes Toward the Across the Border Country and Toward Linkages with That Country,""Desire for Linkage and Collaboration: Its Predictability and Explanation," and "The Meaning of the Linkage-Contrasts of Mexico and the United States." It was concluded that in all samples, informants with more formal education had higher mean scores measuring their contacts in across the border and Anglo-Latino relations than did those with low educational attainment. It was also found that higher educational attainment was less frequently concomitant with high interaction between Anglos and Latinos in interaction arenas, such as church, formal groups, neighborhoods, and work places, than it was for other forms of interaction. (HBC)

A method for estimating power scores is described. By way of illustration, it is applied to 21 students who were improperly timed on a standard test. Some empirical results are given in support of the estimation procedure. (Author)