This article presents the results of a qualitative research with a group of 15 university students of social sciences on informal inferential reasoning developed in a computer environment on concepts involved in the confidence intervals. The results indicate that students developed a correct reasoning about sampling variability and visualized…

The sampling distribution is a common source of misuse and misunderstanding in the study of statistics. The sampling distribution, underlying distribution, and the Central Limit Theorem are all interconnected in defining and explaining the proper use of the sampling distribution of various statistics. The sampling distribution of a statistic is…

Replication is important to viable scientific inquiry; results that will not replicate or generalize are of very limited value. Statistical significance enables the researcher to reject or not reject the null hypothesis according to the sample results obtained, but statistical significance does not indicate the probability that results will be…

A pivotal theorem which is of critical importance to statistical inference in probability and statistics is the Central Limit Theorem (CLT). The theorem concerns the sampling distribution of random samples taken from a population, including population distributions that do not have to be normal distributions. This paper contains a brief history of…

This paper identifies typical sampling problems, including improper application of the Central Limit Theorem, that are associated with the probability-based sampling procedures currently used in clinical psychology research. It then presents two alternative research designs, the theory validation model and the extended case study model, which…

In 1979-80, the Arkansas minimum competency tests were administered to a sample of 5,000 students in grades 3, 6, and 8. To determine how well test objectives matched the curriculum, their teachers estimated how many of the four items per objective a randomly selected student would answer correctly. Because chi square test comparisons of teacher…

This paper describes a study, now in progress, of new methods for representing the sampling variability of Mantel-Haenszel differential item functioning (DIF) results, based on the system for categorizing the severity of DIF that is now in place at the Educational Testing Service. The methods, which involve a Bayesian elaboration of procedures…

A linear classification rule (used with equal covariance matrices) was contrasted with a quadratic rule (used with unequal covariance matrices) for accuracy of internal and external classification. The comparisons were made for seven situations which resulted from combining three data conditions (equal and unequal covariance matrices, minimal and…

This paper summarizes the thinking of 84 middle school mathematics students' about variability in three stochastics tasks that involve repeated trial. Differences in students' acknowledgment of variability were found, depending on whether the task was from a sampling environment, or a probability environment. Students tended to neglect variability…

When studies are conducted over a period of time, the sample size typically decreases. In a study of the effects of exercise therapy and education with recovering congestive heart failure (CHF) patients (Brubaker, Witta, & Angelopoulus, 2003), the sample size decreased from over 40 to 9 participants after an 18-month time span. Although the…

Multiple matrix sampling of three subscales of the California Psychological Inventory was used to investigate the effects of four variables on error estimates of the mean (EEM) and variance (EEV). The four variables were examinee population size (600, 450, 300, 150, 100, and 75); number of subtests, (2, 3, 4, 5, 6, and 7), hence the number of…

A tailored testing model employing the beta distribution, whose mean equals the difficulty of an item and whose variance is approximately equal to the sampling variance of the item difficulty, and employing conditional item difficulties, is proposed. The model provides a procedure by which a minimum number of items of a test, consisting of a set…

Ten high-ability middle school students participated in a 13 week enrichment program on inferential statistics. Consistent with the NCTM Standards, classes emphasized problem solving in real world contexts and the communication of mathematical ideas. Students struggled with written assignments, yet worked effectively in pairs, small groups, and…

Development of The Assessment of Basic Competencies (ABC), a test battery based on the three-parameter logistic model, is described. Eleven dimensions of intellectual growth are measured, from the pre-kindergarten level through ninth grade. An educationally relevant skill domain is represented by each test. Unique properties of the test, based on…

This paper provides an overview of common sampling methods (both the good and the bad) likely to be used in community college self-evaluations and presents the results from several simulated trials. The report begins by reviewing various survey techniques, discussing the negative and positive aspects of each method. The increased accuracy and…