A Procedure For Selecting A Best Multinomial Distribution With Application To Population Income Mobility

A procedure is developed for selecting a subset which is asserted to contain the “best” of several multinomial populations with a pre-assigned probability of correct selection. According to a pre-chosen linear combination of the multinomial cell probabilities, the “best” population is defined to be the one with the highest such linear combination. As an illustration, the proposed procedure is applied to data relating to the economics of happiness and population income mobility

A Nonparametric Test For Homogeneity Of Variances: Application To GPAs Of Students Across Academic Majors

We propose a nonparametric (or distribution-free) procedure for testing the equality of several population variances (or scale parameters). The proposed test is a modification of Bakir’s (1989, Commun. Statist., Simul-Comp., 18, 757-775) analysis of means by ranks (ANOMR) procedure for testing the equality of several population means. A proof is given to establish the distribution-free property of the modified procedure. The proposed procedure is then applied to test whether or not the variability in the grade point averages (GPAs) of students differs across five business academic majors. We collect the GPAs (observations) of a random sample of students from each major under study. The absolute deviations of the observations from the overall median of the combined sample are then calculated and ranked from least to largest. The average ranks and two decision lines are then plotted on a graph paper to detect not only the existence of significant differences among variances, but also to pinpoint which variances are causing those differences

Monitoring The Level Of Students GPA's Over Time

A nonparametric (or distribution-free) statistical quality control chart is used to monitor the cumulative grade point averages (GPAs) of students over time. The chart is designed to detect any statistically significant positive or negative shifts in student GPAs from a desired target level. This nonparametric control chart is based on the signed-ranks of the GPAs of the sampled students. The exact false alarm rate and the in-control average run length of the proposed chart can be computed exactly and are independent of the underlying probability distribution of GPAs. The traditional Shewhart X-bar control chart for monitoring the mean of a process is based on the assumption that data follows a normal distribution. However, student GPAs may differ significantly from the normal distribution. As a result, using a traditional control chart to monitor the GPAs of students may lead to incorrectly specifying the control limits and the average run length and/or the false alarm rate of the chart. A test study was conducted at the College of Business Administration at Alabama State University. The study monitored the median cumulative GPAs of management majors during the period Spring 2005 through Spring 2009. The study revealed that the GPAs of students were stable at a median level of 2.6 over the period of the study

A Simple Tool For Quality Assessment In Education

A quality assessment tool is presented to detect the presence of out-of-control conditions in a school course system. The tool detects whether or not a set of courses offered by a certain discipline constitutes a stable (or in-control) system of courses. A system of courses is said to be stable if the variation in students' performance from course to course is only due to common causes. Students' performance in a course may be measured by their term grades in that course or any other method of evaluation. The proposed quality tool has the advantage of being applicable to numerical grades as well as to ordinal letter grades such as A, B, C, etc. A further advantage is that the proposed tool can be implemented graphically as a quality control chart. A pilot case study of the proposed tool was initiated in Fall 1995 to monitor a system of six of basic 200-level courses in the Department of Business Administration at Alabama State University. The results of this pilot study show that the system was out-of-control for the period Fall 1995 to Fall 1999 and then became in-control in Fall 2001