A "Reverse Order" Elementary Statistics Course

Students in elementary statistics traditionally see experiments and data as words and numbers in a text. They receive little exposure to the important statistical activities of sample selection, data collection, experimental design, development of statistical models, the need for randomization, selection of factors, etc. They often leave the first course without a firm understanding of the role of applied statistics or of the statistician in scientific investigations. In an attempt to improve elementary statistics education, we have developed a statistics laboratory similar to those of other elementary science courses. We will discuss our experiences in teaching a laboratory component with the traditional elementary statistics course. In each lab session, students, working in teams, discuss the design of an experiment, carry out the experiment, and analyze their data using Minitab on a Macintosh or MS-DOS based computer. The students then individually either answer a series of short answer questions or write a formal scientific report. The labs are designed to be relatively inexpensive and portable. They do not require a prior background in science, statistics or computing.

Hand calculators have come into common use for performing calculations in high school and undergraduate courses in elementary statistics. Computers have also been used to do standard statistical computations and tests. However, computers can be used in elementary statistics courses not only to do standard statistical tests, but to perform simulations which clarify concepts and theorems of statistics. These simulations allow the nonmathematically oriented student in elementary statistics to have inductive experiences with statistical concepts in a time-efficient manner. A basic concept in statistics is that of a sample distribution. The sampling distribution of a sample statistic is defined to be the theoretical probability distribution of values for that sample statistic obtained from all possible samples of a certain fixed size from the population. Typically elementary texts illustrate this concept by using a very small finite population which has a small number of possible samples of a given size. Although large or infinite populations are of interest since they have a large or infinite number of samples of a certain size it is difficult to develop a sample distribution. Computer simulation, however, makes this easy to explore. The computer can simulate taking many samples of a certain size from a population. By taking many samples the law of large numbers guarantees that the observed frequency distribution of the sample statistic is close to the theoretical sample distribution. The sample distribution of the mean is the most important sample distribution. The computer simulations in Figure 1 explore a sample distribution of the mean. These simulations employ an elementary statistical package called MINITAB developed at Pennsylvania State University. The MINITAB command URANDOM simulates random observations from a population where numbers between 0 and 1 all have an equal probability of occurring. The first simulation consists of drawing 200 samples of size 2 and computing the means of the samples. A histogram of the results is given. Continuing with samples of size 2, drawing 750 samples is simulated and then 1500 samples. As the number of samples increases the student can see the isosceles triangle-shaped theoretical sample distribution emerging. Note that, because of the small sample size and the nonnormal population, the sample distribution should not be expected to be normal.

One of the main themes of statistics courses is to teach about variability, as well as location. This is especially important for non-statistics students, who often overlook variability. We consider particularly the problem of comparing variability among k samples (k > 2) that are not necessarily drawn from Gaussian populations. This can also be viewed as testing for homoskedasticity of samples. We examine tools for this problem from the perspective of their suitability for inclusion in elementary statistics courses for students of non-mathematical subjects. The ideas are illustrated by an example that arose in a student project.Supplemental data for this article can be accessed on the publisher's website.

The Statistics Anxiety Rating Scale has 51 items, each scored on a 5-point rating scale to measure statistics anxiety with six subscales, Worth of Statistics, Interpretation Anxiety, Test and Class Anxiety, Computational Self-concept, Fear of Asking for Help, and Fear of Statistics Teachers. Psychometric properties included analyses of construct and concurrent validities an internal consistency and test-retest reliability. 221 college students (74% women; M age=28 yr.) in elementary statistics courses at several southwestern state universities participated. The findings are consistent with previous reports and indicate adequate concurrent validity, internal consistency, and split-half reliability, but for construct validity confirmatory factor analysis yielded marginal support.

This month, we bring you some “Technology Tips” that are related to probability and statistics. We begin with a contribution by Bishnu Naraine and Peiyi Zhao: an exploration that uses The Geometer's Sketchpad to discuss the broken-stick problem, which is also known as the spaghetti problem. This totally geometric solution nicely complements the analytic solution of the same problem, given in “The Spaghetti Problem Problem,” by Dennis Ippolito, which appeared on pages 422–26 of the May 2000 issue of the Mathematics Teacher. Next is a feature by Allen Holmes that discusses obtaining an explicit definition for a recursively defined sequence by using the built-in statistics regression ability of graphing calculators to model the equation of the sequence. Then a short program by John Jose for the TI-83 and TI-83 Plus graphing calculator helps investigate the law of large numbers by simulating the results of a simple two-dice experiment. Finally our “Surfing note” features a Web site that is devoted to statistics. It contains many resources for an elementary statistics course.

This article illustrates ways that dynamic software using some sophisticated techniques in Excel can be used to demonstrate fundamental ideas related to regression and correlation analysis to increase student understanding of the concepts and methods in elementary statistics courses and in courses at the college algebra/precalculus level that stress ideas on curve fitting techniques.

A collaborative, statistics education research project (Lovett, 2001) is discussed. Some results of the project were applied in the computer lab sessions of my elementary statistics course. I detail the process of applying these research results, as well as the use of knowledge surveys. Furthermore, I give general suggestions to teachers who want to put educational research results into effective use in their own classes.

This study qualitatively investigates the nature of the challenges that a student who is highly successful in mathematics faces in learning college-level elementary statistics. The study draws on the constructs of eagerness, flexibility and willingness to characterize the necessary disposition for critical thinking that is essential in learning statistics. The case study is based on data collected through a survey assessment and a follow-up interview with a mathematics major enrolled in an elementary college statistics course at the time of the study. The qualitative analysis relies on the student's verbal descriptions of the challenges he was experiencing in the course. The findings suggest that while his strong inclination towards inquisitive learning and strong understanding of mathematical concepts supported this student's mathematics learning, the same characteristics might have been causing him difficulties in learning college-level elementary statistics.

Tertiary students of elementary statistics often have difficulty developing a conceptual understanding of the subject. This article proposes a didactic method that stimulates students to self-explain the study material. This stimulus to self-explanation is directed, because the instructor decides which particular links and relationships between concepts the student should explore. The method is composed of two major steps: having the students identify the propositions that underlie the statistical theory, and then having them manipulate these propositions by constructing arguments showing a given statement to be either true or false. A practical way of implementing the method in a large-scale introductory statistics course is briefly described.

SummaryIn a course in elementary statistics for psychology students using criterion‐referenced achievement tests, the total test score, based on dichotomously scored items, was used for classifying students into those who passed and those who failed. The score on a test is considered as depending on a latent variable; it is assumed that the students can be dichotomized into the categories “mastery” (with scores on the latent variable above a cutting score), and “no mastery” (with scores below the cutting score on the latent variable). Two problems are considered: (a) How many students are classified incorrectly? Using the binomial error model a procedure is described for computing the classification proportions: p(mastery, passed), p(mastery, failed), p(no mastery, passed), and p(no mastery, failed), (b) What is the optimal cutting score on a test? Using a loss function a procedure for computing the optimal curring score is described.

Subject Elementary Statistics, Statistical Methods and Statistical Methods Practicum aimed to equip students of Mathematics Education about descriptive statistics and inferential statistics. The students' understanding about descriptive and inferential statistics were important for students on Mathematics Education Department, especially for those who took the final task associated with quantitative research. In quantitative research, students were required to be able to present and describe the quantitative data in an appropriate manner, to make conclusions from their quantitative data, and to create relationships between independent and dependent variables were defined in their research. In fact, when students made their final project associated with quantitative research, it was not been rare still met the students making mistakes in the steps of making conclusions and error in choosing the hypothetical testing process. As a result, they got incorrect conclusions. This is a very fatal mistake for those who did the quantitative research.There were some things gained from the implementation of reflective pedagogy on teaching learning process in Statistical Methods and Statistical Methods Practicum courses, namely: 1. Twenty two students passed in this course and and one student did not pass in this course. 2. The value of the most accomplished student was A that was achieved by 18 students. 3. According all students, their critical stance could be developed by them, and they could build a caring for each other through a learning process in this course. 4. All students agreed that through a learning process that they undergo in the course, they can build a caring for each other.