Confidence interval estimation is a fundamental technique in statistical inference. Margin of error is used to delimit the error in estimation. Dispelling misinterpretations that teachers and students give to these terms is important. In this note, we give examples of the confusion that can arise in regard to confidence interval estimation and margin of error

This study compared levels of statistics anxiety and attitude toward statistics for graduate students in on-campus and online statistics courses. The Survey of Attitudes Toward Statistics and three subscales of the Statistics Anxiety Rating Scale were administered at the beginning and end of graduate level educational statistic courses. Significant effects were observed for two anxiety scales (Interpretation and Test and Class Anxiety) and two attitude scales (Affect and Difficulty). Observed decreases in anxiety and increases in attitudes by online students offer encouragement to faculty that materials and techniques can be used to reduce anxiety and hopefully enhance learning within online statistics courses.

This research shows that active learning is not universally effective and, in fact, may inhibit learning for certain types of students. The results of this study show that as increased levels of active learning are utilized, student test scores decrease for those with a high grade point average. In contrast, test scores increase as active learning is introduced for students in the lower level grade point average group. Every student involved in the experiment is taught three topics, each one by a different teaching method. Students take a test following each learning session to assess comprehension. The experiment involves more than 300 business statistics students in seven class sections. Method topic combinations are randomly assigned to class sections so that each student in every class section is exposed to all three experimental teaching methods. The effect of method on student score is not consistent across grade point average. Performance of students at three different grade point average levels tended to

In the recent past, qualitative research methods have become more prevalent in the field of statistics education. This paper offers thoughts on the process of framing a qualitative study by means of an illustrative example. The decisions that influenced the framing of a study of pre-service teachers. understanding of the concept of statistical sample are explained by describing the goals, knowledge, and beliefs brought to the research project. Each framing decision is portrayed as a function of these three overarching cognitions. It is suggested that mapping one.s goals, knowledge, and beliefs while framing and carrying out a qualitative study can be useful for maintaining the quality of the study.

Two improvements in teaching linear regression are suggested. The first is to include the population regression model at the beginning of the topic. The second is to use a geometric approach: to interpret the regression estimate as an orthogonal projection and the estimation error as the distance (which is minimized by the projection). Linear regression in finance is described as an example of practical applications of the population regression model. The paper also describes a geometric approach to teaching the topic of finding an optimal portfolio in financial mathematics. The approach is to express the optimal portfolio through an orthogonal projection in Euclidean space. This allows replacing the traditional solution of the problem with a geometric solution, so the proof of the result is merely a reference to the basic properties of orthogonal projection. This method improves the teaching of the topic by avoiding tedious technical details of the traditional solution such as Lagrange multipliers and partial derivatives. The described method is illustrated by two numerical examples.

Students learn to examine the distributional assumptions implicit in the usual t-tests and associated confidence intervals, but are rarely shown what to do when those assumptions are grossly violated. Three data sets are presented. Each data set involves a different distributional anomaly and each illustrates the use of a different nonparametric test. The problems illustrated are well–known, but the formulations of the nonparametric tests given here are different from the large sample formulas usually presented. We restructure the common rank-based tests to emphasize structural similarities between large sample rank-based tests and their parametric analogs. By presenting large sample nonparametric tests as slight extensions of their parametric counterparts, it is hoped that nonparametric methods receive a wider audience.

Language and the telling of data stories have fundamental roles in advancing the GAISE agenda of shifting the emphasis in statistics education from the operation of sets of procedures towards conceptual understanding and communication. In this paper we discuss some of the major issues surrounding story telling in statistics, challenge current practices, open debates about what constitutes good verbalization of structure in graphical and numerical summaries, and attempt to clarify what underlying concepts should be brought to students. attention, and how. Narrowing in on the particular problem of comparing groups, we propose that instead of simply reading and interpreting coded information from graphs, students should engage in understanding and verbalizing the rich conceptual repertoire underpinning comparisons using plots. These essential data-dialogues include paying attention to language, invoking descriptive and inferential thoughts, and determining informally whether claims can be made about the underlying populations from the sample data. A detailed teacher guide on comparative reasoning is presented and discussed.

This article looks at a process of integrating real-life data investigation in a course on descriptive statistics. Referring to constructivist perspectives, this article suggests a look at the potential of inculcating alternative teaching methods that encourage students to take a more active role in their own learning and participate in the process of assessing what they have learned. The article illustrates how this teaching method enabled students to realize that imparting meaning to sets of data is a complex activity which involves conceptual flexibility, integration of all the procedures that one has learned, and creative reasoning.

Confidence interval estimation is a fundamental technique in statistical inference. Margin of error is used to delimit the error in estimation. Dispelling misinterpretations that teachers and students give to these terms is important. In this note, we give examples of the confusion that can arise in regard to confidence interval estimation and margin of error.