This paper defines statistical reasoning and reviews research on this topic. Types of correct and incorrect reasoning are summarized, and statistical reasoning about sampling distributions is examined in more detail. A model of statistical reasoning is presented, and suggestions are offered for assessing statistical reasoning. The paper concludes with implications for teaching students in ways that will facilitate the development of their statistical reasoning.
Key Words: Assessment; Statistical reasoning.
This paper focuses on a third arm of statistical development: statistical thinking.
After surveying recent definitions of statistical thinking, implications for
teaching beginning students (including non-majors) are discussed. Several
suggestions are given for direct instruction aimed at developing “habits of
mind” for statistical thinking in students. The paper concludes with
suggestions for assessing students’ ability to think statistically. While
these suggestions are primarily aimed at non-majors, many statistics majors
would also benefit from further development of these ideas in their
Key Words: Introductory statistics; Literacy; Reasoning.
In this paper, I will define statistical literacy (what it is and what
it is not) and discuss how we can promote it in our introductory
statistics courses, both in terms of teaching philosophy and curricular
issues. I will discuss the important elements that comprise statistical
literacy, and provide examples of how I promote each element in my
courses. I will stress the importance of and ways to move beyond the "what"
of statistics to the "how" and "why" of statistics in order to
accomplish the goals of promoting good citizenship and preparing skilled research scientists.
Key Words: Introductory statistics; Statistical literacy.
Similarities and differences in the articles by Rumsey, Garfield and Chance are summarized. An alternative perspective on the distinction between statistical literacy, reasoning, and thinking is presented. Based on this perspective, an example is provided to illustrate how literacy, reasoning and thinking can be promoted within a single topic of instruction. Additional examples of assessment items are offered. I conclude with implications for statistics education research that stem from the incorporation of recommendations made by Rumsey, Garfield and Chance into classroom practice.
Key Words: Assessment; Cognitive outcomes; Research.
This article explains why and how a course in general linear models was restructured. This restructuring resulted from a need to more fully understand traditional teaching evaluations, coupled with a desire to introduce more meaningful data into the course. This led to the incorporation of a longitudinal dataset of teaching evaluations into the lecture material and assignments. The result was a deeper appreciation of how students perceive my teaching, specifically, and a greater understanding of how statistics courses, in general, can be taught more effectively.
Key Words: General linear models; Longitudinal data; Teaching effectiveness.
This paper discusses reasons for using humor in the statistics classroom. Humor strengthens the relationship between student and
teacher, reduces stress, makes a course more interesting, and, if relevant to the subject, may even enhance recall of the material. The
authors provide examples of humorous material for teaching students such topics as descriptive statistics, probability and
independence, sampling, confidence intervals, hypothesis testing, and regression and forecasting. Also, some references, summarized
strategies, and suggestions for becoming more humorous in the classroom are provided.
Key Words: Learning enhancement; Stress reduction.
This paper describes an interactive Web-based tutorial that supplements instruction on statistical power. This freely available tutorial provides several interactive exercises that guide students as they draw multiple samples from various populations and compare results for populations with differing parameters (for example, small standard deviation versus large standard deviation). The tutorial assignment includes diagnostic multiple-choice questions with feedback addressing misconceptions, and follow-up questions suitable for grading. The sampling exercises utilize an interactive Java applet that graphically demonstrates relationships between statistical power and effect size, null and alternative populations and sampling distributions, and Type I and II error rates. The applet allows students to manipulate the mean and standard deviation of populations, sample sizes, and Type I error rate. Students (n = 84) enrolled in introductory and intermediate statistics courses overwhelmingly rated the tutorial as clear, useful, easy to use, and they reported increased comfort with the topic of statistical power after using the tutorial. Students who used the tutorial outperformed those who did not use the tutorial on a final exam question measuring knowledge of the factors influencing statistical power.
Key Words: Internet; Introductory statistics; Statistical inference; Statistical power; Tutorial.
This paper begins by describing two hands-on activities developed for teaching basic statistical concepts to junior high students. Through generating, collecting, displaying, and analyzing data, students are given the opportunity to explore a variety of descriptive statistical techniques and develop an understanding of the distinction between theoretical, subjective, and empirical (or experimental) probabilities. These activities are then extended to introduce the sampling distribution of a sample proportion. The extension is appropriate for use in grades 9 through 12, in an Advanced Placement (AP) Statistics course, or in an introductory statistics course at the undergraduate level.
Key Words: Active learning; Advanced Placement Statistics; Probability; Sampling distribution of a sample proportion;
Teaching Bits: A Resource for Teachers of Statistics
This department features information sampled from a variety of sources that may be of
interest to teachers of statistics. Deb Rumsey abstracts information from the literature on
teaching and learning statistics, while Bill Peterson summarizes articles from the news and
other media that may be used with students to provoke discussions or serve as a basis for
classroom activities or student projects.
A data set containing n = 210 observations and published by Lieblein and Zelen
(1956) provides a useful example of multiple linear regression applied to an engineering
problem. It relates percentiles of the failure time distribution for ball bearings to
characteristics of the bearings (load, ball diameter, number of balls) in a theoretically
derived equation that can be put into linear form. The analysis requires testing the
equality of regression coefficients between manufacturers and between types of ball bearing
within manufacturer to see if the same equation applies across the industry. Furthermore,
there is special interest in confirming an accepted value for one of these coefficients. The
original analysis employed weighted least squares, although this may have been unnecessary.
In addition to the regression aspects of the problem, the example is useful for the extensive
data manipulation required.
Key Words: Failure times; Multiple linear regression; Percentiles; Weighted least squares.