Amy G. Froelich

Conditional Covariance-Based Subtest Selection for DIMTEST:

DIMTEST is a nonparametric hypothesis-testing procedure designed to test the assumptions of a unidimensional and locally independent item response theory model. Several previous Monte Carlo studies have found that using linear factor analysis to select the assessment subtest for DIMTEST results in a moderate to severe loss of power when the exam lacks simple structure, the ability and difficulty parameter distributions differ greatly, or the underlying model is noncompensatory. A new method of selecting the assessment subtest for DIMTEST, based on the conditional covariance dimensionality programs DETECT and HCA/ CCPROX, is presented. Simulation studies show that using DIMTEST with this new selection method has either similar or significantly higher power to detect multidimensionality than using linear factor analysis for subtest selection, while maintaining Type I error rates around the nominal level.

Training Statistics Teachers at Iowa State University

Graduate teaching assistants at Iowa State University develop their teaching skills through an apprenticeship-like process. First-year graduate students start out as laboratory instructors/graders. After the first year, some graduate teaching assistants teach a section of an introductory statistics course. This article describes this apprenticeship-like process and the mentoring and resources provided to graduate teaching assistants.

Does Your iPod Really Play Favorites

Since the introduction of the first iPod portable music player (MP3 player) by Apple, Inc., users have questioned the randomness of the shuffle feature. Most evidence cited by users claiming to show nonrandom behavior in the shuffle feature is anecdotal in nature and not based on any systematic analysis of its randomness. This article reports on our attempt to investigate the shuffle feature on the iPod and to test its randomness through the use of probability and statistical modeling. We begin by reviewing the research on people’s inability to perceive and understand both random and nonrandom behavior. Probability models are then developed, under the assumption of a random shuffle, for several of the most common types of events cited as evidence of a nonrandom shuffle. Under this null hypothesis of a random shuffle, several goodness-of-fit tests of one of the probability models are conducted using data collected from real iPods. No evidence to support user claims of a nonrandom shuffle was found. Finally, we conclude with some reflections on and ideas for incorporating these examples into undergraduate probability and statistics courses.

Does My Baby Really Look Like Me? Using Tests For Resemblance Between Parent and Child to Teach Topics in Categorical Data Analysis

In this article, we present a study to test whether neutral observers perceive a resemblance between a parent and a child. We demonstrate the general approach for two separate parent/child pairs using survey data collected from introductory statistics students serving as neutral observers. We then present ideas for incorporating the study design process, data collection, and analysis into different statistics courses from introductory to graduate level.

Does Eye Color Depend on Gender? It Might Depend on Who or How You Ask.

As a part of an opening course survey, data on eye color and gender were collected from students enrolled in an introductory statistics course at a large university over a recent four year period. Biologically, eye color and gender are independent traits. However, in the data collected from our students, there is a statistically significant dependence between the two variables. In this article, we present two ideas for using this data set in the classroom, and explore the potential reasons for the dependence between the two variables in the population of our students.

Developing a Statistics Curriculum for Future Secondary Mathematics Teachers

To support the teaching of statistics in secondary schools as recommended by the National Council of Teachers of Mathematics 2000 Principles and Standards for School Mathematics and the American Statistical Association 2005 Guidelines for Assessment and Instruction in Statistics Education, the faculty at Iowa State University designed a new curriculum in statistical content for future secondary mathematics teachers. Based on recommendations from national mathematics committees, this new curriculum engages future secondary mathematics teachers with data collection and analysis, inferential statistics, and probability, and highlights connections and differences between mathematics and statistics.