This study investigates a range of non-normative ideas that pre-service teachers (PSTs) employ in reasoning about sampling variability. This issue was studied in the context of a content course on statistics and probability for pre-service middle grade teachers at a Midwestern American university. Analysis of seven PSTs' video and screen records…

While many instructors are aware of the "Literary Digest" 1936 poll as an example of biased sampling methods, this article details potential further explorations for the "Digest's" 1924-1936 quadrennial U.S. presidential election polls. Potential activities range from lessons in data acquisition, cleaning, and validation, to…

Proper sampling techniques are of the utmost importance in obtaining accurate and precise results in chemical analysis. A Python language computer simulation providing fast feedback on sampling concepts and statistics was delivered to students through Google Colab. Students used the simulation to aid in their exploration of sampling and sampling…

Online platforms offer new opportunities to study human behavior. However, while social scientists are often interested in using behavioral trace data--data created by a user over the course of their everyday life--to draw inferences about users, many online platforms only allow data to be sampled based on user activities (leading to data sets…

Computer simulation can be used to demonstrate why the unbiased sample variance uses degrees of freedom (n-1). This is first demonstrated for sampling from a normal random variable, and in additional simulations for some selected non-normal random variables, namely, chi-square and binomial.

We describe an activity that introduces students to population modelling, enables them to use estimates obtained from a sample to infer back to the population, and understands how the findings are translatable via penguins and their poo!

Testing whether items fit the assumptions of an item response theory model is an important step in evaluating a test. In the literature, numerous item fit statistics exist, many of which show severe limitations. The current study investigates the root mean squared deviation (RMSD) item fit statistic, which is used for evaluating item fit in…

Although the use of real-world data sets is encouraged when teaching statistics, it can be difficult for instructors to find meaningful data for introducing students to univariate descriptive statistics such as the mean, median, and percentiles. The recent lead contamination of the water supply in Flint, Michigan, provides a real-life data set…

Sample survey design is a topic usually taught to students undertaking a minor or major in statistics in the latter part of their bachelor's degree. This article describes an assessment project that fosters active learning and helps to develop a set of essential skills for statistical practice. The project is completed in pairs and submitted in…

Researchers have documented many misconceptions students hold about sampling variability. This study takes a different approach--instead of identifying shortcomings, we consider the productive reasoning pieces students construct as they reason about sampling distributions. We interviewed eight undergraduate students newly enrolled in an…

While various studies suggest that informal statistical inference (ISI) can be developed by young students, more research is needed to translate this claim into a well-founded learning trajectory (LT). As a contribution, this paper presents the results of a cycle of design research that focuses on the design, implementation, and evaluation of the…

In psychological and survey research, the prevalence and serious consequences of careless responses from unmotivated participants are well known. In this study, we propose to iteratively detect careless responders and cleanse the data by removing their responses. The careless responders are detected using person-fit statistics. In two simulation…

This paper explores the implementation of service-learning projects in a survey sampling statistics course. In these projects, students worked with a community partner to develop and administer a survey, analyze the data collected, and present the results. A study with 23 participants was conducted to investigate whether students' attitudes…

Introductory statistics courses, which are important in preparing students for their daily lives, generally derive inferential statistics from informal knowledge. In this transition process, sampling distributions have an important place, yet research has shown that students often have difficulties with this concept. In order to increase their…

The ability to reason inferentially is increasingly important in today's society. It is hypothesized here that engaging primary school students in informal statistical reasoning (ISI), defined as making generalizations without the use of formal statistical tests, will help them acquire the foundations for inferential and statistical thinking.…