This article discusses the basics of the "4 scales of measurement" and how they are applicable to research or everyday tools of life. To do this you will be able to list and describe the four types of scales of measurement used in quantitative research; provide examples of uses of the four scales of measurement; and determine the…

Increasingly students, particularly those in the social sciences, work with survey data collected through a more complex sampling method than a simple random sample. Failing to understand how to properly approach survey data can lead to inaccurate results. In this article, we describe a series of online data visualization applications and…

Although many parametric statistical tests are considered to be robust, as recently shown in Methodologist's Corner, it still pays to be circumspect about the assumptions underlying statistical tests. In this paper I show that robustness mainly refers to "[alpha]", the type-I error. If the underlying distribution of data is ignored there…

This article tackles the problem of what should be done with real textual data that are contaminated by errors of recording, particularly when the data contain words that are misspelt, unintentionally or otherwise. (Contains 5 tables and 2 figures.)

Learning about statistics is a lot like learning about science: the learning is more meaningful if you can actively explore. This seventh installment of "Explorations in Statistics" explores regression, a technique that estimates the nature of the relationship between two things for which we may only surmise a mechanistic or predictive…

We derive an estimator of the standardized value which, under the standard assumptions of normality and homoscedasticity, is more efficient than the established (asymptotically efficient) estimator and discuss its gains for small samples. (Contains 1 table and 3 figures.)

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…

In 1988, the National Center for Education Statistics (NCES) introduced a proposal to develop a private school data collection that would improve on the sporadic collection of private school data dating back to 1890 and improve on commercially available private school sampling frames. Since 1989, the U.S. Bureau of the Census has conducted the…

Learning about statistics is a lot like learning about science: the learning is more meaningful if you can actively explore. This series in "Advances in Physiology Education" provides an opportunity to do just that: we will investigate basic concepts in statistics using the free software package R. Because this series uses R solely as a vehicle…

This article reports on a delicious finding from a recent study claiming a causal link between dark chocolate consumption and blood pressure reductions. In the article, I provide ideas for using this study to whet student appetites for a discussion of statistical ideas, including experimental design, measurement error and inference methods.

Almost all introductory and intermediate level statistics textbooks include the topic of confidence interval for the population mean. Almost all these texts introduce the median as a robust measure of central tendency. Only a few of these books, however, cover inference on the population median and in particular confidence interval for the median.…

If students are to understand inferential statistics successfully, they must have a profound understanding of the nature of the sampling distribution. Specifically, they must comprehend the determination of the expected value and standard error of a sampling distribution as well as the meaning of the central limit theorem. Many students in a high…

This article describes a simple computer program which graphically demonstrates both Type I and Type II statistical errors.

Oversampling and cluster sampling must be addressed when analyzing complex sample data. This study: (a) compares parameter estimates when applying weights versus not applying weights; (b) examines subset selection issues; (c) compares results when using standard statistical software (SPSS) versus specialized software (AM); and (d) offers…

Unless the sample encompasses a substantial portion of the population, the standard error of an estimator depends on the size of the sample, but not the size of the population. This is a crucial statistical insight that students find very counterintuitive. After trying several ways of convincing students of the validity of this principle, I have…