The natural experiment proposed in this article extracts three stories from boxes of "100 paper clips". The activity requires students to apply three lessons from inferential statistics, starting with a hypothesis test and including confidence intervals as well as tolerance intervals.

Students studying statistics often misunderstand what statistics represent. Some of the most well-known misunderstandings of statistics revolve around null hypothesis significance testing. One pervasive misunderstanding is that the calculated p-value represents the probability that the null hypothesis is true, and that if p < 0.05, there is…

In recent years, there has been increasing focus on the issue of multiple hypotheses testing in education evaluation studies. In these studies, researchers are typically interested in testing the effectiveness of an intervention on multiple outcomes, for multiple subgroups, at multiple points in time or across multiple treatment groups. When…

Learning to solve a class of problems can be characterized as a search through a space of hypotheses about the rules for solving these problems. A series of four experiments studied how different learning conditions affected the search among hypotheses about the solution rule for a simple computational problem. Experiment 1 showed that a problem…

The statistical output of interest to most elementary statistics students is the p-value, outputted in computer programs like SPSS, Minitab and SAS. Statistical decisions are sometimes made using these values without understanding the meaning or how these values are calculated. Most elementary statistics textbooks calculates p-values for z-tests…

Individuals can partly recreate the "wisdom of crowds" within their own minds by combining nonredundant estimates they themselves have generated. Herzog and Hertwig (2009) showed that this accuracy gain could be boosted by urging people to actively think differently when generating a 2nd estimate ("dialectical bootstrapping").…

This dissertation is composed of three distinct chapters, each of which addresses issues of estimating treatment effects. The first chapter empirically tests the Value-Added (VA) model using school lotteries. The second chapter, co-authored with Michael Wood, considers properties of inverse probability weighting (IPW) in simple treatment effect…

This dataset contains the results of a quasi-experiment, testing Karl Pearson's "drunkard's walk" analogy for an abstract random walk. Inspired by the alternate hypothesis that drunkards stumble to the side of their dominant hand, it includes data on intoxicated test subjects walking a 10' line. Variables include: the…

The common way to calculate confidence intervals for item response theory models is to assume that the standardized maximum likelihood estimator for the person parameter [theta] is normally distributed. However, this approximation is often inadequate for short and medium test lengths. As a result, the coverage probabilities fall below the given…

We compared 5 different statistics (i.e., G index, gamma, "d'", sensitivity, specificity) used in the social sciences and medical diagnosis literatures to assess calibration accuracy in order to examine the relationship among them and to explore whether one statistic provided a best fitting general measure of accuracy. College…

Our ability to statistically analyze data has grown significantly with the maturing of computer hardware and software. However, the evolution of our statistics capabilities has taken place without a corresponding evolution in the curriculum for the undergraduate chemistry major. Most faculty understands the need for a statistical educational…

The use of confidence intervals (CIs) as an addition or as an alternative to null hypothesis significance testing (NHST) has been promoted as a means to make researchers more aware of the uncertainty that is inherent in statistical inference. Little is known, however, about whether presenting results via CIs affects how readers judge the…

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…

In standard treatments of probability, Pr(A[vertical bar]B) is defined as the ratio of Pr(A[intersection]B) to Pr(B), provided that Pr(B) greater than 0. This account of conditional probability suggests a psychological question, namely, whether estimates of Pr(A[vertical bar]B) arise in the mind via implicit calculation of…

In Volume 23(2) of the "Australian Senior Mathematics Journal," Boncek and Harden present an exercise in fitting a Markov chain model to rainfall data for Darwin Airport (Boncek & Harden, 2009). Days are subdivided into those with precipitation and precipitation-free days. The author abbreviates these labels to wet days and dry days.…