Resource Library

This activity represents a very general demonstration of the effects of the Central Limit Theorem (CLT). The activity is based on the SOCR Sampling Distribution CLT Experiment. This experiment builds upon a RVLS CLT applet (http://www.ruf.rice.edu/~lane/stat_sim/sampling_dist/) by extending the applet functionality and providing the capability of sampling from any SOCR Distribution. Goals of this activity: provide intuitive notion of sampling from any process with a well-defined distribution; motivate and facilitate learning of the central limit theorem; empirically validate that sample-averages of random observations (most processes) follow approximately normal distribution; empirically demonstrate that the sample-average is special and other sample statistics (e.g., median, variance, range, etc.) generally do not have distributions that are normal; illustrate that the expectation of the sample-average equals the population mean (and the sample-average is typically a good measure of centrality for a population/process); show that the variation of the sample average rapidly decreases as the sample size increases.

A cartoon using a classic example for teaching the idea that correlation does not imply causation. Cartoon by John Landers (www.landers.co.uk) based on an idea from Dennis Pearl and Deb Rumsey (The Ohio State University). Free to use in the classroom and on course web sites.

This website is a resource of teaching methods and approaches that instructors at all levels of statistics education can use to generate student interest in pursuing more study or a career in the field of statistics.

This applet relates the pdf of the Normal distribution to the cdf of the Normal distribution. The graph of the cdf is shown above with the pdf shown below. Click "Move" and the scroll bar will advance across the graph highlighting the area under the pdf in red. The z-score is shown as well as the probability less than z (F(z)) and the probability greater than z (1-F(z)).

This lesson introduces the Central Limit Theorem and discusses it in terms of the normal distribution, binomial distribution, and Poisson distribution.

This applet demonstrates the Central Limit Theorem. First, select a distribution (Normal, Uniform, Skewed, Custom) and add or delete data points by clicking on the graph. Then, sample from the parent population and the distribution of the sample mean is shown. Users can also choose to see the distribution of the median, standard deviation, variance, and range.

This page provides links to distribution calculators, conceptual demonstration applets, statistical tables, online data analysis packages, function and image-processing tools, and other online computing resources. Key Words: Binomial; Normal; Exponential; Chi-Square; Geometric; Hypergeometric; Negative Binomial; Poisson; Student's T; F-Distribution; Wilcoxon Rank-Sum; Central Limit Theorem; Regression; Normal Approximation to Poisson; Confidence Intervals; Hypothesis Tests; Power; Sample-Size; ANOVA; Galton's Board; Function Plots; Edge Detection; Image Warping & Stretching; Polynomial Model Fitting; Wilcoxon-Mann-Whitney Statistic.

This collection of datasets comes from several phases of drug research. Each dataset comes with a full description and questions to answer from the data.

It is a good morning exercise for a research scientist to discard a pet hypothesis every day before breakfast. It keeps him young. A quote of Austrian animal behaviorist Konrad Lorenz (1903 - 1989) in "On Aggression", (English translation: 1966, Harvest books) p. 12. Quote also found in "Statistically Speaking - a Dictionary of Quotations" compiled by Carl Gaither and Alma Cavazos-Gaither p. 119.

During this simulation activity, students generate sampling distributions of the sample mean for n = 5 and n = 50 with Fathom 2 and use these distributions to confirm the Central Limit Theorem. Students sample from a large population of randomly selected pennies. Given that the variable of interest is the age of the pennies, which has a geometric distribution, this is a particularly convincing demonstration of the Central Limit Theorem in action. This activity includes detailed instructions on how to use Fathom to generate sampling distributions. The author will provide the Fathom data file upon request.