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  • Normality is a myth; there never has, and never will be, a normal distribution. A quote by Irish statistician and econometrician Roy C. Geary (1896 - 1983) found in "Biometrika" volume 34, 1947, page 241.
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  • Statistics is the art of stating in precise terms that which one does not know. A quote by American Statistician William Henry Kruskal (1919 - 2005) in his article "Statistics, Moliere, and Henry Adams," in "American Scientist Magazine" (1967; vol. 55, page 417).The quote also appears in "Statistically Speaking: A dictionary of quotations" compiled by Carl Gaither and Alma Cavazos-Gaither.
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  • If you can't measure it, I'm not interested. A quote by Canadian educator and management theorist Laurence Johnston Peter (1919 - 1990) from "Peter's People" in "Human Behavior" (August, 1976; page 9). The quote also appears in "Statistically Speaking: A dictionary of quotations" compiled by Carl Gaither and Alma Cavazos-Gaither.
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  • This pdf text file gives a short introduction to the methods of Bayesian inference. It gives a simple example that deals with jumping a paper frog. The topics listed in this document include: An example, comparison of frequentist and Bayesian methods, credible vs. confidence intervals, choice of prior and its effect on the posterior distribution.
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  • In this activity, students explore calculations with simple rates and proportions, and basic time series data, in the context of news coverage of an important statistical study. From 1973 to 1995, a total of 4578 US death penalty cases went through the full course of appeals, with the result that 68% of the sentences were overturned! Reports of the study in various newspapers and magazines fueled public debate about capital punishment.
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  • In this activity, students learn the true nature of the chi-square and F distributions in lecture notes (PowerPoint file) and an Excel simulation. This leads to a discussion of the properties of the two distributions. Once the sum of squares aspect is understood, it is only a short logical step to explain why a sample variance has a chi-square distribution and a ratio of two variances has an F-distribution. In a subsequent activity, instances of when the chi-square and F-distributions are related to the normal or t-distributions (e.g. Chi-square = z2, F = t2) will be illustrated. Finally, the activity will conclude with a brief overview of important applications of chi-square and F distributions, such as goodness-of-fit tests and analysis of variance.
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  • This group activity illustrates the concepts of size and power of a test through simulation. Students simulate binomial data by repeatedly rolling a ten-sided die, and they use their simulated data to estimate the size of a binomial test. They carry out further simulations to estimate the power of the test. After pooling their data with that of other groups, they construct a power curve. A theoretical power curve is also constructed, and the students discuss why there are differences between the expected and estimated curves. Key words: Power, size, hypothesis testing, binomial distribution
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  • This activity allows students to explore the relationship between sample size and the variability of the sampling distribution of the mean. Students use a Java applet to specify the shape of the "parent" distribution and two sample sizes. The simulation then samples from the parent distribution to approximate the sampling distributions for the two sample sizes. Students can see both sampling distributions at the same time making them easy to compare. The activity also allows students to determine the probability of extreme sample means for the different sample sizes so that they can discover that small sample sizes are much more likely than large samples to produce extreme values. Keywords: sampling distribution, sample size, simulation
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  • This interactive lecture activity motivates the need for sampling. "Why sample, why not just take a census?" Under time pressure, students count the number of times the letter F appears in a paragraph. The activity demonstrates that a census, even when it is easy to take, may not give accurate information. Under the time pressure measurement errors are more frequently made in the census rather than in a small sample.
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  • The t-distribution activity is a student-based in-class activity to illustrate the conceptual reason for the t-distribution. Students use TI-83/84 calculators to conduct a simulation of random samples. The students calculate standard scores with both the population standard deviation and the sample standard deviation. The resulting values are pooled over the entire class to give the simulation a reasonable number of iterations. This document provides the instructor with learning objectives, context, mechanics, follow-up, and evidence from use associated with the in-class activity.
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