Bruce E. Trumbo

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all rights reserved. This text may be freely shared among individuals, but it may not be republished in any medium without express written consent from the authors and advance notification of the editor. Abstract Null distributions of permutation tests for two-sample, paired, and block designs are simulated using the R statistical programming language. For(More)
• 25 randomly chosen people in a room • What is the probability two or more of them have the same birthday? • Model simplifications for a simple combinatorial solution: – Ignore leap years – Assume all 365 days equally likely • What error from assumptions? • As n increases, clearly P{X = 1} increases. • If n = 366 (still ignoring leap years), we are sure to(More)
The one-way random-effect ANOVA model is presented, and two simulated datasets are analyzed. and discussed from three points of view: (1) The standard ANOVA table, F test, and method-of-moments estimates of variance components, which can lead to negative estimates. (2) Maximum likelihood estimates of variance components. (3) Bayesian probability intervals(More)
Graphical and numerical illustrations of the effects of moderate to severe rounding of normal data on the values of test statistics, actual significance level, and power for one-sample t tests and paired t tests. Goodness-of-fit tests confirm that rounded normal data are not normal. Combinatorial computations, simulations, and graphs are made using R. The(More)
When population variances of observations in an ANOVA are a known function of their population means, many textbooks recommend using variance-stabilizing transformations. Examples are: square root transformation for Poisson data, arcsine of square root for binomial proportions, and log for exponential data. We investigate the usefulness of transformations(More)
Appropriate simulations can be used effectively in a beginning statistics course to illustrate important principles—either before the underlying theory is accessible or along with a presentation of the theory. Here we use a very few fundamental functions in R to illustrate the margin of error of a public opinion poll. Polls using 25 and 2500 subjects from a(More)
Statistical packages can perform several different goodness-of-fit tests of normality. We consider the normality tests of Anderson-Darling, Shapiro-Wilk, Cramér-von Mises, and Kolmogorov-Smirnov. For a given dataset these tests sometimes lead to different conclusions, possibly leaving students and practitioners confused about which test to believe. We use(More)
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