Bruce E. Trumbo

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Appropriate simulations can enliven a beginning probability course by focusing on model building, exploring generalizations that would lead to analytically intractable results, and teaching computer skills that are valuable in the job market. Here we use R to simulate the probability of birthday matches in a room with n people. The first simulation model(More)
Null distributions of permutation tests for two-sample, paired, and block designs are simulated using the R statistical programming language. For each design and type of data, permutation tests are compared with standard normal-theory and nonparametric tests. These examples (often using real data) provide for classroom discussion use of metrics that are(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)
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)
When population variances of observations in an ANOVA are a known function of their population means, many textbooks recommend using variancestabilizing 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 in(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)
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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