Significance Testing Principles

  • This collection of free, interactive Java applets provides a graphical interface for studying the power of the most commonly encountered experimental designs. Intended to be useful in planning statistical studies, these applets cover confidence intervals for means or proportions, one and two sample hypothesis tests for means or proportions, linear regression, balanced ANOVA designs, and tests of multiple correlation, Chi-square, and Poisson. Each applet opens in its own window with sliders, which are convertible to number-entry fields, for manipulating associated parameters. Controlling for the other parameters, users can change sample size, standard deviation, type I error (alpha) and effect size one at a time to see how each affects power. Conversely, users can manipulate the power for the test to determine the necessary sample size or margin of error. Additional features include a graph option by which the program plots a dependent variable (i.e. power) over a range of parameter values; the graph is automatically updated as the parameters are changed. Each dialog window also offers a Help menu which provides instructions for using the applet. The applets can be used over the Internet or downloaded onto the user's own computer.
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  • This set of pages describes software the author wrote to implement bootstrap and resampling procedures. It also contains an introduction to resampling and the bootstrap; and examples applying these procedures to the mean, the median, correlation between two groups, and analysis of variance.
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  • This journal article is a summary of resampling methods such as the jackknife, bootstrap, and permutation tests. It summarizes the tests, describes various software to perform the tests, and has a list of references.
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  • This journal article gives examples of erroneous beliefs about probability. It specifically examines the belief that a random sample must be representative of the true population.
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  • This applet allows the user to enter data, then returns the values of empirical cumulative distribution function by sorting the data and reporting the height of the curve at each point. It does not show the graph.

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  • This page introduces the Cramer-Rao lower bound, discusses it's usefulness, and proves the inequality.
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  • This page contains course notes and homework assignments with solutions for a mathematical statistics class. The course covers statistical inference, probability, and estimation principles.
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  • This site gives an explanation, a definition of and an example for tests of significance. Topics include null and alternative hypotheses for population mean, one-sided and two-sided z and t tests, levels of significance, and matched pairs analysis.
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  • This site gives an explanation, a definition of, and an example using comparison of two means. Topics include confidence intervals and significance tests, z and t statistics, and pooled t procedures.
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  • This online, interactive lesson on expected value provides examples, exercises, and applets in which students will explore relationships between the expected value of real-valued random variables and the center of the distribution. Students will also examine how expected values can be used to measure spread and correlation.
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