# Significance Testing Principles

• ### Belief in the Law of Small Numbers

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.
• ### Analysis Tool: Empirical Cumulative Distribution

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.

• ### The Cramer-Rao Lower Bound

This page introduces the Cramer-Rao lower bound, discusses it's usefulness, and proves the inequality.
• ### Statistical Inference

This page contains course notes and homework assignments with solutions for a mathematical statistics class. The course covers statistical inference, probability, and estimation principles.
• ### Tests of Significance

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.
• ### Comparison of Two Means

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.
• ### Expected Value

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.
• ### Special Distributions

This online, interactive lesson on special distributions provides examples, exercises, and applets covering normal, gamma, chi-square, student t, F, bivariate normal, multivariate normal, beta, weibull, zeta, pareto, logistic, lognormal, and extreme value distributions.
• ### Computer Animated Statistics

This site offers a collection of applets in which standard topics of statistics and probability are presented in a novel and visual way using computer animated images. Topics include dependence, independence, conditional probabilities, expectation and variance, normal, exponential, Poisson distributions, law of large numbers and the central limit theorem, hypothesis testing maximum likelihood estimation, sampling, chi-square tests, and the construction of confidence intervals.