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Mathematica: Applied Statistical Analysis

This course provides experience with the statistical tools that are available in Mathematica. Using real-world and simulated datasets, participants will import and analyze data, work with statistical distributions, and visualize results. Course topics are presented in alternating sessions of lectures and exercises with small class size and ample opportunity for Q&A.

Level: Intermediate

The course is for those who have a basic familiarity with Mathematica. Basic knowledge of descriptive statistics, mathematical statistics, hypothesis testing, ANOVA, and regression is recommended.

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Outline

  • Descriptive Statistics
    Descriptive statistics and visualization of univariate and multivariate data, working with continuous and categorical data, and clustering and smoothing of data
  • Statistical Distributions
    Working with theoretical and empirical statistical distributions, descriptive statistics and functions of random variables, visualizations of distributions, random number generation, transformations, and empirical distributions and bootstrapping
  • Hypothesis Testing
    Common parametric tests such as t and Chi2 tests, nonparametric tests of location and scale, distributional goodness of fit tests, and confidence intervals and power curves
  • Model Fitting
    Linear, nonlinear, and generalized linear model fitting; logistic models with nominal predictors; Poisson count models; and ANOVA models
  • Model Refinements and Diagnostics
    Obtaining and visualizing diagnostics for models, comparing models, model transformations, and weighted regression
  • Special Topics
    Maximum likelihood estimation, implicitly defined models, robust regression using iterative re-weighting, and alternate metrics or merit functions for fitting data to curves
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