Lesson 1: Overview

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This lesson is an overview of the course content as well as a review of some advanced statistical concepts involving discrete random variables and distributions, relevant for STAT 504 -- Analysis of Discrete Data. This Lesson assumes that you have glanced through the review materials included in the Start Here! block.

Key concepts:

  • Discrete data types
  • Discrete distributions: Binomial, Poission, Multinomial
  • Likelihood & Loglikelhood
  • Observed & Expected Information
  • Likelihood based Confidence Intervals & Tests: Wald Test, Likelihood-ratio test, Score test

Objectives:

  • Learn what discrete data are and their taxonomy
  • Learn the properties of Binomial, Poission and Multinomial distributions
  • Understand the basic principles of likelihood-based inference and how to apply it to tests and intervals regarding population proportions
  • Introduce the basic SAS and R code

Useful links:

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The outline below can be viewed as a general template of how to approach data analysis regardless of the type of statistical problems you are dealing with. For example, you can model a continuous response variable such as income, or a discrete response such as a true proportion of U.S. individuals who support new health reform. This approach has five main steps. Each step typically requires an understanding of a number of elementary statistical concepts, e.g., a difference between a parameter to be estimated and the corresponding statistic (estimator).

The General Data Analysis Approach