Unit 1: Exploratory Methods and Inference in Case CQ

Learning Objectives

Introduction to Regression

  • Define regression analysis.
  • Explain the reasons regression analysis can be used in practice.
  • Recognize common statistical analyses which can be put into a regression framework.
  • Define the steps in regression analysis.
  • Define the types of regression models.
  • Explain how linear regression with a continuous outcome models the average value of the response as the values of predictors change.
  • Define the two essential ingredients in regression models.

Exploratory Data Analysis

  • Discuss how exploratory data analysis is useful in the regression analysis process.
  • Explain the process of data checking including useful methods and common types of errors.
  • Determine types of variables.

Exploratory Data Analysis for One Variable

  • Choose appropriate exploratory data analysis methods based upon the types of variables.
  • Provide a written summary of the distribution of one variable based upon SAS output using appropriate methods.
  • Correctly use and interpret Normal Quantile-Quantile plots .
  • Create transformations of quantitative variables and conduct exploratory data analysis on the transformed variable.
  • Perform exploratory data analysis for one variable in SAS.

Exploratory Data Analysis for Two Variables

  • Choose appropriate exploratory data analysis methods based upon the types of variables.
  • Provide a written summary of the observed association between two variables based upon SAS output using appropriate methods.
  • Perform exploratory data analysis for two variables in SAS.

Exploratory Data Analysis for Multiple Variables

  • Choose appropriate exploratory data analysis methods based upon the types of variables.
  • Provide a written summary of any patterns when investigating multi-variable associations based upon SAS output using appropriate methods.
  • Perform exploratory data analysis for multiple variables in SAS.

Review of Important Statistical Concepts

  • Define parameters, statistics, sampling distributions, standard error, bias, variability of estimators, p-values, errors in hypothesis testing, and power
  • Correctly use and interpret confidence intervals and hypothesis test results.
  • Explain practical/clinical Significance vs. statistical significance.
  • Explain association vs. causation

Review of Inference in Case CQ

  • Use appropriate inferential methods in Case CQ where we have one categorical predictor and one (reasonably continuous) quantitative outcome.
  • Perform appropriate data analysis in SAS.

Preview of Multi-Variable Inference

  • Explain a data situation resulting in a two-way ANOVA model.
  • Explain a data situation resulting in an ANCOVA model.
  • Explain the concept of an interaction between two predictors.
  • Determine the significance of an interaction term in a two-way ANOVA or ANCOVA model.
  • Based upon interaction plots, discuss the effects of interest in context.

Broad Course Objectives:

  • CO-1: Select appropriate methods for a scenario; determine if a linear or a nonlinear approach is appropriate
  • CO-2: Use statistical software for performing regression analysis in the SAS language
  • CO-3: Test and interpret linear models for continuous outcome data (normal linear model)
  • CO-4: Test and interpret models for categorical outcome data (logistic and Poisson regression)
  • CO-5: Draw appropriate conclusions for both randomized designed experiments and observational studies
  • CO-6: Communicate clearly to subject matter experts the purposes and results of complex statistical analysis, both orally and in writing.