Description

Course Content

Important note: Time constraints may preclude all topics being covered.

1. Preliminaries

• The nature of statistical science
• Levels of measurement and implications for estimation and inference
• Discrete and continuous probability models
• Concept of sampling distributions of sample statistics
• Frequentist and Bayesian statistical paradigms

 

2. Data Wrangling

• Getting data into and out of R – reading/writing ASCII files, XLSX files, CSV files
• Creating data frames
• Manipulating data – subsetting, reshaping, grouping, reorganizing
• Using the tidyr and dplyr packages

 

3. Descriptive Statistics and Graphing

• Exploratory data analysis using R
• Numerical, tabular and graphical summaries
  • Histograms – with density smoothers;
  • Q-Q plots
  • Boxplots – individual and multiple with grouping;
  • Bi-plots – with smoothing and regression lines;
  • Rug plots;
  • Matrix plots;
  • Cross-tabulation tools for categorical data and summarising quantitative data by classifying factors.
• Handling missing values
• Elegant graphics using the ggplot2 package
  • Philosophy of ggplot (the grammar of graphics)
  • qplot() basics
  • plot geoms
  • faceting
  • building plots by layer

 

4. Inferential Statistics – Preliminaries

• Basic probabilistic concepts
  • Using R’s intrinsic functions for computing probability densities/functions; quantiles, generating random data.
• Sampling distribution of a sample statistic
• The central limit theorem
• Working with the normal distribution

 

5. Inferential Statistics – Estimation

• Estimating an unknown parameter
• Properties of estimators – point and interval estimates
• Distinction between confidence, tolerance, and prediction intervals
• Small and large sample interval estimation

 

6. Inferential Statistics – Hypothesis testing

• Key concepts: level of significance; P-value; Type I and II errors; statistical power
• Inference about a single population mean
• Multiple-comparison techniques (Dunnett’s test)
• Extension to 2-samples and testing equality of variances
• Extension to more than 2 samples – Analysis of Variance for the one-way ANOVA model
  • Basic logic of one-way ANOVA model
  • Critical assumptions
  • Test of homogeneity of variances
• ANOVA – more complex designs
  • Multi-factor designs, blocking, interactions
  • Using R’s lm() function
  • Interpreting the output
  • Diagnostic checking

 

7. Power and Sample-size calculations

• Key concepts – understanding what a power analysis can and can’t do
• How to compute power – writing an R function
• The non-central t-distribution
• Constructing power curves
• Using R’s intrinsic functions to compute power

 

8. Regression Models

• Simple linear regression models and ordinary least squares
• Using R’s lm() function
• Assessing the model fit
  • Residuals versus fitted values plots
  • Q-Q plot for checking normality
  • Scale-location plot
  • Cook’s distance
  • Residual versus leverage plot
  • Cook’s distance versus leverage plot
• Inference about the fitted model
  • Inference about the model parameters
  • Inference concerning predicted values
• Statistical calibration
• Logistic Regression
  • Parameter estimation