• STA258: Statistics with Applied Probability
    University of Toronto Mississauga
  • Table of Contents
  • About the Authors
  • Acknowledgements
  • Introduction and Overview
  • 1 Introduction
    • 1.1 Foundations
    • 1.2 Types of data
    • 1.3 Introduction to Inferential statistics
  • 2 An Introduction to R
    • 2.1 The Statistical Computing Language
    • 2.2 Installing R and RStudio
      • 2.2.1 Installing R
      • 2.2.2 Installing RStudio
      • 2.2.3 Positron
    • 2.3 An Introduction to programming in R
      • 2.3.1 R as a Powerful Calculator
      • 2.3.2 Basic R Data Structures
      • 2.3.3 Using Basic Functions in R
      • 2.3.4 Make a Histogram Using RStudio
      • 2.3.5 Installing and Loading Packages
  • 3 Descriptive Statistics
    • 3.1 Representing Data
    • 3.2 Numerical Measures
      • 3.2.1 Mean
      • 3.2.2 Median
      • 3.2.3 Mode
      • 3.2.4 Variance
      • 3.2.5 Standard Deviation
      • 3.2.6 Range
      • 3.2.7 Percentiles
      • 3.2.8 Quartiles
    • 3.3 Graphical Techniques
      • 3.3.1 Histograms
      • 3.3.2 Boxplots
  • 4 Foundations of Inference
    • 4.1 Some Important Statistical Distributions
      • 4.1.1 Introduction to the Normal Distribution
      • 4.1.2 Introduction to the Chi-Square distribution
      • 4.1.3 Introduction to the t-Distribution
      • 4.1.4 Introduction to the F-Distribution
      • 4.1.5 Arithmetics of RV’s
    • 4.2 Sampling Distributions
    • 4.3 The Central Limit Theorem
    • 4.4 Law of Large Numbers
      • 4.4.1 Convergence in Probability
      • 4.4.2 Weak Law of Large Numbers (WLLN)
  • 5 Confidence Intervals
    • 5.1 Introduction
    • 5.2 Interpretation
    • 5.3 One Sample Confidence Intervals
      • 5.3.1 On a Population Mean
      • 5.3.2 On a Population Proportion
      • 5.3.3 On a Population Variance
      • 5.3.4 Assumptions
    • 5.4 Two Sample Confidence Intervals
      • 5.4.1 On a Difference of Means
      • 5.4.2 On a Difference of Proportions
      • 5.4.3 On a Ratio of Variances
    • 5.5 Confidence Intervals on Paired Data
    • 5.6 Sample Size Selection using Confidence Intervals
      • 5.6.1 Calculating Sample Size for a Confidence Interval on a Mean
      • 5.6.2 Calculating Sample Size for a Confidence Interval on a Proportion
  • 6 Hypothesis Tests
    • 6.1 Introduction
    • 6.2 One Sample Hypothesis Tests
      • 6.2.1 On a Population Mean
      • 6.2.2 On a Population Proportion
      • 6.2.3 On a Population Variance
    • 6.3 Two Sample Hypothesis Tests
      • 6.3.1 On a Difference of Means
      • 6.3.2 On a Difference of Proportions
      • 6.3.3 On a Ratio of Variances
    • 6.4 Hypothesis Tests on Paired Data
  • 7 Statistical Power
    • 7.1 Introduction
    • 7.2 Type I and Type II Errors
    • 7.3 Using Power to Determine Sample Size
  • 8 Analysis of Variance
  • 9 Simple Linear Regression
    • 9.1 Introduction to the Linear Model
      • 9.1.1 Least Squares Method
      • 9.1.2 Estimating Parameters for the Simple Linear Model
      • 9.1.3 Measures of Linear Relationship
      • 9.1.4 SSE, SSR and SST
    • 9.2 Inference for Simple Linear Regression
      • 9.2.1 Estimating Variance in Linear Regression
      • 9.2.2 Confidence Intervals and Hypothesis Tests
      • 9.2.3 ANOVA Table for Simple Linear Regression
      • 9.2.4 Residual Plots
  • 10 Analysis of Categorical Data
    • 10.1 Multinomial Response Model
    • 10.2 The Chi-square Test for Goodness of fit
    • 10.3 Sample Size Assumption

Table of Contents

  • Section 1: Introduction
  • Section 2: An Introduction to R
  • Section 3: Descriptive Statistics
  • Section 4: Foundations of Inference
  • Section 5: Confidence Intervals
  • Section 6: Hypothesis Tests
  • Section 7: Statistical Power
  • Section 8: Analysis of Variance
  • Section 9: Simple Linear Regression
  • Section 10: Analysis of Categorical Data