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
Acknowledgements
The authors would like to thank the following people for their feedback and review of this e-book:
Dr. Steve Tully, Okanagan College
Ms. Avanti Coonghe, United Nations (World Health Organization)