Foundational Statistics Bi 610
1
Book Overview
2
Introduction to the course
2.1
Instructors
2.2
Course Information
2.3
Software
2.4
Inclusion and Accessibility
3
Course Schedule
3.1
Weeks 1-2
3.2
Week 3
3.3
Week 4
3.4
Week 5
3.5
Week 6
3.6
Week 7
3.7
Week 8
3.8
Week 9
3.9
Week 10
4
Background material for the course
4.1
Description of the course
4.2
Course goals:
4.3
Introduction to R and RStudio
4.3.1
Learning resources
5
Organizing and manipulating data files
5.1
Introduction
5.2
Navigating file systems from the command line
5.2.1
Access to the command line
5.2.2
Navigating directories and files
5.2.3
Useful UNIX commands for file manipulation
5.2.4
A quick word on pipes and carrots
5.3
Data file and data file entry dos and don’ts
5.4
Exercises associated with this chapter:
5.5
Additional learning resources
6
An Introduction to the R language
6.1
Background
6.2
Why use
R
?
6.3
Important
R
terms and definitions
6.4
Getting started with
R
via the RStudio Environment
6.4.1
R Programming Basics
6.5
Exercises associated with this chapter:
6.6
Additional learning resources:
7
More R Functions, Complex Objects, Basic Plotting, and RMarkdown
7.1
Background
7.2
More on functions
7.2.1
More base
R
functions useful for working with vectors
7.3
Indexing vectors
7.4
More complex data objects in
R
7.4.1
Lists
7.4.2
Data frames
7.4.3
Matrices
7.4.4
A few additional base
R
functions for working with complex
R
objects
7.5
Some brief notes on basic programming in
R
7.5.1
conditional statements with
ifelse()
7.6
The Split-Apply-Combine approach to data analysis
7.6.1
replicate()
,
apply()
,
tapply()
, and
aggregate()
7.6.2
For loops in
R
7.7
Fundamentals of plotting in
R
7.7.1
Basic plotting with
plot()
7.7.2
Histograms using
hist()
7.7.3
Boxplots using
boxplot()
7.8
A brief introduction to
RMarkdown
7.8.1
RMarkdown
formatting basics
7.9
Experiment with headers
7.9.1
Try a third-level header
7.9.2
RMarkdown
code chunk options
7.10
Exercises associated with this chapter:
7.11
Additional learning resources:
8
Introduction to Probability and Probability Distributions
8.1
Background
8.2
What is probability?
8.3
Random variables & probability
8.4
Probability and the Bernoulli distribution
8.5
Probability rules
8.6
Joint probability
8.7
Conditional probability
8.8
A brief note on likelihood vs. probability
8.9
Probability distributions commonly used in biological statistics
8.9.1
Discrete Probability Distributions
8.9.2
Continuous probability distributions
8.10
Exercises associated with this chapter:
8.11
Additional learning resources:
9
Parameter Estimation Basics and the Sampling Process
9.1
Background
9.2
Understanding populations and their parameters
9.3
More on parameter estimation and sampling distributions
9.4
Calculating the standard error of the mean
9.5
The bootstrap to estimate parameters and the standard error
9.6
Confidence intervals
9.7
The relationship between mean and variance
9.8
Exercises associated with this chapter:
9.9
Additional learning resources:
10
Principles of Experiment and Study Design
10.1
Background
10.2
What is an experimental study?
10.2.1
A hypothetical study example
10.3
Basic study design terminology
10.4
Clinical trials
10.4.1
A clinical trial example
10.4.2
Simultaneous control groups
10.4.3
Randomization
10.4.4
Blinding
10.4.5
Replication
10.4.6
A note on pseudoreplication
10.4.7
Balance
10.4.8
Blocking
10.5
What if you can’t do experiments?
10.6
Exercises associated with this chapter:
10.7
Additional learning resources:
11
Introduction to Hypothesis Tests
11.1
Background
11.2
Null and alternative hypotheses
11.3
Hypotheses tests
11.3.1
p
-values, Type I, and Type II error
11.3.2
Statistical power
11.3.3
A note on
p
-values and Null-Hypothesis Significance Testing (NHST)
11.4
The
t
-test and
t
sampling distribution
11.4.1
Assumptions of parameteric t-tests
11.5
Comparing means using resampling and randomization tests
11.6
A summary of key components of hypothesis testing
11.7
Exercises associated with this chapter:
11.8
Additional learning resources:
12
Correlation and Simple Linear Regression
12.1
Background
12.2
Covariance and correlation
12.2.1
Covariance
12.2.2
Correlation
12.2.3
Hypothesis tests for correlation
12.3
Simple linear regression
12.3.1
Hypothesis tests in linear regression
12.3.2
Linear regression in
R
12.3.3
A note on the coefficient of determination
12.3.4
A note on model II regression
12.4
Exercises associated with this chapter:
12.5
Additional learning resources:
13
Introduction to Analysis of Variance
13.1
Background
13.2
General linear models
13.3
Single-factor ANOVA
13.3.1
Single-factor ANOVA hypothesis tests
13.3.2
ANOVA assumptions
13.3.3
Post-hoc comparisons
13.3.4
Single-factor ANOVA in
R
13.3.5
A note on nonparametric tests similar to single-factor ANOVA
13.4
Multi-factor ANOVA
13.4.1
Nested ANOVA
13.4.2
Factorial ANOVA
13.5
Exercises associated with this chapter:
13.6
Additional learning resources:
14
Introduction to Frequency Analysis
14.1
Background
14.2
Goodness of fit tests
14.2.1
Assumptions of the chi-square test
14.2.2
goodness of fit tests in
R
14.3
Tests of independence for frequencies
14.3.1
G-test of independence in
R
14.3.2
odds ratios
14.4
A final note on presenting statistical test results in writing
14.4.1
Differences, directionality, and magnitude
14.4.2
Other statistical results reporting formalities
14.5
Exercises associated with this chapter:
14.6
Additional learning resources:
References
Published with bookdown
Foundational Compuational and Statistical Tools for the Natural Sciences
References