Probability and Statistical Modeling
Preface
I Data and Models
1
Data Basics
1.1
R and RStudio essentials
1.1.1
The basics
1.1.2
Working with R Script Files
1.1.3
Working with R Markdown
1.1.4
Importing a dataset into R
1.2
How is data organized?
1.3
Variables
1.4
Models
1.5
Types of data-generating studies
2
Summarizing data
2.1
One quantitative variable
2.1.1
Measures of location
2.1.2
Measures of dispersion
2.1.3
Histograms
2.1.4
Density plots
2.1.5
Boxplots
2.1.6
Shapes of distributions
2.2
One categorical variable
2.2.1
Barplots
2.2.2
Pie charts
2.3
Two quantitative variables
2.3.1
Scatterplots
2.3.2
Correlations
2.4
Two categorical variables
2.4.1
Contingency tables
2.4.2
Stacked barplots
2.4.3
Mosaic plots
2.5
One quantitative and one categorical variable
2.5.1
Side-by-side boxplots
2.5.2
Side-by-side density plots
2.6
A word on statistical inference
2.6.1
Malaria vaccine example
2.6.2
Simulating the study
3
Simple linear regression
3.1
Least squares model
3.2
LAD model
3.3
Categorical predictors
3.3.1
Categorical predictor with two levels
3.3.2
Categorical predictor with three or more levels
3.4
Analysis of variance (one predictor)
3.4.1
The ANOVA table
3.4.2
Coeficient of determination
3.5
Correlations
3.5.1
Pearson’s correlation coefficient
3.5.2
Spearman’s correlation coefficient
4
Multiple linear regression
4.1
LS model
4.2
Categorical predictors
4.3
ANOVA
4.3.1
Sequential sum of squares
4.4
Adjusted R-squared
5
More on LS regression
5.1
A word on statistical inference for regression
5.2
Regression diagnostics
5.3
Model selection
5.3.1
Backward elimination
5.3.2
Forward selection
6
Logistic regression
6.1
The model
6.2
Multivariable
6.3
Interpretation
II Probability and Random Variables
7
Probability
7.1
Definitions, laws, and examples
7.2
Independence
7.3
PMFs, PDFs, and CDFs
8
Special distributions
8.1
Binomial distribution
8.2
Normal distribution
8.3
t distribution
8.4
Chi-square distribution
8.5
F distribution
9
Properties of random variables
9.1
Expected value
9.2
Variance
9.3
Covariance and correlation
III Statistical Inference
10
Sampling distributions
10.1
Population and sample
10.2
Estimators
10.3
Central Limit Theorem
11
Confidence intervals
11.1
Confidence interval for
\(\mu\)
11.2
Confidence interval for
\(p\)
11.3
Confidence interval for
\(\mu_1 - \mu_2\)
11.4
Confidence interval for
\(p_1 - p_2\)
12
Statistical inference for two variables
13
Appendix
13.1
Statistical criteria for location of measures
References
Published with bookdown
MA 217 - Probability and Statistical Modeling
12
Statistical inference for two variables