Statistics and the Physical World
Preface
1
Introduction
1.1
Basic Concepts of Statistical Analysis
1.2
Data Collection
1.3
Variable Types
2
Describing Data
2.1
Graphical Description of a Single Variable
2.2
Numerical Descriptive Measures of a Single Variable
2.2.1
Measures of Central Tendency
2.2.2
Measures of Variability
2.3
Describing More than One Variable
3
Probability
3.1
Terminology and Probability Rules
3.2
Basic Probability
3.2.1
Bayes’ Rule
3.3
Random Variables and Probability Distributions
3.4
Discrete Random Variables
3.4.1
Population Numerical Descriptive Measures
3.4.2
Common Families of Discrete Probability Distributions
3.5
Continuous Random Variables
3.5.1
Common Families of Continuous Probability Distributions
3.6
Sampling Distributions and the Central Limit Theorem
4
Inferences for Population Means
4.1
Estimation
4.2
Hypothesis Testing
5
Introduction to Experimentation
6
Comparing Two Population Means
6.1
Independent Samples
6.1.1
Large-Sample tests
6.1.2
Small Sample Tests with Normal Data
6.2
Paired Sample Designs
6.3
Nonparametric Tests
6.3.1
Independent Samples - Wilcoxon Rank-Sum Test
6.3.2
Paired Samples - Wilcoxon Signed Rank Test
7
Experimental Design and the Analysis of Variance
7.1
Completely Randomized Design (CRD) For Independent Samples
7.1.1
Analysis of Variance and
\(F\)
-Test for Normal Data
7.1.2
Comparisons among Treatment Means
7.2
Randomized Block Design (RBD) For Studies Based on Matched Units
7.3
Factorial Designs
8
Categorical Data Analysis
8.1
Inference Concerning a Single Variable
8.1.1
Variables with Two Possible Outcomes
8.1.2
Variables with More than Two Possible Outcomes
8.2
Introduction to Tests for Association for Two Categorical Variables
8.2.1
2 x 2 Tables
8.2.2
Nominal Explanatory and Response Variables
9
Regression Models
9.1
Simple Linear Regression
9.1.1
Estimation of Model Parameters
9.1.2
Inference Regarding
\(\beta_1\)
and
\(\beta_0\)
9.1.3
Estimating a Mean and Predicting a New Observation @
\(X=X^*\)
9.1.4
Analysis of Variance
9.1.5
Correlation
9.2
Multiple Linear Regression
9.2.1
Testing and Estimation for Partial Regression Coefficients
9.2.2
Analysis of Variance
9.2.3
Testing a Subset of
\(\beta^s = 0\)
9.2.4
Models With Categorical (Qualitative) Predictors
9.2.5
Models With Interaction Terms
9.3
Logistic Regression
Published with bookdown
Statistics and the Physical World
Statistics and the Physical World
Larry Winner
2025-06-22
Preface
These notes are for STA 2170 at the University of Florida.