Patrick Thornham

Introduction to Statistical Investigations

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Table of Contents


   1.1 Preliminary: Introduction to the six-step method

   1.2 Preliminary: Exploring data

   1.3 Preliminary: Exploring random processes

   1.4 Data and formulas

   2.1 Example: Introduction to chance models

   2.2 Example: Measuring the strength of evidence

   2.3 Example: Alternative measure of strength of evidence

   2.4 Example: What impacts strength of evidence?

   2.5 Example: Inference on a single proportion: Theory-based approach

   2.6 Supplemental Exploration: Introduction to chance models

   2.7 Supplemental Exploration: Measuring the strength of evidence

   2.8 Supplemental Exploration: Do People Use Facial Prototyping?

   2.9 Supplemental Exploration: Competitive Advantage to Uniform Colors?

   2.10 Supplemental Exploration: Eye Dominance

   2.11 Investigation: Tire story falls flat

   2.12 Tools, data, and formulas

   3.1 Example: Sampling from a finite population

   3.2 Example: Inference for a single quantitative variable

   3.3 Example: Theory-based Inference for a Population Mean

   3.4 Example: Other Statistics

   3.5 Supplemental Exploration: Sampling Words

   3.6 Supplemental Exploration: Inference for a single quantitative variable

   3.7 Supplemental Exploration: Sleepless Nights?

   3.8 Supplemental Exploration: Other statistics

   3.9 Investigation: Faking cell phone calls

   3.10 Tools, data, and formulas

   4.1 Example: Statistical inference: Confidence intervals

   4.2 Example: 2SD and theory-based confidence intervals for a single proportion

   4.3 Example: 2SD and theory-based confidence intervals for a single mean

   4.4 Example: Factors that affect the width of a confidence interval

   4.5 Supplemental Exploration: Statistical inference: Confidence intervals

   4.6 Supplemental Exploration: 2SD and theory-based confidence intervals for a single proportion

   4.7 Supplemental Exploration: 2SD and theory-based confidence intervals for a single mean

   4.8 Supplemental Exploration A: Factors that affect the width of a confidence interval

   4.9 Supplemental Exploration B: Factors that affect the width of a confidence interval

   4.10 Investigation: Cell phones while driving

   4.11 Tools, data, and formulas

   5.1 Example: Association and confounding

   5.2 Example: Observational studies vs. experiments

   5.3 Supplemental Exploration: Association and confounding

   5.4 Supplemental Exploration: Observational studies versus experiments

   5.5 Investigation: High anxiety and sexual attraction

   5.6 Tools and data

   6.1 Example: Comparing two groups: Categorical response

   6.2 Example: Comparing two proportions: Simulation-based approach

   6.3 Example: Comparing two proportions: Theory-based approach

   6.4 Supplemental Exploration: Comparing two groups: Categorical response

   6.5 Supplemental Exploration: Comparing two proportions: Simulation-based approach

   6.6 Supplemental Exploration: Comparing two proportions: Theory-based approach

   6.7 Investigation: Does vitamin C improve your health?

   6.8 Tools, data, and formulas

   7.1 Example: Comparing two groups: Quantitative response

   7.2 Example: Comparing two means: Simulation-based approach

   7.3 Example: Comparing two means: Theory-based approach

   7.4 Supplemental Exploration: Comparing two groups: Quantitative response

   7.5 Supplemental Exploration: Comparing two means: Simulation-based approach

   7.6 Supplemental Exploration: Comparing two means: Theory-based approach

   7.7 Investigation: Memorizing letters

   7.8 Tools, data, and formulas

   8.1 Example: Paired designs

   8.2 Example: Simulation-based approach for analyzing paired data

   8.3 Example: Theory-based approach to analyzing data from paired samples

   8.4 Supplemental Exploration: Paired designs

   8.5 Supplemental Exploration: Simulation-based approach for analyzing paired data

   8.6 Supplemental Exploration: Theory-based approach for analyzing paired data

   8.7 Investigation: Filtering water in Cameroon

   8.8 Tools, data, and formulas

   9.1 Example: Comparing multiple proportions: Simulation-based approach

   9.2 Example: Comparing multiple proportions: Theory-based approach

   9.3 Example: Chi-square goodness-of-fit test

   9.4 Supplemental Exploration: Comparing multiple proportions: Simulation-based approach

   9.5 Supplemental Exploration A: Comparing multiple proportions: Theory-based approach

   9.6 Supplemental Exploration B: Comparing multiple proportions: Theory-based approach

   9.7 Supplemental Exploration: Chi-square goodness-of-fit test

   9.8 Investigation: Who yields to pedestrians?

   9.9 Tools, data, and formulas

   10.1 Example: Comparing multiple means: Simulation-based approach

   10.2 Example: Comparing multiple means: Theory-based approach

   10.3 Supplemental Exploration: Comparing multiple means: Simulation-based approach

   10.4 Supplemental Exploration: Comparing multiple means: Theory-based approach

   10.5 Investigation: Aggression

   10.6 Tools, data, and formulas

   11.1 Example: Two quantitative variables: Scatterplot and correlation

   11.2 Example: Inference for correlation coefficient: A simulation-based approach

   11.3 Example: Least squares regression

   11.4 Example: Inference for regression slope: Simulation-based approach

   11.5 Example: Inference for regression slope: Theory-based approach

   11.6 Supplemental ​​Exploration: Two quantitative variables: Scatterplot and correlation

   11.7 Supplemental Exploration: Inference for correlation coefficient: A simulation-based approach

   11.8 Supplemental Exploration: Least squares regression

   11.9 Supplemental Exploration: Inference for regression slope: Simulation-based approach

   11.10 Supplemental Exploration: Inference for regression slope: Theory-based approach

   11.11 Investigation: Association between hand span and candy?

   11.12 Tools, data, and formulas

   12.1 Example: Basics of probability

   12.2 Example: Probability rules

   12.3 Example: Conditional probability and independence

   12.4 Example: Discrete random variables

   12.5 Example: Random variable rules

   12.6 Example: Binomial and geometric random variables

   12.7 Example: Continuous random variables and normal distribution

   12.8 Example: Revisiting theory-based approximations of sampling distributions

   12.9 ​​Supplemental Exploration: Basics of probability

   12.10 ​​Supplemental Exploration: Probability rules

   12.11 ​​Supplemental Exploration A: Conditional probability and independence

   12.12 ​​Supplemental Exploration B: Conditional probability and independence

   12.13 ​​Supplemental Exploration: Discrete random variables

   12.14 ​​Supplemental Exploration: Random variable rules

   12.15 ​​Supplemental Exploration: Binomial and geometric random variables

   12.16 ​​Supplemental Exploration A: Continuous random variables and normal distribution

   12.17 ​​Supplemental Exploration B: Continuous random variables and normal distribution

   12.18 ​​Supplemental Exploration A: Revisiting theory-based approximations of sampling distributions

   12.19 ​​Supplemental Exploration B: Revisiting theory-based approximations of sampling distributions

   13.1 Under the Spiral:  How the ISI zyBook teaches the Statistical Investigation Process

   13.2 Examples and Explorations

Students become immersed in the process of “doing statistics,” which builds confidence and empowers success

The Introduction to Statistical Investigations zyBook offers the popular 2nd edition text and the authors’ spiral approach to the statistical investigation in a new experiential paradigm.

  • Bring text authors’ Simulation-Based Inference (SBI) approach to learning statistics into a new course management platform
  • Students interact with assignable reading made up of embedded in-the-text guided animations, simulation tools, and learning questions with answer-specific feedback
  • Build confidence and conceptual understanding of the statistical investigation process
  • Challenge Activities deliver higher-stakes assessment
  • Adopters have access to a test bank with over 300 questions


Scaffolding in the ISI zyBook:





What is a zyBook?

Introduction to Statistical Investigations is a web-native, interactive zyBook that helps students visualize concepts to learn faster and more effectively than with a traditional textbook. (Check out our research.)

Since 2012, over 1,700 academic institutions have adopted digital zyBooks to transform their STEM education.

zyBooks benefit both students and instructors:


  • Instructor benefits
  • Customize your course by reorganizing existing content, or adding your own content
  • Continuous publication model updates your course with the latest content and technologies
  • Robust reporting gives you insight into students’ progress, reading and participation
  • Save time with auto-graded labs and challenge activities that seamlessly integrate with your LMS gradebook
  • Build quizzes and exams with hundreds of included test questions
  • Student benefits
  • Learning questions and other content serve as an interactive form of reading
  • Instant feedback on labs and homework
  • Concepts come to life through extensive animations embedded into the interactive content
  • Review learning content before exams with different questions and challenge activities
  • Save chapters as PDFs to reference the material at any time

Authors

Nathan Tintle / Professor, Statistics, University of Illinois Chicago
Beth Chance / Professor, Statistics, California Polytechnic State University
George Cobb / Robert L. Rooke Professor Emeritus, Statistics, Mount Holyoke College
Allan Rossman / Professor, Statistics, California Polytechnic State University
Soma Roy / Professor, Statistics, California State Polytechnic University
Todd Swanson / Associate Professor, Mathematics and Statistics, Hope College
Jill VanderStoep / Assistant Professor, Mathematics and Statistics, Hope College

zyBooks Authors

Julia Schedler / PhD in Statistics, Rice University
Ayla Sánchez / Senior Content Developer, Statistics / PhD in Mathematics, Tufts University


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Harris Salat

Applied Statistics with Data Analytics (Python)

in , , /by

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Table of Contents


1.1 What is data?
1.2 What is statistics?
1.3 Observational studies and experiments
1.4 Surveys and sampling methods

2.1 What is data visualization?
2.2 Python for data visualization
2.3 Data frames
2.4 Bar charts
2.5 Pie charts
2.6 Scatter plots
2.7 Line charts
2.8 Data visualization example

3.1 Measures of center
3.2 Measures of variability
3.3 Box plots
3.4 Histograms
3.5 Violin plots

4.1 Introduction to probability
4.2 Addition rule and complements
4.3 Multiplication rule and independence
4.4 Conditional probability
4.5 Bayes’ Theorem
4.6 Combinations and permutations

5.1 Introduction to random variables
5.2 Properties of discrete probability distributions
5.3 Binomial distribution
5.4 Hypergeometric distribution
5.5 Poisson distribution
5.6 Properties of continuous probability distributions
5.7 Normal distribution
5.8 Student’s t-Distribution
5.9 F-distribution
5.10 Chi-square distribution

6.1 Confidence intervals
6.2 Confidence intervals for population means
6.3 Confidence intervals for population proportions
6.4 Hypothesis testing
6.5 Hypothesis test for a population mean
6.6 Hypothesis test for a population proportion
6.7 Hypothesis test for the difference between two population means
6.8 Hypothesis test for the difference between two population proportions
6.9 One-way analysis of variance (one-way ANOVA)

7.1 Categorical data
7.2 Fisher’s exact test
7.3 Introduction to chi-square tests
7.4 Chi-square test for homogeneity and independence
7.5 Relative risk and odds ratios

8.1 Introduction to simple linear regression (SLR)
8.2 SLR assumptions
8.3 Correlation and coefficient of determination
8.4 Interpreting SLR models
8.5 Confidence and prediction intervals for SLR models
8.6 Testing SLR parameters
8.7 Linear regression example

9.1 Introduction to multiple regression
9.2 Multiple regression assumptions and diagnostics
9.3 Coefficient of multiple determination
9.4 Multicollinearity
9.5 Interpreting multiple regression models
9.6 Confidence and prediction intervals for MLR models
9.7 Testing multiple regression parameters
9.8 Multiple regression example

10.1 Categorical predictor variables
10.2 Interaction terms
10.3 Quadratic models
10.4 Complete second order models
10.5 Comparing nested models: F-test
10.6 Higher order models

11.1 Introduction to logistic regression (LR)
11.2 Estimating LR parameters
11.3 LR models with multiple predictors
11.4 LR assumptions and diagnostics
11.5 Testing LR parameters
11.6 Interpreting LR models
11.7 Comparing nested models: Likelihood ratio tests and AIC
11.8 Classification using LR models

12.1 Logarithmic transformations
12.2 Ladder of powers
12.3 Box-Cox transformation

13.1 Introduction to stepwise regression
13.2 Forward selection
13.3 Backward selection
13.4 Stepwise selection

14.1 Parametric vs. nonparametric statistics
14.2 Resampling: Randomization and bootstrapping
14.3 Wilcoxon rank-sum test
14.4 Kruskal-Wallis test
14.5 Multiple tests

15.1 What is data mining?
15.2 Data formats
15.3 Machine learning methods
15.4 scikit-learn

16.1 What is data cleansing?
16.2 Handling missing values
16.3 Outliers
16.4 Standardization and normalization
16.5 Dimensionality reduction
16.6 Training, validation, and test sets

17.1 k nearest neighbors
17.2 Logistic regression
17.3 Evaluating classification models
17.4 Supervised learning examples

18.1 Clustering methods
18.2 Association rules
18.3 Evaluating clustering models
18.4 Unsupervised learning examples

19.1 Introduction to decision trees
19.2 Classification and regression trees (CART)
19.3 ID3 and C4.5 algorithms
19.4 Classification tree example
19.5 Regression tree example
19.6 Random forests

20.1 Introduction to principal component analysis (PCA)
20.2 Calculating principal components for two variables
20.3 Extending PCA to more variables
20.4 Determining the number of components
20.5 Interpreting principal components

21.1 What is a time series?
21.2 Time series patterns and stationarity
21.3 Moving average and exponential smoothing forecasting
21.4 Forecasting using regression

22.1 What is a Monte Carlo simulation?
22.2 Building simulations
22.3 Optimization and forecasting
22.4 What-if analysis
22.5 Advanced simulations

23.1 Misleading statistics
23.2 Abuse of the p-value
23.3 Data privacy
23.4 Ethical guidelines

14.1 t-distribution table
14.2 z-distribution table
14.3 Chi-squared distribution table

25.1 Data sets

Teach applied statistics through a powerful interactive approach that includes programming using Jupyter Notebooks

Applied Statistics with Data Analytics (Python) focuses on statistical concepts and techniques used in data analysis. Important Python libraries are introduced to visualize data, perform statistical inference, and make predictions.

  • Packed with interactive animations, questions, and learning activities to help students master the material
  • Covers elementary statistical concepts, modeling relationships between two or more variables, and advanced topics such as time series and Monte-Carlo methods
  • Data analytics and data mining techniques such as logistic regression, clustering, and decision trees are also covered
  • Built-in Python environment and Jupyter Notebooks allow students to experiment with real-world data sets
  • Adopters have access to a test bank with over 400 questions
  • zyLabs users can add their own Jupyter Notebooks via custom content


What is a zyBook?


Applied Statistics with Data Analytics (Python) is a web-native, interactive zyBook that helps students visualize concepts to learn faster and more effectively than with a traditional textbook. Check out our research.

Since 2012, over 1,700 academic institutions have adopted web-native zyBooks to transform their STEM education.

zyBooks benefit students and instructors:


  • Instructor benefits
  • Customize your course by reorganizing existing content or adding your own
  • Continuous publication model automatically updates your course with the latest content and technologies
  • Robust reporting gives you insight into students’ progress, reading and participation
  • Save time with auto-graded labs and challenge activities that seamlessly integrate with your LMS gradebook
  • Student benefits
  • Learning questions and other content serve as an interactive form of reading
  • Instant feedback on labs and homework
  • Concepts come to life through extensive animations embedded into the interactive content
  • Save chapters as PDFs to reference the material at any time


Give students real-life practice with a data set using embedded Jupyter Notebooks.



Senior Contributors

Heather Berrier
Content Developer, Mathematics / PhD Physics and Astronomy, Univ. of California, Irvine

Joel Berrier
Assistant Professor, Dept. of Physics and Astronomy, Univ. of Nebraska, Kearney / PhD Physics and Astronomy, UC Irvine

Chris Chan
MA Mathematics, San Francisco State Univ.

Scott Nestler
Associate Teaching Professor, Mendoza College of Business, Univ. of Notre Dame / PhD Management Science, Univ. of Maryland, College Park

Iain Pardoe
Mathematics and Statistics Instructor, Thompson Rivers Univ., Pennsylvania State Univ., and Statistics.com / PhD Statistics, Univ. of Minnesota

Rodney X. Sturdivant
Professor, Dept. of Mathematics and Physics, Azusa Pacific Univ. / PhD Biostatistics, Univ. of  Massachusetts, Amherst

Krista Watts
Assistant Professor, Director—Center for Data Analysis and Statistics, United States Military Academy, West Point / PhD Biostatistics, Harvard


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Ricky Porco

Applied Regression Analysis (R)

in /by


Table of Contents


1.1 Introduction to simple linear regression (SLR)
1.2 SLR assumptions
1.3 Correlation and coefficient of determination
1.4 Interpreting SLR models
1.5 Confidence and prediction intervals for SLR models
1.6 Testing SLR parameters

2.1 Introduction to multiple regression
2.2 Multiple regression assumptions and diagnostics
2.3 Coefficient of multiple determination
2.4 Multicollinearity
2.5 Interpreting multiple regression models
2.6 Confidence and prediction intervals for MLR models
2.7 Testing multiple regression parameters
2.8 Multiple regression example

3.1 Interaction terms
3.2 Categorical predictor variables
3.3 Quadratic models
3.4 Complete second order models
3.5 Comparing nested models: F-test
3.6 Higher order models

4.1 Introduction to logistic regression (LR)
4.2 Estimating LR parameters
4.3 LR models with multiple predictors
4.4 LR assumptions and diagnostics
4.5 Testing LR parameters
4.6 Interpreting LR models
4.7 Comparing nested models: Likelihood ratio tests and AIC
4.8 Classification using LR models

5.1 Logarithmic transformations
5.2 Ladder of powers
5.3 Box-Cox transformation

6.1 Introduction to stepwise regression
6.2 Forward selection
6.3 Backward selection
6.4 Stepwise selection

7.1 Introduction to principal component analysis (PCA)
7.2 Calculating principal components for two variables
7.3 Extending PCA to more variables
7.4 Determining the number of components
7.5 Interpreting principal components

8.1 What is a time series?
8.2 Time series patterns and stationarity
8.3 Moving average and exponential smoothing forecasting
8.4 Forecasting using regression

9.1 What is a Monte Carlo simulation?
9.2 Building simulations
9.3 Optimization and forecasting
9.4 What-if analysis
9.5 Advanced simulations

10.1 Parametric vs. nonparametric statistics
10.2 Resampling: Randomization and bootstrapping
10.3 Wilcoxon rank-sum test
10.4 Kruskal-Wallis test
10.5 Multiple tests

11.1 t-distribution table
11.2 z-distribution table
11.3 Chi-squared distribution table

12.1 Data sets

13.1 What is statistics?
13.2 What is data?
13.3 What is data visualization?
13.4 R for data visualization
13.5 Data frames
13.6 Scatter plots
13.7 Box plots
13.8 Histograms
13.9 Normal distribution
13.10 Student’s t-Distribution
13.11 F-distribution
13.12 Chi-square distribution
13.13 Confidence intervals
13.14 Confidence intervals for population means
13.15 Hypothesis testing
13.16 Hypothesis test for a population mean
13.17 Hypothesis test for the difference between two population means
13.18 Chi-square tests for categorical variables
13.19 One-way analysis of variance (one-way ANOVA)

What You’ll Find In This zyBook:

More action with less text.

  • An exceptionally student-focused introduction to regression analysis.
  • Traditionally difficult topics are made easier using animations and learning questions.
  • R coding environments are provided throughout to allow students to experiment.
  • Commonly combined with “Applied Statistics with Data Analytics” with numerous configurations possible.

Instructors: Interested in evaluating this zyBook for your class? Sign up for a Free Trial and check out the first chapter of any zyBook today!

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The zyBooks Approach

Less text doesn’t mean less learning.

This zyBook builds on the techniques introduced in linear regression and provides the tools needed to analyze the relationship between two or more variables. Ideal for students enrolled in a second applied statistics course, Applied Regression Analysis dives deeper into model selection and evaluation. The following questions are answered: Which variables should be included or removed to better predict the target variable? Are the conditions for a specific technique satisfied? Which transformations can be performed on the data when certain conditions are violated? Additional topics covered are time series, Monte-Carlo methods, bootstrapping and randomization, and non-parametric statistics.


Senior Contributors

Joel Berrier
Assistant Professor, Dept. of Physics and Astronomy, Univ. of Nebraska, Kearny, Ph.D. Physics and Astronomy, UC Irvine

Chris Chan
Content lead: Mathematics, zyBooks, M.A. Mathematics, San Francisco State Univ.

Iain Pardoe
Mathematics and Statistics Instructor, Thompson Rivers Univ., Pennsylvania State Univ., and Statistics.com, PhD Statistics, Univ. of Minnesota

Rodney X. Sturdivant
Professor, Dept. of Mathematics and Physics, Azusa Pacific Univ., Ph.D. Biostatistics, U Mass Amherst

Krista Watts
Assistant Professor, Director—Center for Data Analysis and Statistics, United States Military Academy, West Point, Ph.D. Biostatistics, Harvard