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Introductory statistics courses prepare students to think statistically but cover relatively few statistical methods. Building on the basic statistical thinking emphasized in an introductory course, a second course in statistics at the undergraduate level can explore a large number of statistical methods. This text covers more advanced graphical summaries, One-Way ANOVA with pair-wise comparisons, Two-Way ANOVA, Chi-square testing, and simple and multiple linear regression models. Models with interactions are discussed in the Two-Way ANOVA and multiple linear regression setting with categorical explanatory variables. Randomization-based inferences are used to introduce new parametric distributions and to enhance understanding of what evidence against the null hypothesis “looks like”. Throughout, the use of the statistical software R via Rstudio is emphasized with all useful code and data sets provided within the text. This is Version 3.0 of the book.

Subject:
Mathematics
Statistics and Probability
Material Type:
Textbook
Provider:
Montana State University
Author:
Mark C. Greenwood
10/26/2023
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This course provides graduate students in the sciences with an intensive introduction to applied statistics. Topics include descriptive statistics, probability, non-parametric methods, estimation methods, hypothesis testing, correlation and linear regression, simulation, and robustness considerations. Calculations will be done using handheld calculators and the Minitab Statistical Computer Software.

Subject:
Mathematics
Statistics and Probability
Material Type:
Full Course
Syllabus
Provider:
UMass Boston
Provider Set:
UMass Boston OpenCourseWare
Author:
Eugene Gallagher
04/25/2019
Unrestricted Use
CC BY
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In this course, the student will learn the basic terminology and concepts of probability theory, including sample size, random experiments, outcome spaces, discrete distribution, probability density function, expected values, and conditional probability. The course also delves into the fundamental properties of several special distributions, including binomial, geometric, normal, exponential, and Poisson distributions. Upon successful completion of this course, the student will be able to: Define probability, outcome space, events, and probability functions; Use combinations to evaluate the probability of outcomes in coin-flipping experiments; Calculate the union of events and conditional probability; Apply Bayes's theorem to simple situations; Calculate the expected values of discrete and continuous distributions; Calculate the sums of random variables; Calculate cumulative distributions and marginal distributions; Evaluate random processes governed by binomial, multinomial, geometric, exponential, normal, and Poisson distributions; Define the law of large numbers and the central limit theorem. (Mathematics 252)

Subject:
Mathematics
Statistics and Probability
Material Type:
Full Course
Provider:
The Saylor Foundation
04/29/2019
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This work has been superseded by Introduction to Statistics in the Psychological Sciences available from https://irl.umsl.edu/oer/25/.

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We are constantly bombarded by information, and finding a way to filter that information in an objective way is crucial to surviving this onslaught with your sanity intact. This is what statistics, and logic we use in it, enables us to do. Through the lens of statistics, we learn to find the signal hidden in the noise when it is there and to know when an apparent trend or pattern is really just randomness. The study of statistics involves math and relies upon calculations of numbers. But it also relies heavily on how the numbers are chosen and how the statistics are interpreted.

This work was created as part of the University of Missouri’s Affordable and Open Access Educational Resources Initiative (https://www.umsystem.edu/ums/aa/oer). The contents of this work have been adapted from the following Open Access Resources: Online Statistics Education: A Multimedia Course of Study (http://onlinestatbook.com/). Project Leader: David M. Lane, Rice University. Changes to the original works were made by Dr. Garett C. Foster in the Department of Psychological Sciences to tailor the text to fit the needs of the introductory statistics course for psychology majors at the University of Missouri – St. Louis. Materials from the original sources have been combined, reorganized, and added to by the current author, and any conceptual, mathematical, or typographical errors are the responsibility of the current author.

Subject:
Mathematics
Psychology
Social Science
Statistics and Probability
Material Type:
Textbook
Provider:
University of Missouri St. Louis
Author:
Dan Osherson
Foster Garett C
Garett C Foster
Hebl Mikki
Mikki Hebl
Rice University
Rudy Guerra
Scott David
University Of Missouri-st Louis
Zimmer Heidi
10/26/2023
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CC BY-NC-SA
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" This course will provide a solid foundation in probability and statistics for economists and other social scientists. We will emphasize topics needed for further study of econometrics and provide basic preparation for 14.32. Topics include elements of probability theory, sampling theory, statistical estimation, and hypothesis testing."

Subject:
Economics
Mathematics
Social Science
Statistics and Probability
Material Type:
Full Course
Provider:
M.I.T.
Provider Set:
M.I.T. OpenCourseWare
Author:
01/01/2009
Unrestricted Use
CC BY
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The target audience for this book is college students who are required to learn statistics, students with little background in mathematics and often no motivation to learn more. It is assumed that the students do have basic skills in using computers and have access to one. Moreover, it is assumed that the students are willing to actively follow the discussion in the text, to practice, and more importantly, to think.

Teaching statistics is a challenge. Teaching it to students who are required to learn the subject as part of their curriculum, is an art mastered by few. In the past I have tried to master this art and failed. In desperation, I wrote this book.

This book uses the basic structure of generic introduction to statistics course. However, in some ways I have chosen to diverge from the traditional approach. One divergence is the introduction of R as part of the learning process. Many have used statistical packages or spreadsheets as tools for teaching statistics. Others have used R in advanced courses. I am not aware of attempts to use R in introductory level courses. Indeed, mastering R requires much investment of time and energy that may be distracting and counterproductive for learning more fundamental issues. Yet, I believe that if one restricts the application of R to a limited number of commands, the benefits that R provides outweigh the difficulties that R engenders.

Another departure from the standard approach is the treatment of probability as part of the course. In this book I do not attempt to teach probability as a subject matter, but only specific elements of it which I feel are essential for understanding statistics. Hence, Kolmogorov’s Axioms are out as well as attempts to prove basic theorems and a Balls and Urns type of discussion. On the other hand, emphasis is given to the notion of a random variable and, in that context, the sample space.

I Introduction to Statistics
1 Introduction
2 Sampling and Data Structures
3 Descriptive Statistics
4 Probability
5 Random Variables
6 The Normal Random Variable
7 The Sampling Distribution
8 Overview and Integration
II Statistical Inference
9 Introduction to Statistical Inference
10 Point Estimation
11 Confidence Intervals
12 Testing Hypothesis
13 Comparing Two Samples
14 Linear Regression
15 A Bernoulli Response
16 Case Studies

Subject:
Mathematics
Statistics and Probability
Material Type:
Textbook
Author:
Benjamin Yakir
09/21/2021
Unrestricted Use
CC BY
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0.0 stars

The target audience for this book is college students who are required to learn statistics, students with little background in mathematics and often no motivation to learn more. It is assumed that the students do have basic skills in using computers and have access to one. Moreover, it is assumed that the students are willing to actively follow the discussion in the text, to practice, and more importantly, to think.

Subject:
Mathematics
Statistics and Probability
Material Type:
Textbook
Author:
Benjamin Yakir
10/26/2023
Unrestricted Use
Public Domain
Rating
0.0 stars

Introduction to Statistics is a resource for learning and teaching introductory statistics. This work is in the public domain. Therefore, it can be copied and reproduced without limitation. However, we would appreciate a citation where possible. Please cite as: Online Statistics Education: A Multimedia Course of Study (http://onlinestatbook.com/). Project Leader: David M. Lane, Rice University. Instructor's manual, PowerPoint Slides, and additional questions are available.

Subject:
Mathematics
Statistics and Probability
Material Type:
Textbook
Author:
David Lane
10/26/2023
Unrestricted Use
CC BY
Rating
0.0 stars

This course covers descriptive statistics, the foundation of statistics, probability and random distributions, and the relationships between various characteristics of data. Upon successful completion of the course, the student will be able to: Define the meaning of descriptive statistics and statistical inference; Distinguish between a population and a sample; Explain the purpose of measures of location, variability, and skewness; Calculate probabilities; Explain the difference between how probabilities are computed for discrete and continuous random variables; Recognize and understand discrete probability distribution functions, in general; Identify confidence intervals for means and proportions; Explain how the central limit theorem applies in inference; Calculate and interpret confidence intervals for one population average and one population proportion; Differentiate between Type I and Type II errors; Conduct and interpret hypothesis tests; Compute regression equations for data; Use regression equations to make predictions; Conduct and interpret ANOVA (Analysis of Variance). (Mathematics 121; See also: Biology 104, Computer Science 106, Economics 104, Psychology 201)

Subject:
Mathematics
Statistics and Probability
Material Type:
Full Course
Provider:
The Saylor Foundation
04/29/2019
Unrestricted Use
Public Domain
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0.0 stars

Introduction to Statistics is a resource for learning and teaching introductory statistics. This work is in the public domain. Therefore, it can be copied and reproduced without limitation. However, we would appreciate a citation where possible. Please cite as: Online Statistics Education: A Multimedia Course of Study (http://onlinestatbook.com/). Project Leader: David M. Lane, Rice University. Instructor's manual, PowerPoint Slides, and additional questions are available.

1. Introduction
2. Graphing Distributions
3. Summarizing Distributions
4. Describing Bivariate Data
5. Probability
6. Research Design
7. Normal Distributions
9. Sampling Distributions
10. Estimation
11. Logic of Hypothesis Testing
12. Testing Means
13. Power
14. Regression
15. Analysis of Variance
16. Transformations
17. Chi Square
18. Distribution-Free Tests
19. Effect Size
20. Case Studies
21. Glossary

Subject:
Mathematics
Statistics and Probability
Material Type:
Textbook
Author:
06/25/2020
Conditional Remix & Share Permitted
CC BY-NC-SA
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STUDENT LEARNING OUTCOMES (SLOS)
CO1 - Students should be able to describe important characteristics of a data set. (Describe can be in words or can mean to calculate values when appropriate)

CO2 - Students should be able to infer appropriate information from sample data. (verify, validate, conclude...to the population)

CO3 - Students should be able to interpret their results (from CO1 and CO2). (what does it mean? why is it useful?)

CO4 - Students should be able to communicate their results (from CO1, CO2, and CO3). (tell others, show others)

MODULES
Topic 1 - Sampling and Data

Topic 2 - Probability

Topic 3 - Probability and Sampling Distributions

Topic 4 - 1-Sample Confidence Intervals

Topic 5 - 1-Sample Hypothesis Testing

Topic 6 - 2-Sample Inference for Means

Topic 7 - 2-Sample Inference for Proportions

Topic 8 - Regression

Subject:
Mathematics
Statistics and Probability
Material Type:
Full Course
Module
Author:
University of North Carolina System
UNC System Digital Course Enhancement Initiative
04/16/2021
Unrestricted Use
CC BY
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The main goal of the course is to highlight the general assumptions and methods that underlie all statistical analysis. The purpose is to get a good understanding of the scope, and the limitations of these methods. We also want to learn as much as possible about the assumptions behind the most common methods, in order to evaluate if they apply with reasonable accuracy to a given situation. Our goal is not so much learning bread and butter techniques: these are pre-programmed in widely available and used software, so much so that a mechanical acquisition of these techniques could be quickly done "on the job". What is more challenging is the evaluation of what the results of a statistical procedure really mean, how reliable they are in given circumstances, and what their limitations are.Login: guest_oclPassword: ocl

Subject:
Mathematics
Statistics and Probability
Material Type:
Full Course
Homework/Assignment
Lecture Notes
Syllabus
Provider:
Washington State Board for Community & Technical Colleges
Provider Set:
Open Course Library
10/31/2011
Unrestricted Use
CC BY
Rating
0.0 stars

Introductory Business Statistics is designed to meet the scope and sequence requirements of the one-semester statistics course for business, economics, and related majors. Core statistical concepts and skills have been augmented with practical business examples, scenarios, and exercises. The result is a meaningful understanding of the discipline, which will serve students in their business careers and real-world experiences.

Subject:
Mathematics
Statistics and Probability
Material Type:
Textbook
Provider:
Rice University
Provider Set:
OpenStax College
Author:
Alexander Holmes
Barbara Illowsky
Susan Dean
11/30/2017
Unrestricted Use
CC BY
Rating
0.0 stars

The book "Introductory Business Statistics" by Thomas K. Tiemann explores the basic ideas behind statistics, such as populations, samples, the difference between data and information, and most importantly sampling distributions. The author covers topics including descriptive statistics and frequency distributions, normal and t-distributions, hypothesis testing, t-tests, f-tests, analysis of variance, non-parametric tests, and regression basics. Using real-world examples throughout the text, the author hopes to help students understand how statistics works, not just how to "get the right number."

1. Descriptive statistics and frequency distributions

Descriptive statistics
2. The normal and t-distributions

Normal things
The t-distribution
3. Making estimates

Estimating the population mean
Estimating the population proportion
Estimating population variance
4. Hypothesis testing

The strategy of hypothesis testing
5. The t-test

The t-distribution
6. F-test and one-way anova

Analysis of variance (ANOVA)
7. Some non-parametric tests

Do these populations have the same location? The Mann-Whitney U testTesting with matched pairs: the Wilcoxon signed ranks test.
Are these two variables related? Spearman's rank correlation
8. Regression basics

What is regression?
Correlation and covariance
Covariance, correlation, and regression

Subject:
Mathematics
Statistics and Probability
Material Type:
Textbook
Author:
Thomas K. Tiemann
06/25/2020
Unrestricted Use
CC BY
Rating
0.0 stars

The book "Introductory Business Statistics" by Thomas K. Tiemann explores the basic ideas behind statistics, such as populations, samples, the difference between data and information, and most importantly sampling distributions. The author covers topics including descriptive statistics and frequency distributions, normal and t-distributions, hypothesis testing, t-tests, f-tests, analysis of variance, non-parametric tests, and regression basics. Using real-world examples throughout the text, the author hopes to help students understand how statistics works, not just how to "get the right number."

Subject:
Mathematics
Statistics and Probability
Material Type:
Textbook
Provider:
BCcampus
Provider Set:
BCcampus Open Textbooks
Author:
Thomas K. Tiemann
10/26/2023
Unrestricted Use
CC BY
Rating
0.0 stars

Subject:
Mathematics
Statistics and Probability
Material Type:
Textbook
Provider:
BCcampus
Provider Set:
BCcampus Open Textbooks
Author:
Mohammad Mahbobi, Thompson Rivers University; Thomas K. Tiemann, Elon University
04/19/2016
Conditional Remix & Share Permitted
CC BY-NC-SA
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In many introductory level courses today, teachers are challenged with the task of fitting in all of the core concepts of the course in a limited period of time. The Introductory Statistics teacher is no stranger to this challenge. To add to the difficulty, many textbooks contain an overabundance of material, which not only results in the need for further streamlining, but also in intimidated students. Shafer and Zhang wrote Introductory Statistics by using their vast teaching experience to present a complete look at introductory statistics topics while keeping in mind a realistic expectation with respect to course duration and students' maturity level.

Subject:
Mathematics
Statistics and Probability
Material Type:
Textbook
Provider:
The Saylor Foundation
Provider Set:
Saylor Textbooks
Author:
Douglas S. Shafer
Zhiyi Zhang
10/26/2023
Conditional Remix & Share Permitted
CC BY-SA
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Chapter 1: Sampling and Data
Introduction to Chapter 1: Sampling and Data
1.1 Definitions of Statistics, Probability, and Key Terms
1.2 Data, Sampling, and Variation in Data and Sampling
1.3 Frequency, Frequency Tables, and Levels of Measurement
1.4 Experimental Design and Ethics
Chapter 1 Review
Chapter 1 Practice
Chapter 1 Homework

Chapter 2: Descriptive Statistics
Introduction to Chapter 2: Descriptive Statistics
2.1 Stem-and-Leaf Graphs (Stemplots), Line Graphs, and Bar Graphs
2.2 Histograms, Frequency Polygons, and Time Series Graphs
2.3 Measures of the Location of the Data
2.4 Box Plots
2.5 Measures of the Center of the Data
2.6 Skewness and the Mean, Median, and Mode
2.7 Measures of the Spread of the Data
Chapter 2 Review
Chapter 2 Practice
Chapter 2 Homework

Chapter 3: Probability Topics
Introduction to Chapter 3: Probability Topics
3.1 Terminology
3.2 Independent and Mutually Exclusive Events
3.3 Two Basic Rules of Probability
3.4 Contingency Tables
3.5 Tree and Venn Diagrams
Chapter 3 Review
Chapter 3 Practice
Chapter 3 Homework

Chapter 4: Discrete Random Variables
Introduction to Chapter 4: Discrete Random Variables
4.1 Probability Distribution Function (PDF) for a Discrete Random Variable
4.2 Measures of General Discrete Random Variables
4.3 Binomial Distribution
4.4 Geometric Distribution
4.5 Hypergeometric Distribution
4.6 Poisson Distribution
Chapter 4 Review
Chapter 4 Practice
Chapter 4 Homework

Chapter 5: Continuous Random Variables
Introduction to Chapter 5: Continuous Random Variables
5.1 Continuous Probability Functions
5.2 The Uniform Distribution
5.3 The Exponential Distribution
Chapter 5 Review
Chapter 5 Practice
Chapter 5 Homework

Chapter 6: The Normal Distribution and The Central Limit Theorem
Introduction to Chapter 6a: The Normal Distribution
6.1 The Standard Normal Distribution
6.2 Using the Normal Distribution
Introduction to Chapter 6b: The Central Limit Theorem
6.3 The Central Limit Theorem for Sample Means (Averages)
6.4 The Central Limit Theorem for Sums
6.5 The Normal Approximation to the Binomial
Chapter 6 Review
Chapter 6 Practice
Chapter 6 Homework

Chapter 7: Confidence Intervals
Introduction to Chapter 7: Confidence Intervals
7.1 A Single Population Mean Using the Normal Distribution
7.2 A Single Population Mean using the Student t Distribution
7.3 A Population Proportion
Chapter 7 Review
Chapter 7 Practice
Chapter 7 Homework

Chapter 8: Hypothesis Testing with One Sample
Introduction to Chapter 8: Hypothesis Testing with One Sample
8.1 Null and Alternative Hypotheses
8.2 Outcomes and the Type I and Type II Errors
8.3 Distribution Needed for Hypothesis Testing
8.4 Rare Events, the Sample, Decision, and Conclusion
8.5 Additional Information and Full Hypothesis Test Examples
Chapter 8 Review
Chapter 8 Practice
Chapter 8 Homework

Chapter 9: Hypothesis Testing with Two Samples
Introduction to Chapter 9: Hypothesis Testing with Two Samples
9.1 Two Population Means with Unknown Standard Deviations
9.2 Two Population Means with Known Standard Deviations
9.3 Comparing Two Independent Population Proportions
9.4 Matched or Paired Samples
Chapter 9 Review
Chapter 9 Practice
Chapter 9 Homework

Chapter 10: Linear Regression and Correlation
Introduction to Chapter 10: Linear Regression and Correlation
10.1 Linear Equations
10.2 Scatter Plots
10.3 The Regression Equation
10.4 Testing the Significance of the Correlation Coefficient
10.5 Prediction
10.6 Outliers
Chapter 10 Review
Chapter 10 Homework
Chapter 10 Practice

Chapter 11: The Chi-Square Distribution
Introduction to Chapter 11: The Chi-Square Distribution
11.1 Facts About the Chi-Square Distribution
11.2 Goodness-of-Fit Test
11.3 Test of Independence
11.4 Test for Homogeneity
11.5 Comparison of the Chi-Square Tests
11.6 Test of a Single Variance
Chapter 11 Review
Chapter 11 Practice
Chapter 11 Homework

Class Group Activities/Projects

This textbook was created through Connecting the Pipeline: Libraries, OER, and Dual Enrollment from Secondary to Postsecondary, a \$1.3 million project funded by LOUIS: The Louisiana Library Network and the Institute of Library and Museum Services. This project supports the extension of access to high-quality post-secondary opportunities to high school students across Louisiana and beyond by creating materials that can be adopted for dual enrollment environments. Dual enrollment is the opportunity for a student to be enrolled in high school and college at the same time.

The cohort-developed OER course materials are released under a license that permits their free use, reuse, modification and sharing with others. This includes a corresponding course available in Moodle and Canvas that can be imported to other platforms.

Subject:
Mathematics
Statistics and Probability
Material Type:
Textbook
Provider:
LOUIS: The Louisiana Library Network
Provider Set:
Connecting the Pipeline Grant
Author:
Jared Eusea
Phyllis Okwan
Rachid Belmasrour
Stephan Patterson
Stephen Andrus
05/23/2024
Unrestricted Use
CC BY
Rating
0.0 stars

Introductory Statistics follows scope and sequence requirements of a one-semester introduction to statistics course and is geared toward students majoring in fields other than math or engineering. The text assumes some knowledge of intermediate algebra and focuses on statistics application over theory. Introductory Statistics includes innovative practical applications that make the text relevant and accessible, as well as collaborative exercises, technology integration problems, and statistics labs.

Subject:
Mathematics
Statistics and Probability
Material Type:
Textbook
Provider:
Rice University
Provider Set:
OpenStax College
Author:
Barbara Ilowsky
Susan Dean