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  • Statistics and Probability
ANOVA Calculations
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This supplemental material is an online resource of OpenIntro Statistics, a textbook available for free in PDF at openintro.org and in paperback for about $10 at amazon.com.

Subject:
Mathematics
Statistics and Probability
Material Type:
Reading
Provider:
OpenIntro
Author:
Emiliano Vega
Ralf Youtz
Date Added:
04/25/2019
Adapting Open Educational Resources for AGSC Statistical Methods Course
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Syllabus, videos, and student responses from the adoption of OpenIntro's Biostatistics text. The text has its own accompanying videos and a mostly self-grading homework platform.Instructor resources are available: https://www.openintro.org/teachers/. These resources accompany the open textbook Introductory Statistics for the Life and Biomedical Sciences.

Subject:
Statistics and Probability
Material Type:
Lecture
Syllabus
Textbook
Author:
Jason Holderieath
Date Added:
01/02/2021
Advanced High School Statistics
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We hope readers will take away three ideas from this book in addition to forming a foundation
of statistical thinking and methods.

(1) Statistics is an applied field with a wide range of practical applications.
(2) You don't have to be a math guru to learn from real, interesting data.
(3) Data are messy, and statistical tools are imperfect. But, when you understand the strengths and weaknesses of these tools, you can use them to learn about the real world.
Textbook overview
The chapters of this book are as follows:

1. Data collection. Data structures, variables, and basic data collection techniques.
2. Summarizing data. Data summaries and graphics.
3. Probability. The basic principles of probability.
4. Distributions of random variables. Introduction to key distributions, and how the normal model applies to the sample mean and sample proportion.
5. Foundation for inference. General ideas for statistical inference in the context of estimating the population proportion.
6. Inference for categorical data. Inference for proportions using the normal and chisquare distributions.
7. Inference for numerical data. Inference for one or two sample means using the t distribution, and comparisons of many means using ANOVA.
8. Introduction to linear regression. An introduction to regression with two variables.
Instructions are also provided in several sections for using Casio and TI calculators.

Subject:
Statistics and Probability
Material Type:
Textbook
Author:
Christopher Barr
David Diez
Leah Dorazio
Mine Çetinkaya-Rundel
Date Added:
06/23/2020
Advanced High School Statistics
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This textbook is part of the OpenIntro Statistics series and offers complete coverage of the high school AP Statistics curriculum. Real data and plenty of inline examples and exercises make this an engaging and readable book. Links to lecture slides, video overviews, calculator tutorials, and video solutions to selected end of chapter exercises make this an ideal choice for any high school or Community College teacher. In fact, Portland Community College recently adopted this textbook for its Introductory Statistics course, and it estimates that this will save their students $250,000 per year. Find out more at: openintro.org/ahss

View our video tutorials here:
openintro.org/casio
openintro.org/TI

Subject:
Statistics and Probability
Material Type:
Textbook
Provider:
OpenIntro
Author:
Christopher Barr
David Diez
Leah Dorazio
Mine Cetinkaya-Rundel
Date Added:
04/24/2019
Advanced Statistics
Unrestricted Use
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This course is oriented toward US high school students. The course is divided into 10 units of study. The first five units build the foundation of concepts, vocabulary, knowledge, and skills for success in the remainder of the course. In the final five units, we will take the plunge into the domain of inferential statistics, where we make statistical decisions based on the data that we have collected.

Subject:
Statistics and Probability
Material Type:
Full Course
Provider:
The Saylor Foundation
Date Added:
04/04/2019
Answering questions with data: Introductory Statistics for Psychology Students
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This is a free textbook teaching introductory statistics for undergraduates in Psychology. This textbook is part of a larger OER course package for teaching undergraduate statistics in Psychology, including this textbook, a lab manual, and a course website. All of the materials are free and copiable, with source code maintained in Github repositories.

Table of Contents
1 Why Statistics?
2 Describing Data
3 Correlation
4 Probability, Sampling, and Estimation
5 Foundations for inference
6 t-Tests
7 ANOVA
8 Repeated Measures ANOVA
9 Factorial ANOVA
10 More On Factorial Designs
11 Simulating Data
12 Thinking about answering questions with data
13 GIFs

Subject:
Statistics and Probability
Psychology
Material Type:
Textbook
Author:
Matthew J. C. Crump
Date Added:
06/23/2020
Applied Probability
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This is a "first course" in the sense that it presumes no previous course in probability. The mathematical prerequisites are ordinary calculus and the elements of matrix algebra. A few standard series and integrals are used, and double integrals are evaluated as iterated integrals. The reader who can evaluate simple integrals can learn quickly from the examples how to deal with the iterated integrals used in the theory of expectation and conditional expectation. Appendix B provides a convenient compendium of mathematical facts used frequently in this work. And the symbolic toolbox, implementing MAPLE, may be used to evaluate integrals, if desired.

In addition to an introduction to the essential features of basic probability in terms of a precise mathematical model, the work describes and employs user defined MATLAB procedures and functions (which we refer to as m-programs, or simply programs) to solve many important problems in basic probability. This should make the work useful as a stand-alone exposition as well as a supplement to any of several current textbooks.

Most of the programs developed here were written in earlier versions of MATLAB, but have been revised slightly to make them quite compatible with MATLAB 7. In a few cases, alternate implementations are available in the Statistics Toolbox, but are implemented here directly from the basic MATLAB program, so that students need only that program (and the symbolic mathematics toolbox, if they desire its aid in evaluating integrals).

Since machine methods require precise formulation of problems in appropriate mathematical form, it is necessary to provide some supplementary analytical material, principally the so-called minterm analysis. This material is not only important for computational purposes, but is also useful in displaying some of the structure of the relationships among events.

Table of Contents
1 Preface
2 Probability Systems
3 Minterm Analysis
4 Conditional Probability
5 Independence of Events
6 Conditional Independence
7 Random Variables and Probabilities
8 Distribution and Density Functions
9 Random Vectors and joint Distributions
10 Independent Classes of Random Variables
11 Functions of Random Variables
12 Mathematical Expectation
13 Variance, Covariance, Linear Regression
14 Transform Methods
15 Conditional Expectation, Regression
16 Random Selection
17 Conditional Independence, Given a Random Vector
18 Appendices

Subject:
Statistics and Probability
Material Type:
Textbook
Author:
Paul Pfeiffer
Date Added:
06/26/2020
Applied Statistics, Spring 2009
Only Sharing Permitted
CC BY-NC-ND
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I designed the course for graduate students who use statistics in their research, plan to use statistics, or need to interpret statistical analyses performed by others. The primary audience are graduate students in the environmental sciences, but the course should benefit just about anyone who is in graduate school in the natural sciences. The course is not designed for those who want a simple overview of statistics; we’ll learn by analyzing real data. This course or equivalent is required for UMB Biology and EEOS Ph.D. students. It is a recommended course for several of the intercampus graduate school of marine science program options.

Subject:
Statistics and Probability
Material Type:
Full Course
Provider:
UMass Boston
Provider Set:
UMass Boston OpenCourseWare
Author:
Eugene Gallagher
Date Added:
04/25/2019
The Art of the Probable: Literature and Probability, Spring 2008
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The Art of the Probable" addresses the history of scientific ideas, in particular the emergence and development of mathematical probability. But it is neither meant to be a history of the exact sciences per se nor an annex to, say, the Course 6 curriculum in probability and statistics. Rather, our objective is to focus on the formal, thematic, and rhetorical features that imaginative literature shares with texts in the history of probability. These shared issues include (but are not limited to): the attempt to quantify or otherwise explain the presence of chance, risk, and contingency in everyday life; the deduction of causes for phenomena that are knowable only in their effects; and, above all, the question of what it means to think and act rationally in an uncertain world. Our course therefore aims to broaden students’ appreciation for and understanding of how literature interacts with--both reflecting upon and contributing to--the scientific understanding of the world. We are just as centrally committed to encouraging students to regard imaginative literature as a unique contribution to knowledge in its own right, and to see literary works of art as objects that demand and richly repay close critical analysis. It is our hope that the course will serve students well if they elect to pursue further work in Literature or other discipline in SHASS, and also enrich or complement their understanding of probability and statistics in other scientific and engineering subjects they elect to take.

Subject:
Arts and Humanities
Literature
Philosophy
Religious Studies
Statistics and Probability
Material Type:
Full Course
Provider:
M.I.T.
Provider Set:
M.I.T. OpenCourseWare
Author:
Jackson, Noel
Kibel, Alvin
Raman, Shankar
Date Added:
01/01/2008
Biological Engineering II: Instrumentation and Measurement, Fall 2006
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This course covers sensing and measurement for quantitative molecular/cell/tissue analysis, in terms of genetic, biochemical, and biophysical properties. Methods include light and fluorescence microscopies; electro-mechanical probes such as atomic force microscopy, laser and magnetic traps, and MEMS devices; and the application of statistics, probability and noise analysis to experimental data.

Subject:
Electronic Technology
Statistics and Probability
Biology
Material Type:
Full Course
Provider:
M.I.T.
Provider Set:
M.I.T. OpenCourseWare
Author:
So, Peter
Date Added:
01/01/2006
Business Statistics
Unrestricted Use
CC BY
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Introductory survey of quantitative methods (QM), or the application of statistics in the workplace. Examines techniques for gathering, analyzing, and interpreting data in any number of fieldsĺÎĺ from anthropology to hedge fund management.

Subject:
Business and Communication
Management
Statistics and Probability
Material Type:
Activity/Lab
Full Course
Homework/Assignment
Reading
Syllabus
Provider:
The Saylor Foundation
Provider Set:
Saylor Textbooks
Date Added:
09/07/2018
City Life - Inquiry and Problem Solving Exercise
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Living in a big city like New York can be very challenging. City planning is an interdisciplinary enterprise where social scientists, humanists, psychologists, scientists, statisticians, citizens, politicians, etc. come together to offer solutions to improve quality of life in the city. To find such solutions, these people need clear and reliable (qualitative and quantitative) information about specific challenges that residents and visitors face For the variety of stakeholders in the city, many different things might be considered worthy of study, depending on their interests and needs regarding, e.g., employment, financial status, family size, healthcare, mobility, and education.
For example, do you know whether your neighborhood issufficiently protected from a fire? What about other neighborhoods in the city? To what extent does a CUNY degree help a person gain employment in the City? In which ways do race or gender or sexual preference play a role in how people experience city life? Can these be quantified in dollar terms? Once you have identified a problem, write an essay that describes a question
about city life that you believe is worthy of a statistical study.

Subject:
Statistics and Probability
Material Type:
Textbook
Provider:
CUNY Academic Works
Provider Set:
LaGuardia Community College
Author:
Milena Cuellar
Date Added:
01/01/2017
Collaborative Statistics
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Table of Contents

1 Sampling and Data
2 Descriptive Statistics
3 Probability Topics
4 Discrete Random Variables
5 Continuous Random Variables
6 The Normal Distribution
7 The Central Limit Theorem
8 Confidence Intervals
9 Hypothesis Testing: Single Mean and Single Proportion
10 Hypothesis Testing: Two Means, Paired Data, Two Proportions
11 The Chi-Square Distribution
12 Linear Regression and Correlation
13 F Distribution and ANOVA
14 Appendix
15 Tables

Collaborative Statistics was written by Barbara Illowsky and Susan Dean, faculty members at De Anza Collegein Cupertino, California. The textbook was developed over several years and has been used in regularand honors-level classroom settings and in distance learning classes. Courses using this textbook have beenarticulated by the University of California for transfer of credit. The textbook contains full materials forcourse offerings, including expository text, examples, labs, homework, and projects. A Teacher's Guide iscurrently available in print form and on the Connexions site at and supplemental course materials including additional problem sets and video lectures are available. The on-line text for each of these collections collections willmeet the Section 508 standards for accessibility.

An on-line course based on the textbook was also developed by Illowsky and Dean. It has won an awardas the best on-line California community college course. The on-line course will be available at a later dateas a collection in Connexions, and each lesson in the on-line course will be linked to the on-line textbookchapter. The on-line course will include, in addition to expository text and examples, videos of courselectures in captioned and non-captioned format.

Subject:
Statistics and Probability
Material Type:
Textbook
Author:
Barbara Illowsky
Susan Dean
Date Added:
06/29/2020
Computation for Biological Engineers, Fall 2006
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This course covers the analytical, graphical, and numerical methods supporting the analysis and design of integrated biological systems. Topics include modularity and abstraction in biological systems, mathematical encoding of detailed physical problems, numerical methods for solving the dynamics of continuous and discrete chemical systems, statistics and probability in dynamic systems, applied local and global optimization, simple feedback and control analysis, statistics and probability in pattern recognition.

Subject:
Statistics and Probability
Genetics
Material Type:
Full Course
Provider:
M.I.T.
Provider Set:
M.I.T. OpenCourseWare
Author:
Alm, Eric
Date Added:
01/01/2006
Confidence Intervals
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The applets in this section of Statistical Java allow you to see how levels of confidence are achieved through repeated sampling. The confidence intervals are related to the probability of successes in a Binomial experiment.

Subject:
Statistics and Probability
Material Type:
Activity/Lab
Provider:
Consortium for the Advancement of Undergraduate Statistics Education
Provider Set:
Causeweb.org
Author:
Anderson-Cook, C.
C.Anderson-Cook
Dorai-Raj, S.
Robinson, T.
S.Dorai-Raj
T.Robinson
Date Added:
04/04/2019
Design of Electromechanical Robotic Systems, Fall 2009
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This course covers the design, construction, and testing of field robotic systems, through team projects with each student responsible for a specific subsystem. Projects focus on electronics, instrumentation, and machine elements. Design for operation in uncertain conditions is a focus point, with ocean waves and marine structures as a central theme. Topics include basic statistics, linear systems, Fourier transforms, random processes, spectra, ethics in engineering practice, and extreme events with applications in design.

Subject:
Environmental Science
Statistics and Probability
Material Type:
Full Course
Provider:
M.I.T.
Provider Set:
M.I.T. OpenCourseWare
Author:
Chin, Harrison
Hover, Franz
Date Added:
01/01/2010
How to Process, Analyze and Visualize Data, January IAP 2012
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This course is an introduction to data cleaning, analysis and visualization. We will teach the basics of data analysis through concrete examples. You will learn how to take raw data, extract meaningful information, use statistical tools, and make visualizations. This was offered as a non-credit course during the Independent Activities Period (IAP), which is a special 4-week term at MIT that runs from the first week of January until the end of the month.

Subject:
Statistics and Probability
Material Type:
Full Course
Provider:
M.I.T.
Provider Set:
M.I.T. OpenCourseWare
Author:
Adam Marcus
Eugene Wu
Date Added:
01/01/2012
Interactive Statistics
Unrestricted Use
CC BY
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Ancillary materials for interactive statistics:

1: Random Number Generator
2: Completing a Frequency, Relative, and Cumulative Relative Frequency Table Activity
3: The Box Plot Creation Game
4: Online Calculator of the Mean and Median
5: Online Mean, Median, and Mode Calculator From a Frequency Table
6: Standard Deviation Calculator
7: Guess the Standard Deviation Game
8: Mean and Standard Deviation for Grouped Frequency Tables Calculator
9: Z-Score Calculator
10. Expected Value and Standard Deviation Calculator
11: Be the Player Or the Casino Expected Value Game
12: Binomial Distribution Calculator
13: Normal Probability Calculator
14: Calculator For the Sampling Distribution for Means
15: Discover the Central Limit Theorem Activity
16: Sampling Distribution Calculator for Sums
17: Observe the Relationship Between the Binomial and Normal Distributions
18: Confidence Interval Calculator for a Mean Calculator With Statistics (Sigma Unknown)
19: Visually Compare the Student's t Distribution to the Normal Distribution
20: Sample Size for a Mean Calculator
21: Confidence Interval for a Mean (With Data) Calculator
22: Interactively Observe the Effect of Changing the Confidence Level and the Sample Size
23: Confidence Interval for a Mean (With Statistics) Calculator
24: Confidence Interval Calculator for a Population Mean (With Data, Sigma Unknown)
25: Confidence Interval For Proportions Calculator
26: Needed Sample Size for a Confidence Interval for a Population Proportion Calculator
27: Hypothesis Test for a Population Mean Given Statistics Calculator
28: Hypothesis Test for a Population Mean With Data Calculator
29: Hypothesis Test for a Population Proportion Calculator
30: Two Independent Samples With Data Hypothesis Test and Confidence Interval Calculator
31: Two Independent Samples With Statistics and Known Population Standard Deviations Hypothesis Test and Confidence Interval Calculator
32: Two Independent Samples With Statistics Calculator
33: Hypothesis Test and Confidence Interval Calculator: Difference Between Population Proportions
34: Hypothesis Test and Confidence Interval Calculator for Two Dependent Samples
35: Visualize the Chi-Square Distribution
36: Chi-Square Goodness of Fit Test Calculator
37: Chi-Square Test For Independence Calculator
38: Chi-Square Test For Homogeneity Calculator
39: Scatter Plot Calculator
40: Scatter Plot, Regression Line, r,and r^2 Calculator
41: Full Regression Analysis Calculator
42: Shoot Down Money at the Correct Correlation Game
43: Visualize How Changing the Numerator and Denominator Degrees of Freedom Changes the Graph of the F-Distribution
44: ANOVA Calculator
45: Central Limit Theorem Activity

Subject:
Statistics and Probability
Material Type:
Interactive
Author:
Larry Green
Date Added:
04/29/2020
Intermediate Statistics with R
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CC BY-NC
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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.

Table of Contents
1 Preface
2 (R)e-Introduction to statistics
3 One-Way ANOVA
4 Two-Way ANOVA
5 Chi-square tests
6 Correlation and Simple Linear Regression
7 Simple linear regression inference
8 Multiple linear regression
9 Case studies

Subject:
Statistics and Probability
Material Type:
Textbook
Author:
Mark C. Greenwood
Montana State University
Date Added:
10/25/2021
Introduction to Applied Statistics, Summer 2011
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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:
Statistics and Probability
Material Type:
Full Course
Reading
Syllabus
Provider:
UMass Boston
Provider Set:
UMass Boston OpenCourseWare
Author:
Eugene Gallagher
Date Added:
04/25/2019
Introduction to Probability
Read the Fine Print
Educational Use
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Probability theory began in seventeenth century France when the two great French mathematicians, Blaise Pascal and Pierre de Fermat, corresponded over two problems from games of chance. Problems like those Pascal and Fermat solved continued to influence such early researchers as Huygens, Bernoulli, and DeMoivre in establishing a mathematical theory of probability. Today, probability theory is a well established branch of mathematics that finds applications in every area of scholarly activity from music to physics, and in daily experience from weather prediction to predicting the risks of new medical treatments.

This text is designed for an introductory probability course taken by sophomores, juniors, and seniors in mathematics, the physical and social sciences, engineering, and computer science. It presents a thorough treatment of probability ideas and techniques necessary for a form understanding of the subject. The text can be used in a variety of course lengths, levels, and areas of emphasis.

For use in a standard one-term course, in which both discrete and continuous probability is covered, students should have taken as a prerequisite two terms of calculus, including an introduction to multiple integrals. In order to cover Chapter 11, which contains material on Markov chains, some knowledge of matrix theory is necessary.

Reviews available here: https://open.umn.edu/opentextbooks/textbooks/introduction-to-probability

Subject:
Statistics and Probability
Material Type:
Textbook
Provider:
American Mathematical Society
Author:
Charles Grinstead
J. Laurie Snell
Date Added:
04/24/2019
Introduction to Probability Theory
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:
Statistics and Probability
Material Type:
Full Course
Provider:
The Saylor Foundation
Date Added:
04/29/2019
Introduction to Statistical Methods in Economics, Spring 2009
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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:
Business and Communication
Statistics and Probability
Economics
Material Type:
Full Course
Provider:
M.I.T.
Provider Set:
M.I.T. OpenCourseWare
Author:
Menzel, Konrad
Date Added:
01/01/2009
Introduction to Statistical Thinking
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:
Statistics and Probability
Material Type:
Textbook
Author:
Benjamin Yakir
Date Added:
09/21/2021
Introduction to Statistics
Unrestricted Use
CC BY
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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:
Statistics and Probability
Material Type:
Full Course
Provider:
The Saylor Foundation
Date Added:
04/29/2019
Introduction to Statistics
Unrestricted Use
Public Domain
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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.

Table of Contents
1. Introduction
2. Graphing Distributions
3. Summarizing Distributions
4. Describing Bivariate Data
5. Probability
6. Research Design
7. Normal Distributions
8. Advanced Graphs
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:
Statistics and Probability
Material Type:
Textbook
Author:
About The Contributors
Date Added:
06/25/2020
Introduction to Statistics I
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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:
Statistics and Probability
Material Type:
Full Course
Module
Author:
UNC System Digital Course Enhancement Initiative
University of North Carolina System
Date Added:
04/16/2021
Introduction to Statistics (MATH 146)
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:
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
Date Added:
10/31/2011
Introductory Business Statistics
Unrestricted Use
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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."

Table of Contents
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:
Business and Communication
Mathematics
Statistics and Probability
Material Type:
Textbook
Author:
Thomas K. Tiemann
Date Added:
06/25/2020
Introductory Business Statistics with Interactive Spreadsheets - 1st Canadian Edition
Unrestricted Use
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"Introductory Business Statistics with Interactive Spreadsheets - 1st Canadian Edition" is an adaptation of Thomas K. Tiemann's book, "Introductory Business Statistics". In addition to covering basics such as populations, samples, the difference between data and information, and sampling distributions, descriptive statistics and frequency distributions, normal and t-distributions, hypothesis testing, t-tests, f-tests, analysis of variance, non-parametric tests, and regression basics, the following information has been added: the chi-square test and categorical variables, null and alternative hypotheses for the test of independence, simple linear regression model, least squares method, coefficient of determination, confidence interval for the average of the dependent variable, and prediction interval for a specific value of the dependent variable. This new edition also allows readers to learn the basic and most commonly applied statistical techniques in business in an interactive way -- when using the web version -- through interactive Excel spreadsheets. All information has been revised to reflect Canadian content.

Reviews available here: https://open.umn.edu/opentextbooks/textbooks/introductory-business-statistics-with-interactive-spreadsheets-1st-canadian-edition

Table of Contents
Chapter 1. Descriptive Statistics and Frequency Distributions
Chapter 2. The Normal and t-Distributions
Chapter 3. Making Estimates
Chapter 4. Hypothesis Testing
Chapter 5. The t-Test
Chapter 6. F-Test and One-Way ANOVA
Chapter 7. Some Non-Parametric Tests
Chapter 8. Regression Basics

Subject:
Business and Communication
Statistics and Probability
Material Type:
Textbook
Provider:
BCcampus
Provider Set:
BCcampus Open Textbooks
Author:
Elon University
Mohammad Mahbobi
Thompson Rivers University; Thomas K. Tiemann
Date Added:
04/19/2016
Introductory Statistics
Unrestricted Use
CC BY
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This book is meant to be a textbook for a standard one-semester introductory statistics course for general education students.Over time the core content of this course has developed into a well-defined body of material that is substantial for a one-semester course. The authors believe that the students in this course are best served by a focus on the core material and not by an exposure to a plethora of peripheral topics. Therefore in writing this book we have sought to present material that comprises fully a central body of knowledge that is defined according to convention, realistic expectation with respect to course duration and students’ maturity level, and our professional judgment and experience.

Subject:
Statistics and Probability
Material Type:
Textbook
Provider:
BCcampus
Provider Set:
BCcampus Faculty Reviewed Open Textbooks
Author:
Douglas S. Shafer
Zhiyi Zhang
Date Added:
10/28/2014
Introductory Statistics
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CC BY-NC-SA
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This book is meant to be a textbook for a standard one-semester introductory statistics course for general education students. Our motivation for writing it is twofold: 1.) to provide a low-cost alternative to many existing popular textbooks on the market; and 2.) to provide a quality textbook on the subject with a focus on the core material of the course in a balanced presentation.

Table of Contents
Chapter 1: Introduction
Chapter 2: Descriptive Statistics
Chapter 3: Basic Concepts of Probability
Chapter 4: Discrete Random Variables
Chapter 5: Continuous Random Variables
Chapter 6: Sampling Distributions
Chapter 7: Estimation
Chapter 8: Testing Hypotheses
Chapter 9: Two-Sample Problems
Chapter 10: Correlation and Regression
Chapter 11: Chi-Square Tests and F-Tests

Access also available here: https://resources.saylor.org/wwwresources/archived/site/textbooks/Introductory%20Statistics.pdf

Subject:
Statistics and Probability
Material Type:
Textbook
Provider:
The Saylor Foundation
Provider Set:
Saylor Textbooks
Author:
Douglas Shafer
Zhiyi Zhang
Date Added:
04/24/2019
Introductory Statistics
Unrestricted Use
CC BY
Rating

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.

Access also available here: https://openstax.org/details/books/introductory-statistics

Table of Contents
Sampling and Data
Descriptive Statistics
Probability Topics
Discrete Random Variables
Continuous Random Variables
The Normal Distribution
The Central Limit Theorem
Confidence Intervals
Hypothesis Testing with One Sample
Hypothesis Testing with Two Samples
The Chi-Square Distribution
Linear Regression and Correlation
F Distribution and One-Way ANOVA

Subject:
Statistics and Probability
Material Type:
Textbook
Provider:
Rice University
Provider Set:
OpenStax College
Author:
Barbara Ilowsky
Susan Dean
Date Added:
07/19/2013
Introductory Statistics (OpenStax) With Multimedia and Interactivity
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Introductory Statistics was conceived and written to fit a particular topical sequence, but it can be used flexibly to accommodate other course structures. One such potential structure, which fits reasonably well with the textbook content, is provided below. Please consider, however, that the chapters were not written to be completely independent, and that the proposed alternate sequence should be carefully considered for student preparation and textual consistency.

1: Sampling and Data
Included in this chapter are the basic ideas and words of probability and statistics. You will soon understand that statistics and probability work together. You will also learn how data are gathered and what "good" data can be distinguished from "bad."
1.1: Introduction
1.2: Definitions of Statistics, Probability, and Key Terms
1.3: Data, Sampling, and Variation in Data and Sampling
1.4: Frequency, Frequency Tables, and Levels of Measurement
1.5: Experimental Design and Ethics
1.6: Data Collection Experiment (Worksheet)
1.7: Sampling Experiment (Worksheet)
1.E: Sampling and Data (Exercises)

2: Descriptive Statistics
In this chapter, you will study numerical and graphical ways to describe and display your data. This area of statistics is called "Descriptive Statistics." You will learn how to calculate, and even more importantly, how to interpret these measurements and graphs.
2.1: Prelude to Descriptive Statistics
2.2: Stem-and-Leaf Graphs (Stemplots), Line Graphs, and Bar Graphs
2.3: Histograms, Frequency Polygons, and Time Series Graphs
2.4: Measures of the Location of the Data
2.4E: Measures of the Location of the Data (Exercises)
2.5: Box Plots
2.6: Measures of the Center of the Data
2.7: Skewness and the Mean, Median, and Mode
2.8: Measures of the Spread of the Data
2.9: Descriptive Statistics (Worksheet)
2.E: Descriptive Statistics (Exercises)

3: Probability Topics
Probability theory is concerned with probability, the analysis of random phenomena. The central objects of probability theory are random variables, stochastic processes, and events: mathematical abstractions of non-deterministic events or measured quantities that may either be single occurrences or evolve over time in an apparently random fashion.
3.1: Introduction
3.2: Terminology
3.3: Independent and Mutually Exclusive Events
3.4: Two Basic Rules of Probability
3.5: Contingency Tables
3.6: Tree and Venn Diagrams
3.7: Probability Topics (Worksheet)
3.E: Probability Topics (Exercises)

4: Discrete Random Variables
4.1: Prelude to Discrete Random Variables
4.2: Probability Distribution Function (PDF) for a Discrete Random Variable
4.3: Mean or Expected Value and Standard Deviation
4.4: Binomial Distribution
4.5: Discrete Distribution (Playing Card Experiment)
4.6: Discrete Distribution (Lucky Dice Experiment)
4.E: Discrete Random Variables (Exercises)

5: Continuous Random Variables
5.1: Introduction
5.2: Continuous Probability Functions
5.3: The Uniform Distribution
5.4: Continuous Distribution (Worksheet)
5.E: Continuous Random Variables (Exercises)
5.E: Exercises

6: The Normal Distribution
In this chapter, you will study the normal distribution, the standard normal distribution, and applications associated with them. The normal distribution has two parameters (two numerical descriptive measures), the mean ( μμ ) and the standard deviation ( σσ ).
6.1: Prelude to The Normal Distribution
6.2: The Standard Normal Distribution
6.1E: The Standard Normal Distribution (Exercises)
6.3: Using the Normal Distribution
6.4: Normal Distribution - Lap Times (Worksheet)
6.5: Normal Distribution - Pinkie Length (Worksheet)
6.E: The Normal Distribution (Exercises)

7: The Central Limit Theorem
In a population whose distribution may be known or unknown, if the size (n) of samples is sufficiently large, the distribution of the sample means will be approximately normal. The mean of the sample means will equal the population mean. The standard deviation of the distribution of the sample means, called the standard error of the mean, is equal to the population standard deviation divided by the square root of the sample size (n).
7.1: Prelude to the Central Limit Theorem
7.2: The Central Limit Theorem for Sample Means (Averages)
7.2E: The Central Limit Theorem for Sample Means (Exercises)
7.3: The Central Limit Theorem for Sums
7.4: Using the Central Limit Theorem
7.4E: Using the Central Limit Theorem (Exercises)
7.5: Central Limit Theorem - Pocket Change (Worksheet)
7.6: Central Limit Theorem - Cookie Recipes (Worksheet)
7.E: The Central Limit Theorem (Exercises)

8: Confidence Intervals
In this chapter, you will learn to construct and interpret confidence intervals. You will also learn a new distribution, the Student's-t, and how it is used with these intervals. Throughout the chapter, it is important to keep in mind that the confidence interval is a random variable. It is the population parameter that is fixed.
8.1: Prelude to Confidence Intervals
8.2: A Single Population Mean using the Normal Distribution
8.2E: A Single Population Mean using the Normal Distribution (Exercises)
8.3: A Single Population Mean using the Student t-Distribution
8.4: A Population Proportion
8.5: Confidence Interval - Home Costs (Worksheet)
8.6: Confidence Interval -Place of Birth (Worksheet)
8.7: Confidence Interval -Women's Heights (Worksheet)
8.E: Confidence Intervals (Exercises)
8.S: Confidence Intervals (Summary)

9: Hypothesis Testing with One Sample
9.1: Prelude to Hypothesis Testing
9.2: Null and Alternative Hypotheses
9.1E: Null and Alternative Hypotheses (Exercises)
9.3: Outcomes and the Type I and Type II Errors
9.2E: Outcomes and the Type I and Type II Errors (Exercises)
9.4: Distribution Needed for Hypothesis Testing
9.3E: Distribution Needed for Hypothesis Testing (Exercises)
9.5: Rare Events, the Sample, Decision and Conclusion
9.4E: Rare Events, the Sample, Decision and Conclusion (Exercises)
9.6: Additional Information and Full Hypothesis Test Examples
9.7: Hypothesis Testing of a Single Mean and Single Proportion (Worksheet)
9.E: Hypothesis Testing with One Sample (Exercises)

10: Hypothesis Testing with Two Samples
You have learned to conduct hypothesis tests on single means and single proportions. You will expand upon that in this chapter. You will compare two means or two proportions to each other. To compare two means or two proportions, you work with two groups. The groups are classified either as independent or matched pairs.
10.1: Prelude to Hypothesis Testing with Two Samples
10.2: Two Population Means with Unknown Standard Deviations
10.3: Two Population Means with Known Standard Deviations
10.4: Comparing Two Independent Population Proportions
10.5: Matched or Paired Samples
10.6: Hypothesis Testing for Two Means and Two Proportions (Worksheet)
10.E: Hypothesis Testing with Two Samples (Exercises)

11: The Chi-Square Distribution
11.1: Prelude to The Chi-Square Distribution
11.2: Facts About the Chi-Square Distribution
11.3: Goodness-of-Fit Test
11.4: Test of Independence
11.5: Test for Homogeneity
11.6: Comparison of the Chi-Square Tests
11.7: Test of a Single Variance (Not Included in the Course)
11.8: Lab 1: Chi-Square Goodness-of-Fit (Worksheet)
11.9: Lab 2: Chi-Square Test of Independence (Worksheet)
11.E: The Chi-Square Distribution (Exercises)

12: Linear Regression and Correlation
Regression analysis is a statistical process for estimating the relationships among variables and includes many techniques for modeling and analyzing several variables. When the focus is on the relationship between a dependent variable and one or more independent variables.
12.1: Prelude to Linear Regression and Correlation
12.2: Linear Equations
12.2E: Linear Equations (Exercises)
12.3: Scatter Plots
12.3E: Scatter Plots (Exercises)
12.4: The Regression Equation
12.4E: The Regression Equation (Exercise)
12.5: Testing the Significance of the Correlation Coefficient
12.5E: Testing the Significance of the Correlation Coefficient (Exercises)
12.6: Prediction
12.6E: Prediction (Exercises)
12.7: Outliers
12.7E: Outliers (Exercises)
12.8: Regression - Distance from School (Worksheet)
12.9: Regression - Textbook Cost (Worksheet)
12.10: Regression - Fuel Efficiency (Worksheet)
12.E: Linear Regression and Correlation (Exercises)

13: F Distribution and One-Way ANOVA
For hypothesis tests comparing averages between more than two groups, statisticians have developed a method called "Analysis of Variance" (abbreviated ANOVA). In this chapter, you will study the simplest form of ANOVA called single factor or one-way ANOVA. You will also study the FF distribution, used for one-way ANOVA, and the test of two variances. This is just a very brief overview of one-way ANOVA.
13.1: Prelude to F Distribution and One-Way ANOVA
13.2: One-Way ANOVA
13.3: The F Distribution and the F-Ratio
13.4: Facts About the F Distribution
13.5: Lab: One-Way ANOVA
13.E: F Distribution and One-Way ANOVA (Exercises)

Subject:
Statistics and Probability
Material Type:
Full Course
Author:
Barbara Illowsky
Susan Dean
Date Added:
04/29/2020
Introductory Statistics with Randomization and Simulation First Edition
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CC BY-SA
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We hope readers will take away three ideas from this book in addition to forming a foundation of statistical thinking and methods.

(1) Statistics is an applied field with a wide range of practical applications.

(2) You don't have to be a math guru to learn from interesting, real data.

(3) Data are messy, and statistical tools are imperfect. However, when you understand the strengths and weaknesses of these tools, you can use them to learn interesting things about the world.

Reviews available here: https://open.umn.edu/opentextbooks/textbooks/introductory-statistics-with-randomization-and-simulation-first-edition

Subject:
Statistics and Probability
Material Type:
Textbook
Provider:
OpenIntro
Author:
Christopher Barr
David Diez
Mine Çetinkaya-Runde
Date Added:
04/24/2019
Lies, Damned Lies, or Statistics: How to Tell the Truth with Statistics
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Textbook for a one-semester, undergraduate statistics course. It was used for Math 156 at Colorado State University–Pueblo in the spring semester of 2017.

Table of Contents
Chapter 1. One-Variable Statistics: Basics
Chapter 2. Bi-variate Statistics: Basics
Chapter 3. Linear Regression
Chapter 4. Probability Theory
Chapter 5. Bringing Home the Data
Chapter 6. Basic Inferences

Subject:
Statistics and Probability
Material Type:
Textbook
Author:
Jonathan A. Poritz
Date Added:
06/23/2020
Mathematical Statistics, Spring 2016
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CC BY-NC-SA
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This course provides students with decision theory, estimation, confidence intervals, and hypothesis testing. It introduces large sample theory, asymptotic efficiency of estimates, exponential families, and sequential analysis.

Subject:
Statistics and Probability
Material Type:
Full Course
Provider:
M.I.T.
Provider Set:
M.I.T. OpenCourseWare
Author:
Peter Kempthorne
Date Added:
01/01/2016
Models, Data and Inference for Socio-Technical Systems, Spring 2007
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In this class, students use data and systems knowledge to build models of complex socio-technical systems for improved system design and decision-making. Students will enhance their model-building skills, through review and extension of functions of random variables, Poisson processes, and Markov processes; move from applied probability to statistics via Chi-squared t and f tests, derived as functions of random variables; and review classical statistics, hypothesis tests, regression, correlation and causation, simple data mining techniques, and Bayesian vs. classical statistics. A class project is required.

Subject:
Statistics and Probability
Material Type:
Full Course
Provider:
M.I.T.
Provider Set:
M.I.T. OpenCourseWare
Author:
Frey, Daniel
Date Added:
01/01/2007
More inference for linear regression
Conditional Remix & Share Permitted
CC BY-SA
Rating

This supplemental material is an online resource of OpenIntro Statistics, a textbook available for free in PDF at openintro.org and in paperback for about $10 at amazon.com.

Subject:
Mathematics
Statistics and Probability
Material Type:
Reading
Provider:
OpenIntro
Author:
Emiliano Vega
Ralf Youtz
Date Added:
04/25/2019