Introductory Statistics
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- 3104
- Book: Introductory Statistics (OpenStax)
- 1: Sampling and Data
- 1.0: Introduction
- 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
- 1.5: Data Collection Experiment (Worksheet)
- 1.6: Sampling Experiment (Worksheet)
- 1.E: Sampling and Data (Exercises)
- 2: Descriptive Statistics
- 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
- 2.5: 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
- 4: Discrete Random Variables
- 4.0: Prelude to Discrete Random Variables
- 4.1: Probability Distribution Function (PDF) for a Discrete Random Variable
- 4.2: Mean or Expected Value and Standard Deviation
- 4.3: Binomial Distribution
- 4.4: Geometric Distribution
- 4.5: Hypergeometric Distribution
- 4.6: Poisson Distribution
- 4.8: Discrete Distribution (Playing Card Experiment)
- 4.9: Discrete Distribution (Lucky Dice Experiment)
- 4.E: Discrete Random Variables (Exercises)
- 5: Continuous Random Variables
- 6: The Normal Distribution
- 7: The Central Limit Theorem
- 7.1: Prelude to the Central Limit Theorem
- 7.2: The Central Limit Theorem for Sample Means (Averages)
- 7.3: The Central Limit Theorem for Sums
- 7.4: Using the Central Limit Theorem
- 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
- 8.1: Prelude to Confidence Intervals
- 8.2: A Single Population Mean using the Normal Distribution
- 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
- 9.0: Prelude to Hypothesis Testing
- 9.1: Null and Alternative Hypotheses
- 9.2: Outcomes and the Type I and Type II Errors
- 9.3: Distribution Needed for Hypothesis Testing
- 9.4: Rare Events, the Sample, Decision and Conclusion
- 9.5: Additional Information and Full Hypothesis Test Examples
- 9.6: Hypothesis Testing of a Single Mean and Single Proportion (Worksheet)
- 9.E: Hypothesis Testing with One Sample (Exercises)
- 10: Hypothesis Testing with Two Samples
- 10.0: Prelude to Hypothesis Testing with Two Samples
- 10.1: Two Population Means with Unknown Standard Deviations
- 10.2: Two Population Means with Known Standard Deviations
- 10.3: Comparing Two Independent Population Proportions
- 10.4: Matched or Paired Samples
- 10.5: 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
- 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
- 12.1: Prelude to Linear Regression and Correlation
- 12.2: Linear Equations
- 12.3: Scatter Plots
- 12.4: The Regression Equation
- 12.5: Testing the Significance of the Correlation Coefficient
- 12.6: Prediction
- 12.7: Outliers
- 12.8: Regression (Distance from School)
- 12.9: Regression (Textbook Cost)
- 12.10: Regression (Fuel Efficiency)
- 12.E: Linear Regression and Correlation (Exercises)
- 13: F Distribution and One-Way ANOVA
- 1: Sampling and Data
- Book: Introductory Statistics (Shafer and Zhang)
- 1: Introduction to Statistics
- 2: Descriptive Statistics
- 3: Basic Concepts of Probability
- 4: Discrete Random Variables
- 5: Continuous Random Variables
- 6: Sampling Distributions
- 7: Estimation
- 8: Testing Hypotheses
- 9: Two-Sample Problems
- 9.1: Comparison of Two Population Means: Large, Independent Samples
- 9.2: Comparison of Two Population Means - Small, Independent Samples
- 9.3: Comparison of Two Population Means - Paired Samples
- 9.4: Comparison of Two Population Proportions
- 9.5: Sample Size Considerations
- 9.E: Two-Sample Problems (Exercises)
- 10: Correlation & Regression
- 10.1: Linear Relationships Between Variables
- 10.2: The Linear Correlation Coefficient
- 10.3: Modelling Linear Relationships with Randomness Present
- 10.4: The Least Squares Regression Line
- 10.5: Statistical Inferences About βₗ
- 10.6: The Coefficient of Determination
- 10.7: Estimation and Prediction
- 10.8: A Complete Example
- 10.9: Formula List
- 10.E: Correlation and Regression (Exercises)
- 11: Chi-Square Tests and F-Tests
- Book: Introductory Statistics (Lane)
- 1: Introduction to Statistics
- 1.1: What are Statistics?
- 1.2: Importance of Statistics
- 1.3: Descriptive Statistics
- 1.4: Inferential Statistics
- 1.5: Sampling Demonstration
- 1.6: Variables
- 1.7: Percentiles
- 1.8: Levels of Measurement
- 1.9: Measurements
- 1.10: Distributions
- 1.11: Summation Notation
- 1.12: Linear Transformations
- 1.13: Logarithms
- 1.14: Statistical Literacy
- 1.E: Introduction to Statistics (Exercises)
- 2: Graphing Distributions
- 3: Summarizing Distributions
- 3.1: Central Tendency
- 3.2: What is Central Tendency
- 3.3: Measures of Central Tendency
- 3.4: Balance Scale Simulation
- 3.5: Absolute Differences Simulation
- 3.6: Squared Differences Simulation
- 3.7: Median and Mean
- 3.8: Mean and Median Demo
- 3.9: Additional Measures
- 3.10: Comparing Measures
- 3.11: Variability
- 3.12: Measures of Variability
- 3.13: Variability Demo
- 3.14: Estimating Variance Simulation
- 3.15: Shapes of Distributions
- 3.16: Comparing Distributions Demo
- 3.17: Effects of Linear Transformations
- 3.18: Variance Sum Law I - Uncorrelated Variables
- 3.19: Statistical Literacy
- 3.E: Summarizing Distributions (Exercises)
- 4: Describing Bivariate Data
- 5: Probability
- 5.1: The Concept of "Probability"
- 5.2: Basic Concepts of Probability
- 5.3: Conditional Probability Demonstration
- 5.4: Gambler's Fallacy
- 5.5: Permutations and Combinations
- 5.6: Birthday Demo
- 5.7: Binomial Distribution
- 5.8: Binomial Demonstration
- 5.9: Poisson Distribution
- 5.10: Multinomial Distribution
- 5.11: Hypergeometric Distribution
- 5.12: Base Rates
- 5.13: Bayes Demo
- 5.14: Monty Hall Problem
- 5.15: Statistical Literacy
- 5.E: Probability (Exercises)
- 6: Research Design
- 7: Normal Distribution
- 7.1: Introduction to Normal Distributions
- 7.2: History of the Normal Distribution
- 7.3: Areas Under Normal Distributions
- 7.4: Varieties Demonstration
- 7.5: Standard Normal Distribution
- 7.6: Normal Approximation to the Binomial
- 7.7: Normal Approximation Demonstration
- 7.8: Statistical Literacy
- 7.E: Normal Distribution (Exercises)
- 8: Advanced Graphs
- 9: Sampling Distributions
- 9.1: Introduction to Sampling Distributions
- 9.2: Basic Demo
- 9.3: Sample Size Demo
- 9.4: Central Limit Theorem Demonstration
- 9.5: Sampling Distribution of the Mean
- 9.6: Difference Between Means
- 9.7: Sampling Distribution of Pearson's r
- 9.8: Sampling Distribution of p
- 9.9: Statistical Literacy
- 9.E: Sampling Distributions (Exercises)
- 10: Estimation
- 10.1: Introduction to Estimation
- 10.2: Degrees of Freedom
- 10.3: Characteristics of Estimators
- 10.4: Bias and Variability Simulation
- 10.5: Confidence Intervals
- 10.6: Confidence Intervals Intro
- 10.7: Confidence Interval for Mean
- 10.8: t Distribution
- 10.9: Confidence Interval Simulation
- 10.10: Difference between Means
- 10.11: Correlation
- 10.12: Proportion
- 10.13: Statistical Literacy
- 10.E: Estimation (Exercises)
- 11: Logic of Hypothesis Testing
- 11.1: Introduction to Hypothesis Testing
- 11.2: Significance Testing
- 11.3: Type I and II Errors
- 11.4: One- and Two-Tailed Tests
- 11.5: Significant Results
- 11.6: Non-Significant Results
- 11.7: Steps in Hypothesis Testing
- 11.8: Significance Testing and Confidence Intervals
- 11.9: Misconceptions of Hypothesis Testing
- 11.10: Statistical Literacy
- 11.E: Logic of Hypothesis Testing (Exercises)
- 12: Tests of Means
- 12.1: Testing a Single Mean
- 12.2: t Distribution Demo
- 12.3: Difference between Two Means
- 12.4: Robustness Simulation
- 12.5: Pairwise Comparisons
- 12.6: Specific Comparisons
- 12.7: Correlated Pairs
- 12.8: Correlated t Simulation
- 12.9: Specific Comparisons (Correlated Observations)
- 12.10: Pairwise (Correlated)
- 12.11: Statistical Literacy
- 12.E: Tests of Means (Exercises)
- 13: Power
- 14: Regression
- 14.1: Introduction to Linear Regression
- 14.2: Linear Fit Demo
- 14.3: Partitioning Sums of Squares
- 14.4: Standard Error of the Estimate
- 14.5: Inferential Statistics for b and r
- 14.6: Influential Observations
- 14.7: Regression Toward the Mean
- 14.8: Introduction to Multiple Regression
- 14.9: Statistical Literacy
- 14.E: Regression (Exercises)
- 15: Analysis of Variance
- 15.1: Introduction to ANOVA
- 15.2: ANOVA Designs
- 15.3: One-Factor ANOVA
- 15.4: One-Way Demo
- 15.5: Multi-Factor Between-Subjects
- 15.6: Unequal Sample Sizes
- 15.7: Tests Supplementing
- 15.8: Within-Subjects
- 15.9: Power of Within-Subjects Designs Demo
- 15.10: Statistical Literacy
- 15.E: Analysis of Variance (Exercises)
- 16: Transformations
- 17: Chi Square
- 18: Distribution-Free Tests
- 18.1: Benefits of Distribution Free Tests
- 18.2: Randomization Tests - Two Conditions
- 18.3: Randomization Tests - Two or More Conditions
- 18.4: Randomization Association
- 18.5: Fisher's Exact Test
- 18.6: Rank Randomization Two Conditions
- 18.7: Rank Randomization Two or More Conditions
- 18.8: Rank Randomization for Association
- 18.9: Statistical Literacy Standard
- 18 E: Distribution Free Tests (Exercises)
- 19: Effect Size
- 20: Case Studies
- 20.1: Angry Moods
- 20.2: Flatulence
- 20.3: Physicians Reactions
- 20.4: Teacher Ratings
- 20.5: Diet and Health
- 20.6: Smiles and Leniency
- 20.7: Animal Research
- 20.8: ADHD Treatment
- 20.9: Weapons and Aggression
- 20.10: SAT and College GPA
- 20.11: Stereograms
- 20.12: Driving
- 20.13: Stroop Interference
- 20.14: TV Violence
- 20.15: Obesity and Bias
- 20.16: Shaking and Stirring Martinis
- 20.17: Adolescent Lifestyle Choices
- 20.18: Chocolate and Body Weight
- 20.19: Bedroom TV and Hispanic Children
- 20.20: Weight and Sleep Apnea
- 20.21: Misusing SEM
- 20.22: School Gardens and Vegetable Consumption
- 20.23: TV and Hypertension
- 20.24: Dietary Supplements
- 20.25: Young People and Binge Drinking
- 20.26: Sugar Consumption in the US Diet
- 20.27: Nutrition Information Sources and Older Adults
- 20.28: Mind Set - Exercise and the Placebo Effect
- 20.29: Predicting Present and Future Affect
- 20.30: Exercise and Memory
- 20.31: Parental Recognition of Child Obesity
- 20.32: Educational Attainment and Racial, Ethnic, and Gender Disparity
- 21: Calculators
- 22: Glossary
- 1: Introduction to Statistics
- Book: OpenIntro Statistics (Diez et al).
- 1: Introduction to Data
- 1.0: Prelude to Introduction to Data
- 1.1: Case Study: Using Stents to Prevent Strokes
- 1.2: Data Basics
- 1.3: Overview of Data Collection Principles
- 1.4: Observational Studies and Sampling Strategies
- 1.5: Experiments
- 1.6: Examining Numerical Data
- 1.7: Considering Categorical Data
- 1.8: Case Study: Gender Discrimination (Special Topic)
- 1.E: Introduction to Data (Exercises)
- 2: Probability
- 3: Distributions of Random Variables
- 4: Foundations for Inference
- 5: Inference for Numerical Data
- 6: Inference for Categorical Data
- 6.1: Inference for a Single Proportion
- 6.2: Difference of Two Proportions
- 6.3: Testing for Goodness of Fit using Chi-Square (Special Topic)
- 6.4: Testing for Independence in Two-Way Tables (Special Topic)
- 6.5: Small Sample Hypothesis Testing for a Proportion (Special Topic)
- 6.6: Randomization Test (Special Topic)
- 6.7: Exercises
- 7: Introduction to Linear Regression
- 8: Multiple and Logistic Regression
- 1: Introduction to Data
- Book: Visual Statistics Use R! (Shipunov)
- Forward
- 1: Data
- 2: How to process the data
- 3: Types of Data
- 3.1: Degrees, hours and kilometers: measurement data
- 3.2: Grades and t-shirts: ranked data
- 3.3: Colors, Names and Sexes - Nominal Data
- 3.4: Fractions, counts and ranks: secondary data
- 3.5: Missing data
- 3.6: Outliers, and how to find them
- 3.7: Changing data: basics of transformations
- 3.8: Inside R
- 3.9: Answers to exercises
- 4: One-Dimensional Data
- 5: Two-Dimensional Data - Differences
- 6: Two-dimensional data: models
- 7: Multidimensional Data - Analysis of Structure
- Appendix A: Example of R session
- Appendix B: Ten Years Later, or use R script
- Appendix C: R fragments
- Appendix D: Most essential R commands
- Appendix E: The short R glossary
- References and reference cards
Mon, 25 Jun 2018 21:21:17 GMT
Introductory Statistics
These introductory statistics texts are intended for students in a wide variety of areas of study. Topics discussed include displaying and describing data, the normal curve, regression, probability, statistical inference, confidence intervals, and hypothesis tests with applications in the real world.