This website is an interactive educational application developed to simulate and visualize various statistical concepts:

Law of Large Numbers
Central Limit Theorem
Confidence Intervals
Hypothesis Testing
ANOVA
Joint Distributions
Least Squares
Sample Distribution of OLS Estimators
The OLS Estimators are Consistent
Omitted Variable Bias
Multiple Regression

Project of Professor Tanya Byker and Professor Amanda Gregg at Middlebury College, with research assistants Kevin Serrao, Class of 2018, Dylan Mortimer, Class of 2019, Ammar Almahdy, Class of 2020, Jacqueline Palacios, Class of 2020, Siyuan Niu, Class of 2021, David Gikoshvili, Class of 2021, and Ethan Saxenian, Class of 2022.

This open course for Elementary Statistics was created through a Round Ten Textbook Transformation Grant:

https://oer.galileo.usg.edu/mathematics-collections/39/

The open course contains ancillary materials for OpenStax Introductory Statistics:

https://openstax.org/details/books/introductory-statistics

Included in the course are introductions to each lesson, lecture slides, videos, and problem questions. Topics include:

Types of Data
Sampling Techniques
Qualitative Data
Frequency Distributions
Descriptive Statistics
Variation and Position
Confidence Intervals
Hypothesis Testing
Chi-Square Goodness of Fit
Linear Regression
Variance ANOVA

A focus on novel, confirmatory, and statistically significant results leads to substantial bias in the scientific literature. One type of bias, known as “p-hacking,” occurs when researchers collect or select data or statistical analyses until nonsignificant results become significant. Here, we use text-mining to demonstrate that p-hacking is widespread throughout science. We then illustrate how one can test for p-hacking when performing a meta-analysis and show that, while p-hacking is probably common, its effect seems to be weak relative to the real effect sizes being measured. This result suggests that p-hacking probably does not drastically alter scientific consensuses drawn from meta-analyses.

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.

Statistical thinking is a way of understanding a complex world by describing it in relatively simple terms that nonetheless capture essential aspects of its structure, and that also provide us some idea of how uncertain we are about our knowledge. The foundations of statistical thinking come primarily from mathematics and statistics, but also from computer science, psychology, and other fields of study.

This 19-minute video lesson gives an example of the Confidence Interval. [Statistics playlist: Lesson 45 of 85]

This 12-minute video lesson looks at the T-Statistic Confidence Interval (for small sample sizes). [Statistics playlist: Lesson 52 of 85]

This course is a broad treatment of statistics, concentrating on specific statistical techniques used in science and industry. Topics include: hypothesis testing and estimation, confidence intervals, chi-square tests, nonparametric statistics, analysis of variance, regression, correlation, decision theory, and Bayesian statistics.

This course offers a broad treatment of statistics, concentrating on specific statistical techniques used in science and industry. Topics include: hypothesis testing and estimation, confidence intervals, chi-square tests, nonparametric statistics, analysis of variance, regression, and correlation.
OCW offers an earlier version of this course, from Fall 2003. This newer version focuses less on estimation theory and more on multiple linear regression models. In addition, a number of Matlab examples are included here.

Provides students with the basic tools for analyzing experimental data, properly interpreting statistical reports in the literature, and reasoning under uncertain situations. Topics organized around three key theories: Probability, statistical, and the linear model. Probability theory covers axioms of probability, discrete and continuous probability models, law of large numbers, and the Central Limit Theorem. Statistical theory covers estimation, likelihood theory, Bayesian methods, bootstrap and other Monte Carlo methods, as well as hypothesis testing, confidence intervals, elementary design of experiments principles and goodness-of-fit. The linear model theory covers the simple regression model and the analysis of variance. Places equal emphasis on theory, data analyses, and simulation studies.

Activity introduces students to the concept of sampling distributions and point estimates, and to how the accuracy of point estimates are affected by sample size.