Students who complete this course will understand fundamentals of probability and study design including statistical significance, categorical data and contingency tables, random sampling, the Bootstrap, confidence intervals and more. You will also learn basics of inference and association including confidence intervals for proportions, correlation and simple regression, multiple regression, and using regression models to make predictions.
- Specify the design of a basic randomized controlled study
- Conduct computer resampling simulations, including the bootstrap and permutation test, to model the effects of chance
- Conduct A-B tests (2-sample comparisons) and test the results for statistical significance
- Measure correlation
- Use regression for prediction and explanation, and assess the model
- Explain the use of k-nearest-neighbor methods for predicting a binary outcome
Who Should Take This Course
Anyone who needs a basic statistics course for refreshing their memory of a previous course taken, or who need a university-level statistics course for academic credit.
Ms. Anuja Kulkarni has managed and taught over 125 online course sessions and more than 1000 students as an Assistant Teacher at The Institute for Statistics Education. She holds a Masters’ degree in Statistics from Kolhapur University, India, where she also taught undergraduate statistics. Ms. Kulkarni teaches Statistics, Optimization Methods and Predictive Analytics and assists in several other course topics here for over six years. In all, her passion is leading new students into the fascinating and practical world of statistics through the introductory statistics course series at The Institute.
Study Design, Statistical Significance
- Intro, Study Design
- Measures of Central Location and Variability
- Data Format
- Null Hypothesis
- Normal Distribution
Categorical Data, Contingency Tables
- Categorical Data
- Graphical Exploration
- Simple Probability
- Normal Distribution again
- 2-Way (Contingency) Tables
- Conditional Probability
More Probability, Random Sampling, The Bootstrap
- Bayes Rule
- Random Sampling
- Point Estimates
- Confidence Intervals
- Formula Counterparts
- Standard Error
- Beyond Random Sampling
Confidence Intervals for Proportions; 2-Sample Comparisons
- CI for a proportion
- The language of hypothesis testing
- A-B tests (2-group comparisons)
- Bandit Algorithms (briefly)
Correlation and Simple (1-variable) Regression
- Correlation coefficient
- Significance testing for correlation
- Fitting a regression line by hand
- Least squares fit
- Using the regression equation
- Explain or predict?
- Multiple predictor variables
- Assessing the regression model
- Goodness-of-fit (R-squared)
- Interpreting the coefficients
- RMSE (root mean squared error)
Prediction; K-Nearest Neighbors
- Using the regression model to make predictions
- Using a hold-out sample
- Assessing model performance
- K-nearest neighbors
The only mathematics you need is arithmetic.
This course requires the use of software. Please read the “Software” section below under “Additional Course Information.”
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Organization of Course
The course is comprised of two parts:
Part 1: Statistics 1 – Probability and Study Design (4 weeks)
Part 2: Statistics 2 – Inference and Association (4 weeks)
This course takes place online at the Institute for 8 weeks. During each course week, you participate at times of your own choosing – there are no set times when you must be online. Course participants will be given access to a private discussion board. In class discussions led by the instructor, you can post questions, seek clarification, and interact with your fellow students and the instructor.
At the beginning of each week, you receive the relevant material, in addition to answers to exercises from the previous session. During the week, you are expected to go over the course materials, work through exercises, and submit answers. Discussion among participants is encouraged. The instructor will provide answers and comments, and at the end of the week, you will receive individual feedback on your homework answers.
This is an 8-week course requiring 10-15 hours per week of review and study, at times of your choosing.
Homework in this course consists of short response exercises; the use of software is required for some exercises.
All needed course material will also be provided electronically as part of the course. The course is based on the book Introductory Statistics and Analytics: A Resampling Perspective by Peter Bruce, (2014, Wiley). It does not synchronize exactly with the course material, which has updates, but is a useful parallel reference if you want to have a printed book.
In this course, software is needed for statistical analysis and simple resampling/simulation operations. We recommend one of these three options:
- Regular Excel (not Excel Starter) and Resampling Stats for Excel (must have Windows)
- StatCrunch (Windows or Mac OS)
Excel: you will need to have some facility with using formulas in Excel.
Resampling Stats for Excel: this is a commercial add-in for Excel, designed as a practitioner’s tool for doing resampling simulations. A free license is available to all course participants, while they are enrolled in the statistics.com sequence of introductory statistics courses. Runs only on Windows. Enrolled students will be given access to a free 1-year trial of Resampling Stats through the software download link on the main Stats course webpage. You can also visit the Resampling Stats website and download the 1-year trial here.
StatCrunch: this is a very affordable web-based statistical software program, which also has simulation and resampling capabilities. Runs over the web, so can be used with both Windows and Mac. Resampling is not as intuitive as with Box Sampler and Resampling Stats for Excel. Learn more at www.statcrunch.com.
NOTE for StatCrunch Users: On all platforms, we recommend that you use the New version of StatCrunch. All examples in the textbook supplement are based on the New version of StatCrunch.
R: R is a powerful opensource statistical scripting language that is widely recognized as an industry standard. You will need to have familiarity with R and RStudio prior to taking the Statistics 1, 2 or 3 courses if you choose to use R as your software package. Comprehensive supplemental materials are available for R users. You can learn more about R here and RStudio here.
Python: Python is a language long used in computer science that has recently become quite popular in data science. You will need to have familiarity with Python prior to taking the Statistics 1, 2 or 3 courses if you choose to use Python as your software package. Comprehensive supplemental materials and support are available for Python users. We recommend the use of Jupyter notebooks and the Anaconda installation package.
Options for Credit and Recognition
ACE CREDIT | Academic Credit
This course has been evaluated by the American Council on Education (ACE) and is recommended for the lower division baccalaureate degree, 3 semester hours in statistics. Please note that the decision to accept specific credit recommendations is up to the academic institution accepting the credit.
Required Exams for Academic Credit via ACE CREDIT
Those seeking ACE Credit, and certificate candidates needing to satisfy their introductory statistics requirement, must pass an online exam to receive credit in either instance.
ACE has evaluated and recommended academic credit of 3.00 Semester Hours in Statistics or Mathematics for Introduction to Statistics by taking this course 2. ACE credit recommendation requires marks of 70% or better on the two courses combined, plus passing an online proctored final online exam scheduled at the end of the course.
While each institution makes its own decisions about whether to grant credit and how much to grant, most U.S. higher education institutions participate in the American Council on Education’s (ACE) credit recommendation service.
Literacy, Accessibility, and Dyslexia
At Statistics.com, we aim to provide a learning environment suitable for everyone. To help you get the most out of your learning experience, we have researched and tested several assistance tools. For students with dyslexia, colorblindness, or reading difficulties, we recommend the following web browser add-ons and extensions:
- Color Enhancer (for colorblindness)
- HelperBird (for colorblindness, dyslexia, and reading difficulties)
- Mobile Dyslexic
- Color Vision Simulation (native accessibility feature)
- Other native accessibility features instructions