Description
Statistical inference is the process of drawing conclusions about populations or scientific truths from data. There are many modes of performing inference including statistical modeling, data oriented strategies and explicit use of designs and randomization in analyses. Furthermore, there are broad theories (frequentists, Bayesian, likelihood, design based, …) and numerous complexities (missing data, observed and unobserved confounding, biases) for performing inference. A practitioner can often be left in a debilitating maze of techniques, philosophies and nuance. This course presents the fundamentals of inference in a practical approach for getting things done. After taking this course, students will understand the broad directions of statistical inference and use this information for making informed choices in analyzing data.
Knowledge
- Understand the process of drawing conclusions about populations or scientific truths from data
- Describe variability, distributions, limits, and confidence intervals
- Use p-values, confidence intervals, and permutation tests
- Make informed data analysis decisions
Outline
- Week 1: Probability & Expected Values
- Introductory video
- 02 01 Introduction to probability
- 02 02 Probability mass functions
- 02 03 Probability density functions
- 03 01 Conditional Probability
- 03 02 Bayes' rule
- 03 03 Independence
- 04 01 Expected values
- 04 02 Expected values, simple examples
- 04 03 Expected values for PDFs
- Welcome to Statistical Inference
- Some introductory comments
- Pre-Course Survey
- Syllabus
- Course Book: Statistical Inference for Data Science
- Data Science Specialization Community Site
- Homework Problems
- Probability
- Conditional probability
- Expected values
- Practical R Exercises in swirl 1
- Quiz 1
- Week 2: Variability, Distribution, & Asymptotics
- 05 01 Introduction to variability
- 05 02 Variance simulation examples
- 05 03 Standard error of the mean
- 05 04 Variance data example
- 06 01 Binomial distrubtion
- 06 02 Normal distribution
- 06 03 Poisson
- 07 01 Asymptotics and LLN
- 07 02 Asymptotics and the CLT
- 07 03 Asymptotics and confidence intervals
- Variability
- Distributions
- Asymptotics
- Practical R Exercises in swirl Part 2
- Quiz 2
- Week: Intervals, Testing, & Pvalues
- 08 01 T confidence intervals
- 08 02 T confidence intervals example
- 08 03 Independent group T intervals
- 08 04 A note on unequal variance
- 09 01 Hypothesis testing
- 09 02 Example of choosing a rejection region
- 09 03 T tests
- 09 04 Two group testing
- 10 01 Pvalues
- 10 02 Pvalue further examples
- Just enough knitr to do the project
- Confidence intervals
- Hypothesis testing
- P-values
- Knitr
- Practical R Exercises in swirl Part 3
- Quiz 3
- Week 4: Power, Bootstrapping, & Permutation Tests
- 11 01 Power
- 11 02 Calculating Power
- 11 03 Notes on power
- 11 04 T test power
- 12 01 Multiple Comparisons
- 13 01 Bootstrapping
- 13 02 Bootstrapping example
- 13 03 Notes on the bootstrap
- 13 04 Permutation tests
- Power
- Resampling
- Practical R Exercises in swirl Part 4
- Post-Course Survey
- Quiz 4
Summary of User Reviews
Discover the fundamentals of statistical inference with this highly-rated course on Coursera. Students rave about the engaging lectures and practical exercises that help them understand complex concepts easily.Key Aspect Users Liked About This Course
The course is highly engaging and practical, making it easy to understand complex concepts.Pros from User Reviews
- Lectures are well-structured and easy to follow
- The course provides practical exercises to reinforce learning
- The instructor is knowledgeable and engaging
- Course materials are well-organized and easy to access
Cons from User Reviews
- Some of the exercises require a lot of time and effort
- The course may be too technical for beginners
- Some of the concepts may be difficult to understand without prior knowledge
- The course may be too focused on theory for some students
- The forum discussions can be overwhelming and hard to follow
Brian Caffo, PhD
4.2 Raiting
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