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Jennifer Bachner, PhD
This course focuses on how analysts can measure and describe the confidence they have in their findings. The course begins with an overview of the key probability rules and concepts that govern the calculation of uncertainty measures. We’ll then apply these ideas to variables (which are the building blocks of statistics) and their associated probability distributions. The second half of the course will delve into the computation and interpretation of uncertainty. We’ll discuss how to conduct a hypothesis test using both test statistics and confidence intervals. Finally, we’ll consider the role of hypothesis testing in a regression context, including what we can and cannot learn from the statistical significance of a coefficient. By the end of the course, you should be able to discuss statistical findings in probabilistic terms and interpret the uncertainty of a particular estimate.
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What's inside
Syllabus
Probability Theory
The Monty Hall problem is a classic brain teaser that highlights the often counterintuitive nature of probability. The problem is typically stated as follows: Suppose you're a contestant on a game show and asked to select one of three doors for your prize. Behind one door is a car and behind the other two doors are goats. You pick one door. The host, who knows what's behind each door, opens another, which has a goat. He then gives you the option to stick with your selected door or switch to the other closed door. What should you do? The answer is that, under these circumstances, you should always switch. There is a 2/3 chance of winning the car if you switch and a 1/3 chance of winning if you stick with your original selection. Most people, however, assume that there is only a 50/50 chance of winning if you switch. Hopefully this brain teaser, and content we cover in this module, will help you better approach probabilistic problems.
Read more
Syllabus
Probability Theory
The Monty Hall problem is a classic brain teaser that highlights the often counterintuitive nature of probability. The problem is typically stated as follows: Suppose you're a contestant on a game show and asked to select one of three doors for your prize. Behind one door is a car and behind the other two doors are goats. You pick one door. The host, who knows what's behind each door, opens another, which has a goat. He then gives you the option to stick with your selected door or switch to the other closed door. What should you do? The answer is that, under these circumstances, you should always switch. There is a 2/3 chance of winning the car if you switch and a 1/3 chance of winning if you stick with your original selection. Most people, however, assume that there is only a 50/50 chance of winning if you switch. Hopefully this brain teaser, and content we cover in this module, will help you better approach probabilistic problems.
Read more
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Read about what's good
what should give you pause and
possible dealbreakers
Focuses on hypothesis testing and confidence intervals, core skills for data science and research
Taught by Jennifer Bachner, PhD, recognized for work in uncertainty quantification
Examines the foundations of probability theory, crucial for understanding statistical models
Covers the basics of probability distributions, providing a solid foundation for further studies
May require prior knowledge in statistics for some learners
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Reviews summary
Understanding probability and statistical uncertainty
According to learners, "What are the Chances?" is a highly effective course for building a foundational understanding of probability and statistical uncertainty. Students frequently commend the instructor's clear explanations, which demystify complex concepts like the Monty Hall problem and probability distributions. The course is particularly lauded for its strong emphasis on conceptual understanding and the "why" behind statistical decisions, rather than just computation, proving highly practical for interpreting data in professional settings. However, some learners with more advanced backgrounds noted the pacing might feel slow and the depth superficial for those seeking rigorous mathematical detail. Recent reviews continue to praise its clarity and relevance.
Appreciated for highlighting limitations of statistical significance.
"I particularly appreciated the discussion on the limitations of statistical significance; it's so important for practical application."
"The part about not relying solely on statistical significance was a good take-away, but the examples could be more complex."
"I especially liked the focus on the practical implications of statistical findings and the critique of statistical significance."
Provides insights highly relevant for data interpretation in work.
"This course filled so many gaps in my understanding from previous stats courses. It's excellent for anyone needing to interpret data correctly, especially in policy-making or research."
"I now feel much more confident interpreting statistical results in my job. The module on regression uncertainty was particularly insightful and practical."
"This course is perfect for anyone in a data-adjacent role who needs to understand how to talk about findings responsibly."
Prioritizes intuition and interpretation over mere computation.
"It definitely helped me understand the 'why' behind certain statistical decisions, which is crucial for my work."
"I loved the practical examples and the emphasis on understanding uncertainty, not just calculating it."
"The strength lies in its emphasis on interpretation rather than just computation. This is very valuable for decision-makers."
Complex statistical concepts are made understandable.
"The instructor's explanations were incredibly clear, especially when tackling topics like the Monty Hall problem, which I always found confusing."
"Absolutely brilliant! The instructor makes complex concepts like probability distributions and regression uncertainty remarkably accessible."
"Highly recommend! This course demystified probability and uncertainty for me. The instructor is top-notch, breaking down complex ideas into manageable pieces."
Pacing is ideal for beginners but may feel slow for advanced learners.
"My only minor critique is that some parts felt a bit slow if you already had a decent grasp of introductory statistics, but for a true beginner, it's probably perfect."
"As someone with an intermediate background in data science, I was hoping for more rigorous mathematical detail or advanced applications. It's good for a conceptual overview, but don't expect to become a statistical expert."
"I struggled with this course. While the topics are important, I found the lectures dry and the examples too simple. It might be okay for a complete novice, but for others, it felt lacking."
Activities
Be better prepared
before
your course. Deepen your understanding
during
and
after
it. Supplement your coursework and achieve mastery of the topics covered
in What are the Chances? Probability and Uncertainty in Statistics with these
activities:
Review fundamentals of probability
Show steps
Ensure you have a good understanding of probability before starting the course to enhance comprehension.
Browse courses on
Probability
Show steps
-
Revisit the basic concepts of probability, including sample space, events, and probability distributions.
-
Practice solving probability problems involving conditional probability and Bayes' theorem.
-
Review key probability rules and their applications.
Read 'Statistical Methods for Psychology' by David C. Howell
Show steps
Supplement your learning with a comprehensive textbook on statistical methods.
View
Fundamental Statistics for the Behavioral...
on Amazon
Show steps
-
Obtain a copy of 'Statistical Methods for Psychology' by David C. Howell.
-
Read the chapters relevant to the course, focusing on chapters covering probability, confidence intervals, and hypothesis testing.
-
Take notes and highlight important concepts.
-
Complete the practice problems at the end of each chapter.
Create a visual representation of probability distributions
Show steps
Deepen your understanding of probability distributions by creating visual representations.
Browse courses on
Probability Distributions
Show steps
-
Choose a probability distribution to focus on, such as the normal distribution or binomial distribution.
-
Use a graphing tool or software to create a visual representation of the distribution, showing its shape, mean, and standard deviation.
-
Analyze the visual representation to identify key features and patterns of the distribution.
-
Present your visual representation and analysis to the class or in an online forum.
Four other activities
Expand to see all activities and additional details
Show all seven activities
Join a study group to discuss course concepts
Show steps
Engage with peers to reinforce your understanding and gain different perspectives.
Show steps
-
Find or create a study group with your classmates.
-
Meet regularly to discuss course materials, work through problems, and ask questions.
-
Actively participate in the study group, sharing your insights and asking for clarification.
Solve practice problems on confidence intervals
Show steps
Gain proficiency in calculating and interpreting confidence intervals.
Browse courses on
Confidence Intervals
Show steps
-
Work through practice problems involving the calculation of confidence intervals for means, proportions, and standard deviations.
-
Interpret the results of confidence intervals, including the level of confidence and the margin of error.
-
Apply confidence intervals to real-world scenarios, such as estimating population parameters or making inferences about data.
Attend a workshop on statistical significance
Show steps
Expand your understanding of statistical significance through a focused workshop.
Browse courses on
Statistical Significance
Show steps
-
Identify and attend a workshop or seminar focused on statistical significance and hypothesis testing.
-
Participate actively in the workshop, asking questions and engaging in discussions.
-
Apply the concepts learned in the workshop to your coursework and research.
Develop a statistical analysis plan for a hypothetical research study
Show steps
Apply your knowledge to a practical scenario by creating a statistical analysis plan.
Browse courses on
Statistical Analysis
Show steps
-
Choose a research question and define the variables to be studied.
-
Determine the appropriate statistical tests to be used based on the research question and data type.
-
Develop a detailed plan outlining the steps involved in data collection, analysis, and interpretation.
Review fundamentals of probability
Show steps
Ensure you have a good understanding of probability before starting the course to enhance comprehension.
Browse courses on
Probability
Show steps
Show steps
Show steps
- Revisit the basic concepts of probability, including sample space, events, and probability distributions.
- Practice solving probability problems involving conditional probability and Bayes' theorem.
- Review key probability rules and their applications.
Read 'Statistical Methods for Psychology' by David C. Howell
Show steps
Supplement your learning with a comprehensive textbook on statistical methods.
View
Fundamental Statistics for the Behavioral...
on Amazon
Show steps
Show steps
Show steps
- Obtain a copy of 'Statistical Methods for Psychology' by David C. Howell.
- Read the chapters relevant to the course, focusing on chapters covering probability, confidence intervals, and hypothesis testing.
- Take notes and highlight important concepts.
- Complete the practice problems at the end of each chapter.
Create a visual representation of probability distributions
Show steps
Deepen your understanding of probability distributions by creating visual representations.
Browse courses on
Probability Distributions
Show steps
Show steps
Show steps
- Choose a probability distribution to focus on, such as the normal distribution or binomial distribution.
- Use a graphing tool or software to create a visual representation of the distribution, showing its shape, mean, and standard deviation.
- Analyze the visual representation to identify key features and patterns of the distribution.
- Present your visual representation and analysis to the class or in an online forum.
Four other activities
Expand to see all activities and additional details
Show all seven activities
Join a study group to discuss course concepts
Show steps
Engage with peers to reinforce your understanding and gain different perspectives.
Show steps
Show steps
Show steps
- Find or create a study group with your classmates.
- Meet regularly to discuss course materials, work through problems, and ask questions.
- Actively participate in the study group, sharing your insights and asking for clarification.
Solve practice problems on confidence intervals
Show steps
Gain proficiency in calculating and interpreting confidence intervals.
Browse courses on
Confidence Intervals
Show steps
Show steps
Show steps
- Work through practice problems involving the calculation of confidence intervals for means, proportions, and standard deviations.
- Interpret the results of confidence intervals, including the level of confidence and the margin of error.
- Apply confidence intervals to real-world scenarios, such as estimating population parameters or making inferences about data.
Attend a workshop on statistical significance
Show steps
Expand your understanding of statistical significance through a focused workshop.
Browse courses on
Statistical Significance
Show steps
Show steps
Show steps
- Identify and attend a workshop or seminar focused on statistical significance and hypothesis testing.
- Participate actively in the workshop, asking questions and engaging in discussions.
- Apply the concepts learned in the workshop to your coursework and research.
Develop a statistical analysis plan for a hypothetical research study
Show steps
Apply your knowledge to a practical scenario by creating a statistical analysis plan.
Browse courses on
Statistical Analysis
Show steps
Show steps
Show steps
- Choose a research question and define the variables to be studied.
- Determine the appropriate statistical tests to be used based on the research question and data type.
- Develop a detailed plan outlining the steps involved in data collection, analysis, and interpretation.
Career center
Learners who complete What are the Chances? Probability and Uncertainty in Statistics will develop knowledge and skills
that may be useful to these careers:
Quantitative Analyst
Quantitative Analyst
A Quantitative Analyst develops and uses mathematical and statistical models to analyze financial data. This course may be useful for Quantitative Analysts, as it provides a solid foundation in probability and uncertainty, which are essential concepts for understanding and working with financial data. The course also covers topics such as confidence intervals and hypothesis testing, which are important for drawing conclusions from financial data.
Machine Learning Engineer
Machine Learning Engineer
A Machine Learning Engineer develops and uses machine learning models to solve problems. This course may be useful for Machine Learning Engineers, as it provides a solid foundation in probability and uncertainty, which are essential concepts for understanding and working with machine learning models. The course also covers topics such as confidence intervals and hypothesis testing, which are important for assessing the performance of machine learning models.
Actuary
Actuary
An Actuary analyzes and manages financial risks for insurance companies and other financial institutions. This course may be useful for Actuaries, as it provides a solid foundation in probability and uncertainty, which are essential concepts for understanding and managing financial risks. The course also covers topics such as confidence intervals and hypothesis testing, which are important for assessing the likelihood and impact of financial risks.
Data Scientist
Data Scientist
A Data Scientist collects, analyzes, and interprets data to help organizations make informed decisions. This course may be useful for Data Scientists, as it provides a solid foundation in probability and uncertainty, which are essential concepts for understanding and working with data. The course also covers topics such as confidence intervals and hypothesis testing, which are important for drawing conclusions from data.
Risk Manager
Risk Manager
A Risk Manager identifies, assesses, and manages risks to an organization. This course may be useful for Risk Managers, as it provides a solid foundation in probability and uncertainty, which are essential concepts for understanding and managing risks. The course also covers topics such as confidence intervals and hypothesis testing, which are important for assessing the likelihood and impact of risks.
Statistician
Statistician
A Statistician collects, analyzes, interprets, and presents data to help organizations make informed decisions. This course may be useful for Statisticians, as it provides a solid foundation in probability and uncertainty, which are essential concepts for understanding and working with data. The course also covers topics such as confidence intervals and hypothesis testing, which are important for drawing conclusions from data.
Researcher
Researcher
A Researcher conducts research to advance knowledge. This course may be useful for Researchers who work on data-driven research, as it provides a solid foundation in probability and uncertainty, which are essential concepts for understanding and working with data. The course also covers topics such as confidence intervals and hypothesis testing, which are important for drawing conclusions from data.
Market Researcher
Market Researcher
A Market Researcher conducts research to understand consumer behavior and market trends. This course may be useful for Market Researchers, as it provides a solid foundation in probability and uncertainty, which are essential concepts for understanding and working with data. The course also covers topics such as confidence intervals and hypothesis testing, which are important for drawing conclusions from data.
Financial Analyst
Financial Analyst
A Financial Analyst analyzes financial data to make investment recommendations. This course may be useful for Financial Analysts, as it provides a solid foundation in probability and uncertainty, which are essential concepts for understanding and working with financial data. The course also covers topics such as confidence intervals and hypothesis testing, which are important for drawing conclusions from financial data.
Data Analyst
Data Analyst
A Data Analyst collects, analyzes, interprets, and presents data to help organizations make informed decisions. This course may be useful for Data Analysts, as it provides a solid foundation in probability and uncertainty, which are essential concepts for understanding and working with data. The course also covers topics such as confidence intervals and hypothesis testing, which are important for drawing conclusions from data.
Product Manager
Product Manager
A Product Manager manages the development and marketing of products. This course may be useful for Product Managers who work on data-driven products, as it provides a solid foundation in probability and uncertainty, which are essential concepts for understanding and working with data. The course also covers topics such as confidence intervals and hypothesis testing, which are important for drawing conclusions from data.
Business Analyst
Business Analyst
A Business Analyst analyzes business processes and makes recommendations for improvement. This course may be useful for Business Analysts who work on data-driven projects, as it provides a solid foundation in probability and uncertainty, which are essential concepts for understanding and working with data. The course also covers topics such as confidence intervals and hypothesis testing, which are important for drawing conclusions from data.
Consultant
Consultant
A Consultant provides advice to organizations on a variety of topics. This course may be useful for Consultants who work on data-driven projects, as it provides a solid foundation in probability and uncertainty, which are essential concepts for understanding and working with data. The course also covers topics such as confidence intervals and hypothesis testing, which are important for drawing conclusions from data.
Software Engineer
Software Engineer
A Software Engineer designs, develops, and maintains software systems. This course may be useful for Software Engineers who work on data-driven applications, as it provides a solid foundation in probability and uncertainty, which are essential concepts for understanding and working with data. The course also covers topics such as confidence intervals and hypothesis testing, which are important for drawing conclusions from data.
Teacher
Teacher
A Teacher teaches students at a variety of levels. This course may be useful for Teachers who teach statistics, as it provides a solid foundation in probability and uncertainty, which are essential concepts for understanding and teaching statistics. The course also covers topics such as confidence intervals and hypothesis testing, which are important for drawing conclusions from data.
For more career information including salaries, visit:
OpenCourser.com/course/odvr6t/what
Featured in The Course Notes
This course is mentioned in our blog,
The Course Notes. Read
one article that features
What are the Chances? Probability and Uncertainty in Statistics:
To read more articles from OpenCourser, visit:
OpenCourser.com/notes
Reading list
We've selected 12 books
that we think will supplement your
learning. Use these to
develop background knowledge, enrich your coursework, and gain a
deeper understanding of the topics covered in
What are the Chances? Probability and Uncertainty in Statistics.
Provides a comprehensive overview of Bayesian reasoning and machine learning, covering topics such as Bayesian inference, Markov chain Monte Carlo methods, and variational inference. It valuable resource for students and professionals alike.
Provides a comprehensive overview of speech and language processing, covering topics such as speech recognition, speech synthesis, and natural language understanding. It valuable resource for students and professionals alike.
Provides a comprehensive overview of machine learning, covering topics such as supervised learning, unsupervised learning, and reinforcement learning. It valuable resource for students and professionals alike.
Provides a comprehensive overview of probability and statistics, covering topics such as probability theory, random variables, and statistical inference. It valuable resource for students and professionals alike.
Provides a comprehensive overview of statistical learning, covering topics such as linear models, regression, and classification. It valuable resource for students and professionals alike.
Provides a comprehensive overview of reinforcement learning, covering topics such as Markov decision processes, value functions, and policy optimization. It valuable resource for students and professionals alike.
Save
Provides a comprehensive overview of deep learning, covering topics such as neural networks, convolutional neural networks, and recurrent neural networks. It valuable resource for students and professionals alike.
Save
Provides a comprehensive overview of computer vision, covering topics such as image formation, feature extraction, and object recognition. It valuable resource for students and professionals alike.
Provides a comprehensive overview of natural language processing, covering topics such as tokenization, stemming, and parsing. It valuable resource for students and professionals alike.
Provides a rigorous treatment of mathematical statistics, covering topics such as probability theory, statistical inference, and linear models. It valuable resource for students and professionals alike.
Provides a rigorous treatment of statistical inference, covering topics such as point estimation, hypothesis testing, and confidence intervals. It valuable resource for students and professionals alike.
Save
Provides a concise introduction to probability and statistics, covering topics such as probability theory, random variables, and statistical inference. It valuable resource for students and professionals alike.
For more information about how these books relate to this course, visit:
OpenCourser.com/course/odvr6t/what
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Effort
4 weeks of study, 2-4 hours per week
Level
Intermediate
Via
Coursera
Institution
Johns Hopkins University
Instructor
Jennifer Bachner, PhD
Language
English
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This course belongs to a
collection
called
Data Literacy. It's comprised of five courses:
- Measurement – Turning Concepts into Data
- What are the Chances? Probability and Uncertainty in Statistics (viewing)
- Quantifying Relationships with Regression Models
- Data Literacy Capstone – Evaluating Research
- Data – What It Is, What We Can Do With It
Featured in The Course Notes
Read
one article that features
this course,
What are the Chances? Probability and Uncertainty in Statistics
from our blog, The Course Notes:
To read more articles from OpenCourser, visit:
OpenCourser.com/notes
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