What are the Chances? Probability and Uncertainty in Statistics from Coursera

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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.

Random Variables and Distributions

In this module, we'll dive into a topic you've likely encountered all of your adult life but perhaps have never explored from a statistical perspective: the normal curve. More generally, we'll discuss probability distributions, including their key features and relevance to quantifying uncertainty. Although studying probability theory can sometimes feel detached from applied statistics, it's valuable to develop a foundational understanding of probability to be able to critically evaluate statistical models. An appreciation for probability, and its counter-intuitive nature, will help you interpret the uncertainty of a statistical result as accurately as possible. This is particularly important when the stakes are high and policy makers want to know whether or not to act based on a statistical finding.

Confidence Intervals and Hypothesis Testing

In this module we will apply the concepts of probability, random variables and distributions to measuring and interpreting uncertainty. In particular, we'll focus on statistical significance. A relationship is statistically significant if it can be distinguished from zero. Suppose you want to examine the effect of exposure to negative campaign ads on one's likelihood of voting. The independent variable is one's exposure to negative campaign ads and the dependent variable is one's likelihood of voting. If we find that exposure to negative campaign ads has no relationship with the likelihood of voting, we would say that this is a statistically insignificant relationship. If, instead, we find that exposure to negative campaign ads leads to a decline in one's likelihood of voting, we have uncovered a statistically significant (i.e., non-zero) relationship.

Quantifying Uncertainty in Regression Analysis and Polling

In this final module of the course, we'll cover how to measure the uncertainty of regression estimates and poll results. It is often the case that a regression model will reveal a non-zero relationship, but it's important to determine whether that relationship sufficiently different from zero such that we can conclude that the relationship is statistically significant. For example, suppose a regression model reveals that a drug improves patient outcomes by 3.2%. Is 3.2% statistically different from 0? A statistical significance test will answer this question. This module, however, will also discuss some of the drawbacks of relying a statistical significance for data-driven decision making. While statistical significance is an important consideration, it is not the only criterion one should use when determining whether to act on a set of a statistical findings.

Good to know

Know what's good

, what to watch for

, 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

Reviews summary

Well received statistics course

Learners say that this statistics course is well received with many excellent ratings. Learners feel that they understand probability and uncertainty after taking this course. Many were looking to finish quickly, but mention that the peer assessment at the end may delay getting a certificate for some. Overall, the material is well taught, with some learners saying the tests are relatively easy compared to the difficulty of the content.

Many learners were positive about the course material.

"Excellent course."

"great and interest course"

"The course is interesting and provided me with basic understanding of probability and uncertainties."

Some learners felt the course was relatively easy. Tests were easy compared to material.

"The course itself is okay I guess. Some topics were well explained, although the tests were quite easy compared to the material."

The peer review assessment may delay receiving a certificate.

"However, my biggest issue with the course is the peer review assessment."

"The course is interesting and provided me with basic understanding of probability and uncertainties. However, I wanted to finish the course as faster as I could to receive my certificate but with final peer review assessment you will need to wait till someone reviews your final assignment."

"It is not comfortable if you would like to receive your certificate asap."

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

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Ensure you have a good understanding of probability before starting the course to enhance comprehension.

Browse courses on Probability

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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

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Supplement your learning with a comprehensive textbook on statistical methods.

View Fundamental Statistics for the Behavioral... on Amazon

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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

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Deepen your understanding of probability distributions by creating visual representations.

Browse courses on Probability Distributions

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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

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Join a study group to discuss course concepts

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Engage with peers to reinforce your understanding and gain different perspectives.

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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

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Gain proficiency in calculating and interpreting confidence intervals.

Browse courses on Confidence Intervals

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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

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Expand your understanding of statistical significance through a focused workshop.

Browse courses on Statistical Significance

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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

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Apply your knowledge to a practical scenario by creating a statistical analysis plan.

Browse courses on Statistical Analysis

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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:

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.

See salaries and explore the career path for Actuary

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.

See salaries and explore the career path for Quantitative Analyst

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.

See salaries and explore the career path for Machine Learning Engineer

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.

See salaries and explore the career path for Data Scientist

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.

See salaries and explore the career path for Statistician

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.

See salaries and explore the career path for Risk Manager

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.

See salaries and explore the career path for Researcher

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.

See salaries and explore the career path for Data 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.

See salaries and explore the career path for Financial Analyst

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.

See salaries and explore the career path for Market Researcher

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.

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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.

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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.

See salaries and explore the career path for Business Analyst

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.

See salaries and explore the career path for Consultant

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.

See salaries and explore the career path for Teacher