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Statistical Methods

Dr Leonid Bogachev

Build your statistics and probability expertise with this short course from the University of Leeds.

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Build your statistics and probability expertise with this short course from the University of Leeds.

The first week introduces you to statistics as the art and science of learning from data. Through multiple real-life examples, you will explore the differences between data and information, discovering the necessity of statistical models for obtaining objective and reliable inferences. You will consider the meaning of "unbiased" data collection, reflecting on the role of randomization. Exploring various examples of data misrepresentation, misconception, or incompleteness will help develop your statistical intuition and good practice skills, including peer review.

In the second week, you will learn and practice R software skills in RStudio for exploratory data analysis, creating graphical and numerical summaries. The final week will involve completing probability experiments and computer simulations of binomial trials, such as tossing a coin or rolling a die. This will help you develop an intuitive concept of probability, encompassing both frequentist and subjective perspectives. Throughout the course, you will acquire vital statistical skills by practicing techniques and software commands and engaging in discussions with fellow students.

By the end of the course, you will be able to:

- Understand and explain the role of statistical models in making inferences from data.

- Implement appropriate tools for numerical and graphical summaries using RStudio, and interpret the results.

- Evaluate the stability of frequencies in computer simulations through experimental justification and "measurement" of probability.

No matter your current level of mathematical skill, you will find practical and real-life examples of statistics in action within this course.

This course is a taster of the Online MSc in Data Science (Statistics) but it can be completed by learners who want an introduction to programming and explore the basics of Python.

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What's inside

Syllabus

The Role of Statistical Models in Data Analysis
This first week introduces you to statistics as the art and science of learning from data. You will learn how to recognise the difference between data and information and realise the need for statistical models to gain objective and reliable inferences. You will consider examples of datasets and reflect on suitable research questions that can be posed and answered using these data. You will see the importance of 'unbiased' data collection and learn about randomisation as a tool to achieve this. Various examples of data misrepresentation, misconception or incompleteness will help you develop statistical intuition and good practice skills. In the activities section, you are introduced to the peer review tool, which is a useful way for you to improve your statistical data analysis skills.
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The Basics of Exploratory Data Analysis
Week 2 gives you the opportunity to learn and practise your R skills in exploratory data analysis by producing numerical and graphical summaries of a variety of datasets. You learn to distinguish between different types of data (categorical vs numerical) and to use appropriate numerical and graphical summaries. You also gain experience in distinguishing between 'normal' and skewed data using box plots and histograms. This week offers a substantive task in RStudio to complete.
Explore and Reflect: Random Experiments and Computer Simulations
This final week gives you the opportunity to explore a remarkable stability of frequencies as an experimental support of the concept of probability. You apply your R skills and conduct computer simulations of repeated random trials (e.g. tossing a coin or rolling a dice). Based on these observations, you develop an intuitive concept of probability (frequentist and subjective). You share your findings on a discussion board or 'forum' to discuss long-term experiments as a way to 'measure' probability of various events of interest (e.g. long runs of 6 in dice rolls, or tied birthdays in a class of students).

Good to know

Know what's good
, what to watch for
, and possible dealbreakers
Develops statistical intuition and critical thinking. This is a core skill for data science and research professionals
Uses RStudio, which is an industry-standard environment for working with statistical data
Taught by Dr. Leonid Bogachev, a recognized expert in statistics and probability
Introduces foundational principles of statistics and probability
Suitable for learners with various mathematical backgrounds
Requires students to come in with basic familiarity with statistics

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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 Statistical Methods with these activities:
Review foundational statistical concepts
Improves retention of foundational statistical knowledge.
Browse courses on Descriptive Statistics
Show steps
  • Review lecture notes or textbooks from previous statistics courses.
  • Complete practice problems to reinforce concepts.
Read Probability and Statistical Inference by Hogg and Tanis
Provides a comprehensive review of probability theory and statistical inference.
Show steps
  • Read the assigned chapters.
  • Take notes and summarize key concepts.
  • Complete the end-of-chapter exercises.
Solve practice problems on statistical concepts
Strengthens understanding of statistical methods and improves problem-solving skills.
Browse courses on Data Analysis
Show steps
  • Find practice problems from textbooks, online resources, or problem sets provided by the instructor.
  • Attempt to solve the problems on your own.
  • Check your solutions against answer keys or consult with the instructor or a tutor for guidance.
Four other activities
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Show all seven activities
Follow online tutorials on R programming
Develops proficiency in using R for statistical analysis and data manipulation.
Browse courses on Data Visualization
Show steps
  • Identify online tutorials that cover the basics of R programming.
  • Follow the tutorials step-by-step and practice the commands.
  • Complete the exercises and quizzes provided in the tutorials.
Participate in peer study groups
Fosters collaboration, enhances understanding through discussions.
Show steps
  • Join or create a peer study group.
  • Meet regularly to discuss course materials, solve problems, and exchange ideas.
  • Take turns leading discussions and presenting concepts.
Create a data visualization project
Applies statistical concepts and R programming skills to solve real-world problems.
Browse courses on Exploratory Data Analysis
Show steps
  • Choose a dataset and identify research questions.
  • Clean and prepare the data using R.
  • Create visualizations to explore the data and draw insights.
  • Write a report summarizing your findings.
Develop a statistical model to predict a business outcome
Provides practical experience in applying statistical methods to solve business problems.
Browse courses on Statistical Modeling
Show steps
  • Define the business problem and gather data.
  • Explore the data and identify potential predictors.
  • Build and evaluate a statistical model.
  • Deploy the model and monitor its performance.

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Course image
Effort
3 weeks of study, 2-3 hours/week
Level
Intermediate
Via
Coursera
Institution
University of Leeds
Instructor
Dr Leonid Bogachev
Session
August 19, 2024 - September 16, 2024
Language
English
Good to know
Develops statistical intuition and critical thinking. This is a core skill for data science and research professionals
Uses RStudio, which is an industry-standard environment for working with statistical data
Taught by Dr. Leonid Bogachev, a recognized expert in statistics and probability
Introduces foundational principles of statistics and probability
Suitable for learners with various mathematical backgrounds
Requires students to come in with basic familiarity with statistics
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