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Statistical Inference and Probability

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Overview

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This course covers key concepts of statistical inference and probability, offering practical insights into hypothesis testing, regression, and effect size. Ideal for those looking to apply these techniques in real-world scenarios. This course provides a comprehensive introduction to statistical inference, covering essential concepts from probability theory to regression analysis. It emphasizes practical understanding through real-world applications, helping learners build confidence in analyzing and interpreting data. Designed for those looking to strengthen their statistical skills, it offers a clear path to mastering key analytical techniques. This course is ideal for students, researchers, and professionals in fields such as science, healthcare, and social research. A basic understanding of mathematics and statistics is recommended to fully benefit from the content. This course presents a structured exploration of statistical inference and probability, progressing from foundational concepts like probability theory to more advanced topics such as hypothesis testing and regression analysis. Real-world case studies and practical exercises provide hands-on learning to solidify key principles. This course is based on Statistical Inference and Probability, by John MacInnes. Copyright ©2022 by Sage Publications Limited. All rights reserved, including rights for text and data mining and training of artificial technologies or similar technologies. Published by Sage Publications Limited, London. Used by arrangement with Sage Publications Limited.

Syllabus

  • The Challenge and Promise of Inference
    • This module examines the process of inference, including how we draw conclusions from evidence, the role of statistical inference in scientific research, and the challenges posed by cognitive biases. It explores the tension between scientific rigor and everyday reasoning, and covers key concepts like reproducibility, replication, and the limitations of null hypothesis testing. Learners will gain a deeper understanding of how to critically evaluate inferences in both academic and real-world contexts.
  • Probability, Randomness, Probability Distributions and Sampling Distributions
    • This module introduces the foundational concepts of probability, including random events, sample spaces, and probability distributions. It explores how to calculate and interpret probabilities, analyze data using visual tools like bar charts and histograms, and apply conditional probability to real-world scenarios. Learners will develop a strong understanding of probabilistic reasoning and its practical implications.
  • Bernoulli, Coke and Pepsi
    • This module explores the fundamentals of statistical inference through a real-world experiment involving taste testing. Learners will understand how to evaluate evidence, interpret p-values, and make decisions based on probability. It covers key concepts like the null hypothesis, sampling distributions, and significance levels.
  • Samples and Populations
    • This module provides an in-depth look at sampling methods, statistical inference, and how to estimate population parameters using sample data. Learners will explore key concepts such as sampling distributions, standard errors, and hypothesis testing, while gaining the ability to analyze and interpret statistical results in real-world scenarios.
  • Inference and Regression
    • This module delves into the principles of statistical inference and regression analysis, covering key topics such as OLS regression, ANOVA, and the F-distribution. Learners will gain the ability to interpret regression models, understand their statistical foundations, and apply these techniques to real-world data. The module also explores common pitfalls and transformations in regression analysis.
  • Power, Effect Size and Inverse Probability
    • This module examines the limitations of Null Hypothesis Significance Testing (NHST), explores Type I and Type II errors, and introduces the concept of power and inverse probability. It also covers the application of these ideas in interpreting conditional probabilities, particularly in medical testing scenarios. Learners will gain a deeper understanding of statistical reasoning and its real-world implications.
  • What Does Sound Inference Comprise?
    • This module explores the principles of sound statistical inference, focusing on the proper interpretation of p-values, the limitations of null hypothesis significance testing, and the role of the American Statistical Association in guiding scientific research. Learners will gain a deeper understanding of how to evaluate and apply statistical methods effectively.

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