Sampling uncertainty
Students learn why sample results vary and how this variation becomes the basis of inference.
Module 5
Statistical Inference Foundations
This module introduces the foundations of statistical inference: sampling distributions, confidence intervals, hypothesis testing, p-values, errors, power and careful interpretation. Students learn how sample evidence is used to reason about population parameters under uncertainty.
Module aim
Learn how statistics support conclusions under uncertainty.
Statistical inference connects data, probability and distributions to real academic conclusions. The emphasis is on reasoning, assumptions and interpretation rather than mechanical calculation.
5
Lessons
Zero
Coding
Foundation
Level
Inference
Focus
Estimation
The module explains confidence intervals as a way to estimate unknown population parameters with uncertainty.
Testing
Students connect hypotheses, p-values, errors and power to careful statistical decision-making.
Module lessons
Study inference as a reasoning process.
Each lesson builds a different part of inference: how statistics vary, how intervals estimate parameters, how tests make decisions, how p-values and errors are interpreted and how conclusions should be reported.
5.1
Lesson 5.1
Sampling distributions
Understand how statistics vary from sample to sample and why sampling distributions are the foundation of statistical inference.
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5.2
Lesson 5.2
Confidence intervals
Learn how confidence intervals use sample information and uncertainty to estimate unknown population parameters.
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5.3
Lesson 5.3
Hypothesis testing
Study the logic of null hypotheses, alternative hypotheses, test statistics, rejection regions and statistical decisions.
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5.4
Lesson 5.4
p-values, errors and power
Understand p-values, Type I error, Type II error, statistical power and why significance is not the same as importance.
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5.5
Lesson 5.5
Statistical inference workflow
Bring inference together through a careful workflow: question, parameter, assumptions, interval, test, interpretation and limitations.
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Final foundation route
Complete the foundation by learning how to report conclusions.
This final module brings the foundation course together. Students should finish with a clearer understanding of how sample data, uncertainty, probability and distributions support statistical conclusions.
Open final lesson →Course pathway
Return to the full Statistics Foundation course.
Use the course homepage to review all modules, revisit earlier lessons and continue using the foundation course as preparation for biostatistics, epidemiology, data science and research methods.
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