Sampling uncertainty
Students learn how sample statistics vary from sample to sample and why standard error is central to inference.
Module 4
Statistical Inference Foundations
This module moves from probability models to statistical reasoning. Students learn how sample statistics vary, how uncertainty is measured, how confidence intervals and hypothesis tests are built, and how to choose an appropriate inference method for real research questions.
Module aim
Learn how sample evidence supports conclusions under uncertainty.
The purpose of this module is to help students reason about estimates, uncertainty, testing, errors, power, study design and method choice rather than only memorising calculations.
6
Lessons
Zero
Coding
Foundation
Level
Inference
Focus
Estimation and testing
The module connects confidence intervals, hypotheses, p-values, errors and power as one reasoning framework.
Method choice
Students learn to choose inference methods from the research question, outcome type, assumptions and study design.
Module lessons
Learn inference step by step.
Lessons 4.1 to 4.5 form the core inference pathway. Lesson 4.6 is a bonus capstone that helps students choose the correct method in applied problems.
4.1
Lesson 4.1
ReadySampling Distributions and Standard Error
How sample statistics vary from sample to sample, why standard error matters, and how probability becomes statistical inference.
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4.2
Lesson 4.2
ReadyConfidence Intervals
Interval estimation, margin of error, confidence level, long-run coverage, interpretation and common mistakes.
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4.3
Lesson 4.3
ReadyHypothesis Testing Framework
Null and alternative hypotheses, test statistics, null distributions, p-values, rejection rules and statistical decisions.
Open lesson →
4.4
Lesson 4.4
ReadyP-values, Errors and Power
Advanced interpretation of p-values, Type I error, Type II error, significance level, power, effect size and practical importance.
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4.5
Lesson 4.5
ReadySample Size and Study Design
How sample size, variability, effect size, power, allocation, precision and study design influence the quality of statistical evidence.
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4.6
Lesson 4.6
BonusChoosing the Right Inference Method
A bonus capstone lesson on choosing between t-tests, proportion methods, chi-square tests, rank-based methods and correct reporting.
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End of module outcome
Students should be able to reason, not just calculate.
By the end of this module, students should understand how sampling variability, uncertainty, intervals, tests and design choices shape responsible statistical conclusions.
Explain standard error and sampling variability.
Interpret confidence intervals correctly.
Set up null and alternative hypotheses.
Interpret p-values without common mistakes.
Explain Type I error, Type II error and power.
Choose an inference method from outcome and design.
Learning route
Complete inference before moving into regression.
Module 5 assumes that students understand sampling distributions, standard error, confidence intervals, hypothesis testing, p-values, errors, power and study design before moving into regression modelling.
Continue to Module 5 →Course pathway
Return to the full Statistics Foundation course.
Use the course homepage to move between all five modules, review the full structure and continue through the 26-lesson foundation pathway.
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