FREE LEARNING SERIES
Probability and statistical inference
Track conditional probabilities, quantify sampling uncertainty and interpret a regression without confusing association with cause.
3 lessons · Learn at your own pace
Begin the first lesson →
Learn, practise, explain
Try the exercise before reading its explanation. Answer the self-check questions in your own words, then compare your reasoning with the answers. Revisit any difficult section before moving on. No account or payment is needed.
- 01
Conditional probability and independence
“How often is an item defective when an alarm sounds?” differs from “How often does the alarm sound when an item is defective?” Conditioning changes the reference group. Tables and probability trees make that change visible.
Learning outcome: Choose the correct denominator, distinguish independence from mutual exclusion, calculate a posterior probability, and explain why association does not establish causation.
Open lesson → - 02
Sampling variation and confidence intervals
Different random samples produce different estimates even when the population is unchanged. A confidence interval describes this sampling uncertainty under stated assumptions. It does not repair a biased survey or predict where most individual observations lie.
Learning outcome: Distinguish standard deviation from standard error, calculate mean and proportion intervals, interpret confidence correctly, and identify uncertainty that the formulas omit.
Open lesson → - 03
Correlation, regression and confounding
A pattern between two variables can help summarise data or make cautious predictions. It does not automatically explain what would happen if one variable were deliberately changed. Learn to fit a line and then examine what the line leaves out.
Learning outcome: Calculate and interpret a fitted line, inspect residuals, distinguish prediction from causation, and show numerically how changing group composition can reverse an overall comparison.
Open lesson →