Level 8: Reading data honestly

Statistics and data · level 8 of 8 · rough age 17 and beyond (a guide for parents; anyone can start anywhere)

In level 7 you described and modelled data. In this level you learn how far a sample lets you see beyond itself, and how to tell an honest claim from a misleading one. You find out why averages of samples are steadier than single values, decode "accurate within 3 points, 19 times out of 20", run a hypothesis test and read a p-value correctly, see why only experiments show cause, untangle Simpson's paradox and question the numbers in the news. The topic ends with a complete investigation from question to conclusion.

Lesson	You will be able to
Sampling distributions	Describe how sample means and proportions vary, and explain the σ/√n law and the central limit theorem
Margin of error and confidence intervals	Compute a margin of error and a 95% interval, and say exactly what the 95% does and does not mean
Hypothesis tests	Set up null and alternative hypotheses, find and interpret a p-value, and explain why 0.05 is a convention
Experiments versus observational studies	Design a randomised, controlled, blinded experiment and explain why only random assignment shows cause
Simpson's paradox	Explain how a comparison can reverse when groups are combined, using weighted averages, and decide which comparison to trust
Statistics in the news	Turn relative risks into absolute ones, and spot percentage-point confusion, cherry-picked ranges and survivorship bias
A full investigation	Carry out the whole cycle: question, plan, data, analysis and a conclusion that states its limits

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