Statistics: from samples to qualified conclusions
Audit observations, describe distributions, reason about sampling and interval estimation, test a prespecified hypothesis and inspect regression without confusing association with causation.
Choose any lesson or try the project first. Shared lessons retain the same saved work wherever you enter them. Completing a lesson records participation; practice, transfer checks and independent reasoning remain separate.
Recommended preparation and ways to catch up
- Review percentages, means and probability before inference; direct refresher access remains available.
- Before summaries: the data-generating and recording process determines what a row represents.
- Before inference: an independent sample provides separate observations; repeated copies do not increase information.
- Before regression: a function predicts output from input; a residual is observed minus predicted output.
Find a foundation course · Open contextual refreshers. Each investigation includes a short recap; preparation never locks access.
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Your units and lessons
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What was observed and retained?
Identify sampling bias, record errors and the population a conclusion is intended to describe.
Who answered the survey?
Can a large survey still give the wrong answer?
Repair a messy event log
Which rows are observations and which are recording errors?
Describe shape and variation
Compare medians, quantiles, means and variance while stating conventions and tail behavior.
Describe the shape beyond one average
Which summaries change when a tail observation grows?
Describe variation without inventing evidence
Inspect mean, variance, covariance and the assumptions behind uncertainty summaries.
Estimate and test
Explain sampling uncertainty, interpret approximate confidence intervals and calculate an exact prespecified test.
How precise is a sample percentage?
How much more data is needed to halve random uncertainty?
Ask how surprising the result is under a model
What does a small p-value actually say?
Relationships and fair comparisons
Inspect regression residuals and influential points, then separate association from confounding and treatment effects.
Fit a line and inspect what it misses
How much can one observation change a fitted trend?
Design a fair comparison
Can easier tasks make a weak treatment look better?
Separate a comparison from a causal claim
Change cohort composition and diagnose an aggregate reversal.
Produce a reproducible statistical evidence brief
Investigate a fictional service or study claim. Audit its sample, describe the distribution, state an uncertainty or testing procedure before choosing a conclusion, and inspect a relationship for confounding and influential observations.
Build from lesson evidence, compare alternatives, write an artifact, and tackle unfamiliar numerical cases. Use the rubric with a teacher, peer or colleague to assess the quality of your reasoning.
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