How to use this guide
Where this guide comes from. It follows the course's published description (hypothesis tests by formula and by simulation along with their error rates, comparing two groups by interval and by test, chi-square tests on counts, regression with checks on its conditions, and analysis of variance) and the standard topics for a second course in statistics. Instructors' emphasis and notation vary: check your own course outline.
The order. 01 revisits tests and adds the error probabilities. 02 to 04 compare two groups: means, proportions and a simulation approach. 05 and 06 are chi-square tests for counts. 07 compares three or more means. 08 and 09 model one numerical variable from others. 10 gives rank-based tests for when the usual conditions fail. Some sections skip or shorten some of these: check your outline.
Short refresher from STAT 213. A test assumes H₀, measures the sample result in standard errors (a test statistic), and converts that into a p-value: the probability, if H₀ were true, of a result at least as extreme. Small p (below α) means reject H₀; otherwise fail to reject, which is not proof of H₀. A confidence interval is estimate ± critical value × standard error.
Inside a topic: read the idea, look at the formula, then open the worked example and follow every step. Close it and redo it on paper. Then change the numbers in the lab until the answer stops surprising you, and finish with the traps.
Notation used here: x̄, s, p̂, μ, σ and p as in STAT 213. Two groups are numbered 1 and 2: n₁, x̄₁, s₁. A paired difference is d. In regression, b₀ and b₁ are the fitted intercept and slope, ŷ a fitted value, e = y − ŷ a residual, r the correlation and R² the share of variation explained. Chi-square is written χ². Software output varies in layout, so the labs show the steps by hand.
Then practise. The Drill, the multiple-choice bank and the flashcards are all levelled:
| Level | What it asks | Example |
|---|---|---|
| Beginner | A definition, or one step: read one number or apply one formula | Find the expected count for one cell of a table |
| Intermediate | A standard problem in a few steps | Compute a χ² statistic, or the slope of a fitted line |
| Exam level | A full exam-style question that strings several steps together | Run a paired t test and state the conclusion in words |
| Hard | Twists: working backwards, picking the right test, and the traps that cost the most marks | Find power, or a prediction interval at a given x |
The question generator starts on Auto: it begins at Beginner and moves up a level after three correct answers in a row. You can pick a level yourself at any time. The multiple-choice bank and flashcards are ordered from easy to hard, so working through them in order builds each idea from the ground up.
The p-values in labs and drills are computed exactly. A table gives only a range or a nearby row, so answers within the stated rounding are accepted. Check which tables or software your course uses.
Exam format, weight and allowed aids differ between sections and terms. Check your own course outline.
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