26 topics
Statistics help, including what the p-value actually means
Statistics is the course where you can execute every calculation correctly and still lose most of the marks, because the marks are in the interpretation. A confidence interval computed perfectly and then described as 'a 95% chance the mean is in here' is wrong, and it is wrong in the way examiners specifically look for.
Where students get stuck
What does a p-value actually mean?
It is the probability of seeing data at least this extreme IF the null hypothesis were true. It is not the probability that the null hypothesis is true, and it is not the probability you made a mistake. That distinction is worth real marks, and it is also why 'p = 0.06' does not mean 'almost significant' — it means the data are not surprising enough under the null to reject it at your chosen threshold.
Which test do I use?
Three questions settle it almost every time. How many groups — one, two, or more than two? Is the variable numerical or categorical? Is the population standard deviation known? One numerical group with unknown σ is a t-test, two independent numerical groups is a two-sample t-test, three or more is ANOVA, and categorical counts are chi-square. The test follows from the design, not from the chapter you are on.
Confidence intervals — I can compute one but not explain it
The correct reading is about the procedure, not this one interval: if you repeated the sampling many times, 95% of the intervals built this way would contain the true parameter. This particular interval either contains it or does not. Getting this sentence right is often an entire mark on its own, and 'there is a 95% chance the true mean is between…' does not get it.
Correlation, causation, and the r² question
r measures linear association only — a perfect parabola has an r near zero. r² is the proportion of variance in y explained by the model, so r = 0.7 means only about half the variation is accounted for, which is a lot less impressive than 0.7 sounds. And neither says anything about causation without a randomised design, which is the point most conclusion questions are actually testing.
What's covered
Statistics topics you can work through with a tutor, generate practice on, or turn into flashcards and a study plan.
Describing data
- Types of variables and levels of measurement
- Mean, median, mode, and when each misleads
- Standard deviation, variance, and IQR
- Histograms, boxplots, and skew
- Outliers and the 1.5 × IQR rule
- z-scores and standardisation
Probability
- Sample spaces and basic rules
- Conditional probability and independence
- Bayes' theorem
- Permutations and combinations
- Random variables, expected value, and variance
Distributions
- Binomial and geometric distributions
- The normal distribution and normal approximation
- The Central Limit Theorem
- Sampling distributions and standard error
- The t-distribution and degrees of freedom
Inference
- Confidence intervals for means and proportions
- Hypothesis testing and the null and alternative
- Type I and Type II errors, significance, and power
- One- and two-sample t-tests
- Chi-square tests for goodness of fit and independence
- ANOVA
Relationships and design
- Scatterplots, correlation, and r²
- Least-squares regression and residual plots
- Experimental design, control, and randomisation
- Sampling methods and sources of bias
Statistics questions
Can it help me interpret my output, not just calculate?
Yes, and that is usually where the marks are. Share your output — from a calculator, a spreadsheet, R, or SPSS — and it will walk through what each number means and what conclusion the question is actually asking you to write.
Does it cover AP Statistics?
Yes. The topic list above covers the AP Statistics syllabus and a typical introductory university stats course, including the interpretation-heavy free-response style where the reasoning is worth more than the arithmetic.
I keep mixing up when to use z and when to use t.
Common enough that it is worth one focused session. Short version: t whenever you are estimating the population standard deviation from your sample, which in practice is nearly always. It can drill you on the choice specifically until it stops being a coin flip.
Stuck on statistics right now?
Talk it through out loud, share your screen, and watch it worked out step by step on a whiteboard.
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