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CEGEP • Montreal

Advanced Statistics, 201-337

Advanced Statistics, 201-337, breaks with the deterministic mathematics of the earlier courses: the task is no longer to find the right answer but to make a decision under uncertainty. It is a course where writing the conclusion counts as much as the calculation.

5 fully corrected exercise sets (67 exercises), 5 revision sheets, and a practice paper. Free, no account needed. The same course in French.

Describing data

  1. 1 Descriptive statistics One calculation exercise first: ten measures to compute on small data sets, from the mean to the coefficient of variation; then types of variables and sampling methods, mean, median and mode against one extreme salary, the standard deviation and the reason for n minus 1, z-scores and quartiles with the 1.5 times the interquartile range rule. Then an exam-level part: the weighted mean and the trap of the mean of means, data grouped into classes, the ogive and reading percentiles, linear transformations and standardized data, and a critical reading of a statistic in the media. Sheet

Probability models

  1. 2 Probability and distributions One calculation exercise first: ten probabilities to compute directly with the binomial, Poisson and normal distributions; then the rules of probability and the mutually exclusive versus independent trap, Bayes' theorem on a screening test with a surprising result, the expected value and variance of a random variable with a fair game and an insurance policy, the binomial and the normal distributions. Then an exam-level part: sampling without replacement and the limits of the binomial, the four counting cases, the Poisson distribution of rare events, the normal approximation to the binomial and a quality control problem. Sheet
  2. 3 Continuous random variables and density One calculation exercise first: eleven direct calculations of areas, constants and quantiles under a given density; then the chapter where probability stops being a height and becomes an area. Part A sets up Kolmogorov's axioms and reading a step density, the constant that normalizes a linear density, the cumulative distribution function and the median, then the two continuous distributions the rest of the course never treats, the uniform and the memoryless exponential. Part B returns to the normal distribution through its density rather than its table, computes expected value and variance as weighted means read as a centre of gravity, corrects five statements taken from student papers, and works through two problems: waiting time together with the lifetime of a component, then the measurement error of two instruments with the same standard deviation. Sheet

Statistical inference and regression

  1. 4 Estimation and hypothesis testing One calculation exercise first: eleven direct calculations, from the standard error to the test statistic of a test on a proportion; then the central limit theorem and the standard error, the confidence interval for a mean and then for a proportion with the famous plus or minus 3%, the logic of a hypothesis test and Student's t distribution when the population standard deviation is unknown. Then an exam-level part: a complete test from the hypotheses to the written conclusion, the test on a proportion, comparing two means, the chi-square test of independence, and why significant does not mean important. Sheet
  2. 5 Correlation and linear regression One calculation exercise first: ten direct calculations, from the working sums to the residual of a point; then the scatter plot and the correlation coefficient, the least-squares line, the coefficient of determination and prediction, the devastating effect of an outlier or a leverage point, and the causation trap. Then an exam-level part: a complete regression on real data, residual analysis, linearizing exponential growth, the significance test for the correlation coefficient, and a critical reading of published studies. Sheet

When the chapters are done

A full paper under exam conditions, on the whole course. Do it once every chapter is behind you: it measures what you can do on a question you have never seen.

Practice exam

Practice final exam, 201-337

A complete paper in the format of a final exam: 12 exercises in 3 hours, marked out of 100, with detailed solutions question by question. Every exercise draws on several chapters and no question announces its method. Chebyshev's inequality, sample size, the predictive value of a screening test, choosing between the binomial, Poisson and normal distributions, type I and type II errors, power, the duality between confidence interval and test, the chi-square goodness-of-fit test, Simpson's paradox, and the prediction interval of a regression.

  • 12 questions
  • 100 points
  • 180 minutes
Sit the paper

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