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CEGEP • Montreal

Advanced Quantitative Methods, 360-301

Advanced Quantitative Methods is the course that feeds directly into the research project at the end of the Social Science program at CEGEP: comparing more than two groups, controlling for a variable, following a series over time. Every chapter is here with its set of corrected exercises, and each statistical decision is justified one step at a time.

5 fully corrected exercise sets (60 exercises), 5 revision sheets, and a practice paper. Free, no account needed. The same course in French.

Comparing groups

  1. 1 Comparing two groups: t-test and effect size The independent-samples t-test with its pooled variance, equality of variances and the Welch correction, paired samples and what pairing gains, Cohen's d and the confidence interval of the difference, power and the required sample size. Then an exam-level part: the decision tree that leads to the right test, the same gap significant or not depending on sample size, five statements to correct, the complete evaluation of a workshop with intention to treat, and reading the results section of a journal article. Sheet
  2. 2 One-way analysis of variance Why analysis of variance rather than several two-by-two tests, the split of the variation into between-groups and within-groups parts, the complete table and the F statistic, eta squared and its correction, the three assumptions. Then an exam-level part: multiple comparisons with the Bonferroni correction, unequal group sizes and their two traps, five statements to correct, three teaching methods rebuilt from the standard deviations alone, and reading a published table without the data. Sheet

Controlling for a variable

  1. 3 Multiple regression From the raw slope to the partial slope, reading a regression output column by column, the adjusted R squared that falls when noise is added, dummy variables and the trap of one category too many, residuals and what they reveal. Then an exam-level part: multicollinearity and the variance inflation factor, interaction terms and slopes that differ by group, five statements to correct, a full four-variable model, and a published regression to rewrite. Sheet

When the normal model fails: rank tests

  1. 4 Nonparametric tests Why switch to ranks and what they preserve, the Mann-Whitney test worked step by step, the Wilcoxon signed-rank test, the Kruskal-Wallis test for several groups, Spearman's coefficient and monotonicity. Then an exam-level part: the relative efficiency of rank tests according to the shape of the distribution, the sign test computed from the binomial distribution, five statements to correct, a Likert scale on two small groups with its ties, and a methods section to rewrite. Sheet

Following a series over time

  1. 5 Time series and forecasting The four components of a time series, smoothing with a centred moving average, seasonal indices and their renormalization, the trend line and the forecast put back into season, growth rates and the logarithmic scale. Then an exam-level part: reading a deseasonalized series against its raw version, autocorrelation and spurious trend correlations, five statements to correct, a complete forecast carried through from start to finish, and a quarterly economic release to rewrite. 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, 360-301

Three hours and ten exercises on the whole advanced course: a complete independent-samples t-test with effect size, paired samples and power, an analysis of variance with its table, multiple comparisons and the minimum detectable difference, reading a regression output and making a prediction. Then the diagnosis of a model, a Kruskal-Wallis test, a forecast from a deseasonalized time series, five statements to correct, and a research report whose every conclusion has to be rewritten.

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

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