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CEGEP • Montreal

Quantitative Methods in Social Science, 360-300

Quantitative Methods, 360-300 (360-300-RE in the ministerial program), is the one mathematics course that every Social Science student must pass, whatever their profile. Each chapter is here with its set of fully corrected exercises, from choosing a measurement scale to the chi-square test on a cross-tabulation.

8 fully corrected exercise sets (92 exercises), 8 revision sheets, and a practice paper. Free, no account needed. The same course in French.

Measuring and collecting data

  1. 1 Concepts, variables and measurement scales Going down from a concept to its indicators, the four measurement scales and what each one allows, the Likert scale and reverse-coding negative items, independent, dependent and confounding variables, validity and reliability on four targets. Then an exam-level part: building a composite index with weights and a geometric mean, Robinson's ecological fallacy, five statements to correct, operationalizing success in college, and a critical reading of a poll's technical sheet. Sheet
  2. 2 Sampling and questionnaires Target population, sampling frame and coverage defects, the four probability sampling plans, quota, convenience and snowball samples, the required sample size and the finite population correction, proportional and Neyman allocation. Then an exam-level part: the four faults of questionnaire wording, nonresponse bias and its formula, five claims to correct, the full design of a CEGEP survey, and two contradictory polls from the same month. Sheet

Describing and comparing data

  1. 3 Frequency distributions and graphs From raw data to a frequency distribution, class intervals and Sturges' rule, the histogram and its frequency polygon, unequal classes and density, the graph that each measurement scale allows. Then an exam-level part: the truncated axis and the chosen time window, pictographs whose area quadruples, five statements to correct, a dual-axis newspaper graphic taken apart line by line, and the full construction of the table and graph of a survey. Sheet
  2. 4 Z scores, percentile ranks and the R score One calculation exercise first: ten conversions to compute directly, from a mark to a Z score, to an intelligence quotient, to a T score and to a percentile rank; then standardizing a data set and what the Z score keeps, the derived scales from the intelligence quotient to the T score, the percentile rank and its convention, the conversion between Z score and percentile rank through the normal distribution, and the full R score formula with its three corrections. Then an exam-level part: the same mark in two groups of opposite levels, the documented limits of the R score, five statements to correct, the calculation of a four-course record weighted by units, and four candidates from four different systems to rank. Sheet
  3. 5 Index numbers, rates and constant dollars One calculation exercise first: ten direct calculations, from percentage changes to index numbers and constant dollars; then percentage points against percent, successive changes that multiply, index numbers with base 100 and the change of base, constant dollars and purchasing power, the unemployment rate and what its denominator decides. Then an exam-level part: direct standardization of death rates, doubling time and the rule of 70, five statements to correct, twenty years of teacher salary in current and constant dollars, and the critical reading of an economic news release. Sheet

Relationships between variables and polls

  1. 6 Cross-tabulations, chi-square and association The three percentages of a cell and the three questions they answer, the expected frequencies of independence, the chi-square test with its decision and its cell-by-cell contributions, the conditions of application and Yates' correction, Cramér's V. Then an exam-level part: why everything becomes significant with enough respondents, controlling for a third variable and elaboration, five statements to correct, a complete survey from table to conclusion, and reading a table published in a journal. Sheet
  2. 7 The margin of error of a poll What “three points, 19 times out of 20” means, the margin as a function of the estimated proportion, the margin of a subgroup, the margin on the gap between two candidates of the same poll, the 50% threshold and the qualified majority. Then an exam-level part: comparing two waves and the problem of multiple comparisons, aggregating polls and the house effect, five claims to correct, an election night redone figure by figure, and a student referendum with its finite population correction. Sheet

Research design

  1. 8 Research design and critical reading From a question to a falsifiable hypothesis, the five research designs and what each one allows, the two random draws that must not be confused, the three conditions of causation, the threats to internal validity and the difference in differences. Then an exam-level part: regression toward the mean worked out in numbers, the mechanics of multiple tests and p-hacking, five statements to correct, the full evaluation of a peer tutoring program with effect size and intention to treat, and the rewriting of a newspaper article. 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, 360-300

Three hours and ten exercises that revisit the whole course: operationalizing a concept and choosing a measurement scale, sizing a stratified sampling plan, reading a histogram with unequal classes, computing an R score and a weighted record, converting tuition fees into constant dollars. Then a crosstab carried through to Cramér's V, margins on a subgroup and on a gap, regression toward the mean in a program evaluation, five statements to correct, and the annual report of a student success office to rewrite.

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

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