BSTA 17A02 - Statistics applied to Social Sciences - Intermediate / Advanced Levels
Programme: A statistics course composed of 12 discussion sections.
Synopsis: Focusing on the practice of empirical research in the social sciences, this course is intended to provide the foundations in descriptive and inferential statistics.
Students who have followed a Bac-ES and Bac-S course (or their equivalents). The grade average in mathematics from the first semester will provide a basis upon which to arbitrate claims for exemption.
Spring 2020-2021
Continuous assessment accounts for ⅔ of the overall grade, while the final examination contributes a further ⅓.
Session 1: Introduction to empirical research in the social sciences
- Statistics as a tool for answering empirical research questions in the social sciences: examples of research questions
- Basic concepts: statistical individuals, population, sample, variables, modality, size, frequency, statistical distribution
- Types of variables: nominal, ordinal, interval and ratio variables
Session 2: Single-variable statistical series
- Measures of position (median, mean, quartiles)
- Measures of dispersion (variance, standard deviation, range, inter-quartile deviation)
Session 3: Discrete random variables
- Definition
- The law of probability
- Distribution function
- Calculating probabilities of the form P(a < X < b)
- Graphical techniques (histograms, pie charts etc.)
Session 4: Continuous random variables
- Definition
- The notion of density
- Distribution function
- Some simple calculations (e.g. uniform distribution, exponential distribution etc.)
- Graphical representations and interpretations
Session 5: Normal distribution
- Normal distribution (general / reduced centred): equations, graphs, interpretations and reading of a Z-table (for calculating probabilities of the form P(a < X < b))
Session 6: Sampling
- Random sampling and the notion of representative samples in empirical research
- Statistical inference
- Independent and identically distributed variables
- Standard deviation and average absolute deviation
- Central Theorem Limit and the empirical average
Session 7: Fluctuation and confidence intervals
- Definitions
- 95% intervals (and more generally at (1-a)%)
- In the general case, and for a proportion (where the variance is p (1-p))
Sessions 8 and 9: Hypothesis testing
- Null and alternative hypotheses
- Type I errors
- Critical region / acceptance region
- Decision: rejection or not of H0
- Student's t-test and significance level
- The Chi-Square test of independence
Session 10: Two variable statistical series
- Bivariate analysis and variable types
- Two-way tables (crosstabs): single, marginal and conditional frequencies
- Comparison of two averages (Student Test)
- Covariance and correlation
Session 11: Logistic regression
- Scatter plots
- Logistic regression affined using ordinary least squares (OLS)
- Application of a logarithm (regression in log(Y) = a log(X) + b for example)
- The R² coefficient of determination
- Reading and interpretation of an econometric input-output table (estimators, standard errors, different specification models)
Session 12: Final examination
Howell, D., Méthodes statistiques en sciences humaines, Paris, DeBoeck Université;