# FASS512 Quantitative Research Methods 2

## Module description

• Review of basic concepts in descriptive statistics. Summary measures of variables: mean, median, standard deviation, interquartile range, skew. Discrete and continuous variables. Data input and obtaining numerical summaries of data in "R".
• The visual display of data. Graphically exploring the distributions of single variables and the relationships between two or more variables. Bar charts, histograms, scatterplots, boxplots. The normal distribution. Using graphical techniques in "R".
• The basic laws of probability. Combining probabilities. Bayes's rule.
• Hypothesis testing. Credible intervals and their relationship to hypothesis tests. Frequentist versus Bayesian perspectives on testing. P-values and confidence intervals. Resampling methods. Calculating credible/confidence intervals in "R".
• Parametric versus non-parametric testing. One- and two-sample tests for means, medians, and contingency tables.
• Testing more than two samples: the Analysis of Variance (ANOVA) and its non-parametric counterparts. Post-hoc tests and corrections for multiple testing. Performing these tests in "R".
• Relationships and causality. Correlation and simple regression. Multiple regression and model selection. Fitting regression models in "R" and analysing the residuals.

## Aims and objectives

To provide students with the opportunity to acquire:

• A knowledge of probability sufficient for them to understand the design, analysis, and results of a statistical inquiry and to begin to understand social science articles containing statistical content, up to and including multiple regression.
• The skills to select between significance tests and credible/confidence intervals of both a parametric and non-parametric nature and to find the method most appropriate to the data set and specific questions of interest.
• The ability to analyse the strength, direction and general nature of the relationship between two variables, and to say how important this relationship is.
• The ability to use the statistical package "R" to implement the methods they deem most appropriate for the problem at hand.

On successful completion of this module students will be able to:

• Have a knowledge of probability sufficient for them to understand the design, analysis, and results of a statistical inquiry and to begin to understand social science articles containing statistical content, up to and including multiple regression.
• Select between significance tests and credible/confidence intervals of both a parametric and non-parametric nature and find the method most appropriate to the data set and specific questions of interest.
• Analyse the strength, direction and general nature of the relationship between two variables and say how important this relationship is.
• Use the statistical package "R" to implement the methods they deem most appropriate for the problem at hand.

## Prerequisites

FASS508, FASS508d, or an equivalent introduction to statistics. Students not taking FASS508 or FASS508d in the preceding term should contact the convenor in advance, as additional preparatory reading may be required of them.

Altman, D.G. et al. (2000), Statistics With Confidence, 2nd Ed. London, BMJ Books.

Franklin, J. (2009), What Science Knows and How It Knows It, New York, Encounter Books.  [Mainly chapters 1 and 10.]

Haigh, J. (2012), Probability: A Very Short Introduction. Oxford: Oxford University Press

Hand, D. (2008), Statistics: A Very Short Introduction. Oxford, Oxford University Press.

McGrayne, S.B. (2011), The Theory That Would Not Die: How Bayes' Rule Cracked The Enigma Code, Hunted Down Russian Submarines, and Emerged Triumphant from Two Centuries of Controversy, New Haven, Yale University Press.

Paulos, J.A. (1995), A Mathematician Reads the Newspaper: Making Sense of The Numbers in the Headlines, London, Penguin.

Savage, S.L. (2009), The Flaw of Averages: Why We Underestimate Risk in the Face of Uncertainty, Hoboken, NJ, John Wiley.

## Timing and Location

 Term: Lent Date(s): 17/01/18 - 21/03/18 Number of sessions: 10 x 2 hour sessions Timing and Location: Wednesdays, weeks 11-20, 11.00-1.00, Bowland North A064 Computer Lab