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Statistical Methods for the Social Sciences 2010-11 (Introduction to Statistics - Lecture) Course Providers: James Tilley Introduction These lectures are for all graduate social scientists, and aim to introduce and familiarize students with methods of statistical analysis. This is very much an introductory course, using a minimum of formal mathematics. The intermediate course in statistical methods in Hilary term builds on the concepts introduced in Michaelmas and there are also more specialised lectures and workshops in particular topics during Trinity term. In most subjects these lectures are accompanied by a workshop in a computer lab using statistical software such as STATA or SPSS (for politics students the STATA workshop website can be found here: Applied Statistics for Social Scientists classes) to analyse empirical data from the relevant discipline. The outline of the course is below, detailed handouts will be available at each lecture. Lectures are in the Experimental Psychology large lecture theatre (on South Parks Road, opposite Linacre college) from 2-4 every Tuesday in weeks 1-8 of Michaelmas term. Reading I recommend two textbooks, either of which covers virtually all the relevant material. Chapter references for each week are below. Agresti A. and Finley, B. (1997), Statistical Methods for the Social Sciences, New Jersey: Prentice-Hall. Wonnacott, T.H. and Wonnacott, R.J. (1990) Introductory Statistics, New York: Wiley. Course Outline Week 1: Introduction to basic descriptive statistics. This part of the lecture will cover types of variables (interval, ordinal and categorical); centres of distributions (the mode, median and mean); spread of distributions (variance and standard deviation); graphs and misleading ways of using simple statistics. References: Agresti and Finley Ch. 3, Wonnacott and Wonnacott Ch. 2. Week 2: Two parts to this lecture. The first looks at sampling. This will cover simple random sampling; problems of non-probability sampling; cluster and stratified random sampling. The second part of the lecture addresses probability and probability distributions, and will cover: basic probability models; the binomial distribution; the normal distribution; the concept of sampling error. References: (Sampling) Agresti and Finley Ch. 2, Wonnacott and Wonnacott Ch. 6. (Probability) Agresti and Finley Ch. 4, Wonnacott and Wonnacott Ch. 3 and 4. Week 3: This lecture covers accuracy of estimates. The first part of the lecture covers standard errors; confidence intervals for means; confidence intervals for proportions. The second part covers hypothesis testing. In particular, null and alternative hypotheses; p-values; type I and II errors. References: (Estimation) Agresti and Finley Ch. 5, Wonnacott and Wonnacott Ch. 8. (Hypothesis testing) Agresti and Finley Ch. 4, Wonnacott and Wonnacott Ch. 9. Week 4: This lecture covers linear regression, and starts with a short explanation of the idea of dependent and independent variables. Move from scatter-plots and fitting a line `by eye', to discussion of the line equation (e.g. the slope and intercept) to OLS regression (e.g. least squares criterion and the error term). Subsidiary topics of confidence intervals for the independent variable effects; hypothesis testing with regression; assumptions of linearity and problems of extrapolation; correlation. References: Agresti and Finley Ch. 9, Wonnacott and Wonnacott Ch. 11 and 12. Week 5: This lecture extends the concepts dealt with in week 4 to multiple regression with continuous and categorical variables. Discussed are: the reasons for controlling for other variables

(with examples of spurious relationships); causality issues in more depth; including categorical variables as dummies; interaction effects; model fit. References: Agresti and Finley Ch. 10 and 11, Wonnacott and Wonnacott Ch. 13 and part of 14. Week 6: The final lecture on linear regression discusses model building and a variety of common problems with regression techniques. The main section of the lecture will focus on regression diagnostics and residual plots. Using examples, this section will cover non-linear relationships, hetereoscedasticity and outliers. Also included in this lecture is a discussion of multicollinearity. References: Agresti and Finley Ch. 14, Wonnacott and Wonnacott Ch. 14 and part of 15. Week 7: This lecture covers contingency tables and odds ratios. In particular, ideas of expected frequencies; the chi-squared test; difference of proportions; odds ratios; measures of association between ordinal variables. References: Agresti and Finley Ch. 8, Wonnacott and Wonnacott Ch. 17. Week 8: The main part of the final lecture introduces logistic regression. Topics covered here will be the reasoning behind the use of logistic regression for binary dependent variables; the relationship between odds ratios and logistic regression; predicted probabilities for logistic regression. The subsidiary part of the lecture briefly sets out some of the topics to be covered in Hilary term and how these fit in with the techniques described during Michaelmas. References: Agresti and Finley Ch. 15.

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