# DEGREE REGULATIONS & PROGRAMMES OF STUDY 2016/2017

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# Postgraduate Course: Intermediate inferential statistics: testing and modelling (PGSP11321)

 School School of Social and Political Science College College of Humanities and Social Science Credit level (Normal year taken) SCQF Level 11 (Postgraduate) Availability Available to all students SCQF Credits 20 ECTS Credits 10 Summary The course is designed for those students who have already acquired a basic understanding of statistics; for example, through the Core Quantitative Data Analysis course run in the first semester. Its aim is to extend and deepen understanding of statistical approaches to data analysis through an appreciation of the process of statistical reasoning prior to designing appropriate quantitative analysis of data. Attention will be given to discrete probability distributions, including Normal approximations, as well as a range of parametric and nonparametric tests. Students will be shown techniques for data reduction and ways to explore the dimensionality in data for potential production of indexes. A number of approaches to regression under different conditions will be considered in depth. Course description The course is designed for those students who have already acquired a basic understanding of statistics; for example, through the Core Quantitative Data Analysis course run in the first semester. Its aim is to extend and deepen understanding of statistical approaches to data analysis through an appreciation of the process of statistical reasoning prior to designing appropriate quantitative analysis of data. Attention will be given to discrete probability distributions, including Normal approximations, as well as a range of parametric and nonparametric tests. Two of the most common approaches to data reduction will be outlined. A number of approaches to regression under different conditions will be considered in depth. Outline content Section A - Theoretical considerations 1. Issues in quantitative research and statistical reasoning Introduction to the course content; introductions by participants to their research interests and their interest in quantification; issues and criticisms of quantitative methods in knowledge creation; statistical reasoning; reliability and validity; estimation; hypothesis testing; significance, power, effect size and sample size; alternatives to significance testing. 2. Design of empirical quantitative investigations Stages of a statistical investigation; exploration and confirmation; errors, outliers, leverage, and missing data; model fitting and residual analysis; causality; levels of measurement and analytical techniques; validity and reliability; guidelines for modelling, analysis and interpretation. Section B - Probability, measurement and comparisons 3. Discrete probability distributions, inc. Normal approximations; continuity corrections and finite population corrections. Uniform (rectangular), binomial and poisson distributions; Normal approximations to discrete distributions; continuity corrections and finite population correction factors. 4. Parametric and non-parametric tests (a) 1 sample Binomial, chi-square, Kolmogorov-Smirnov and t tests. (b) 2 samples - related and independent McNemar change, Sign, Wilcoxon signed-ranks, paired-samples t tests; Fisher's exact, chi square, Wicoxon-Mann-Whitney, independent t tests. (c) More than 2 samples Multi-sample chi square, Kruskal-Wallis 1-way ANOVA, parametric ANOVA, ANCOVA tests. Section C - Data reduction 5. Principal components analysis / Factor analysis Theories of data reduction; statistical assumptions; sampling adequacy; methods of extraction; axis rotation; graphical and statistical interpretation; factor scores; reliability. Section D - Explanation and prediction 6. Multiple regression: assumptions and approaches Linear models with more than two independent variables; purpose of multiple regression (explanation, prediction, controlling, etc); assumptions of linear regression; dummy variables; comparing models for two groups; interpreting the model; odds ratios and log odds. 7. Logistic regression: (a) Binary and multinomial Testing models with a dichotomous dependent variable; logistic regression model formation; proportional odds model; assessing model fit; interpreting the model; issues in model selection. (b) Ordinal Testing models with an ordered dependent variable; categorical scoring approach; proportional odds model; assessing model fit; interpreting the model. Although the principal audience is designed to be social scientists, the course is open to students with backgrounds in social sciences, natural sciences and the humanities who have an interest in developing knowledge, understanding and skills of a quantitative nature. Assessment will take the form of a personal project, based on the statistical analysis of a dataset of a student's choosing, that uses and illustrates the benefits of some of the testing and modelling techniques of this course.
 Pre-requisites Co-requisites Prohibited Combinations Other requirements None
 Pre-requisites None High Demand Course? Yes
 Not being delivered
 On completion of this course, the student will be able to: Understand how to design research to investigate causal and explanatory relationships with quantitative dataUnderstand the implications of various levels of data measurement and their related probability distributionsDemonstrate ability to understand and to solve problems of an inferential nature based on symmetric and asymmetric relationshipsGain proficiency in the use of statistical software to analyse multivariate dataInterpret and communicate quantitative solutions in their applied context
 Core texts: Argyrous G (2011). Statistics for research: with a guide to SPSS (3rd edn). Sage, London. Congdon P (2005). Bayesian models for categorical data, Wiley, Chichester. Field A (2013). Discovering statistics using SPSS (4th edn). Sage, London. Hair JF, Black WC, Babin BJ, Anderson RE and Tatham RL (2013). Multivariate data analysis, (7th edn). Prentice-Hall, London. Tabachnick BG and Fidell LS (2013). Using multivariate statistics, (6th edition), Pearson International, Harlow. General recommended readings: Stevens J (2009). Applied multivariate statistics for the social sciences (5th edn). Routledge, London. Tarling, R (2009). Statistical modelling for social researchers: principles and practice. Routledge, London. Treiman D (2009). Quantitative data analysis: doing social research to test ideas. Jossey Bass, USA.
 Graduate Attributes and Skills Not entered Additional Class Delivery Information The course will be run as a three-hour, weekly seminar in a lecture room and a computer laboratory, including an introductory lecture and discussion, followed by practical exercise workshops, using SPSS (and possibly other statistical software). Keywords statistical inference testing modelling reduction dimensions
 Course organiser Prof Andrew Thompson Tel: (0131 6)51 1562 Email: Andrew.Thompson@ed.ac.uk Course secretary Ms Nicole Develing-Bogdan Tel: (0131 6)51 5067 Email: v1ndeve2@exseed.ed.ac.uk
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