Postgraduate Course: Intermediate inferential statistics: testing and modelling (PGSP11321)
Course Outline
School  School of Social and Political Science 
College  College of Arts, Humanities and Social Sciences 
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. There will also be an introduction to longitudinal analysis. 
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. There will also be an introduction to longitudinal analysis.
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 nonparametric tests
(a) 1 sample
Binomial, chisquare, KolmogorovSmirnov and t tests.
(b) »1 sample  related and independent
McNemar change, Sign, Wilcoxon signedranks, pairedsamples t tests; Fisher's exact, chi square, WicoxonMannWhitney, independent t tests.
Multisample chi square, KruskalWallis 1way ANOVA
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/ANOVA: 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. Parametric ANOVA and ANCOVA tests.
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.
Section E  Longitudinal data
8. Event history analysis
This technique analyses longitudinal data where observations over time are truncated at particular points; e.g. crimefree time, highest age of education, or death.
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.

Entry Requirements (not applicable to Visiting Students)
Prerequisites 

Corequisites  
Prohibited Combinations  
Other requirements  None 
Information for Visiting Students
Prerequisites  None 
High Demand Course? 
Yes 
Course Delivery Information
Not being delivered 
Learning Outcomes
On completion of this course, the student will be able to:
 Understand how to design research to investigate causal and explanatory relationships with quantitative data
 Understand the implications of various levels of data measurement and their related probability distributions
 Demonstrate ability to understand and to solve problems of an inferential nature based on symmetric and asymmetric relationships
 Gain proficiency in the use of statistical software to analyse multivariate data
 Interpret and communicate quantitative solutions in their applied context

Reading List
Core texts:
Field A (2009). Discovering statistics using SPSS (3rd edn). Sage, London. (HUB short loan/Reserve HA32 Fie)
Hair JF, Black WC, Babin BJ and Anderson RE (2014). Multivariate data analysis, (7th edn). PrenticeHall, London. [Previous editions are fine.] (HUB short loan QA278 Hai)
Argyrous G (2011). Statistics for research: with a guide to SPSS (3rd edn). Sage, London. (2nd edition (2005) currently available: HUB short loan/Reserve HA29 Arg)
Tabachnick BG and Fidell LS (2007). Using multivariate statistics (5th edn). Pearson International Edition, Harlow. (HUB Reserve/Standard loan QA278 Tab)
Congdon P (2005). Bayesian models for categorical data.. Wiley, Chichester. (Murray Library/King¿s Buildings QA279.5 Con; ebook) 
Additional Information
Graduate Attributes and Skills 
Not entered 
Additional Class Delivery Information 
The course will be run as ten, threehour, weekly seminars in a computer laboratory, including an introductory lecture and discussion, interspersed with practical exercises, using SPSS (and possibly other statistical software). 
Keywords  statistical inference testing modelling reduction dimensions 
Contacts
Course organiser  Prof Andrew Thompson
Tel: (0131 6)51 1562
Email: Andrew.Thompson@ed.ac.uk 
Course secretary  Mr Jack Smith
Tel: (0131 6)51 1485
Email: Jack.Smith@ed.ac.uk 

