Statistical Methods 2

Module Catalogue Description:

This is a year long module, covering work over two semesters. You will be examined at the end of the year on work covered in both semesters

This module will cover the basic concepts and assumptions with respect to univariate and multivariate statistics, as well as issues relating to field studies, ethics, the reliability and validity issues as well as basic qualitative techniques. The module will cover ANOVA, post-hoc tests, power, multiple linear regression, factor analysis, the nature of causality and field designs (both experimental and quasi-experimental), ethics, the reliability and validity of measures and field designs, as well as exploring some basic issues in questionnaire design and qualitative methods.

Module Details:

Aims and Objectives

Semester 1:

Students learn about ANOVA and its related techniques, such as ANCOVA and MANOVA. ANOVA is the most commonly used statistical technique in experimental psychology. This module will provide an understanding of how to perform single factor, multifactor, statistically controlled and multiple dependent variable analyses.

Although there is some calculation involved, the topic quickly provides tools to analyse data from complex designs. Students will learn a computer program to analyse this type of data. Furthermore, the advanced techniques lectures will incorporate SPSS instruction.

The aims of the course are to develop students' understanding of the procedures for analysing complex experimental designs and guidelines for the use of these statistical techniques.

Semester 2:

The main aim and objective of this course is to introduce you to some of the more commonly used multivariate statistical tests and to introduce some basic issues and designs relating to 'field work'.

The lectures will, therefore, cover two general topic areas: (1) basic multivariate tests (lectures 1-5) and (2) methods for 'non' laboratory investigations (lectures 6-10).

For the statistics component you will not be required to perform any computation. Rather the focus is on understanding what types of research question(s)/data, techniques may be used and some basic conceptual understanding of how each technique works. The methods component of the course will explore issue pertaining to the philosophy of science, ethics and design issues.

List of Lectures

Semester 1:

Lecture 1: Experimental design and analysis (pdf)
Lecture 2: Analysis of variance (ANOVA) (pdf)
Lecture 3: Comparisons between means (pdf)
Lecture 4: Testing the assumptions of ANOVA (pdf)
Lecture 5: Statistical Power (pdf)
Lecture 6: Factorial design and analysis (pdf)
Lecture 7: Within subjects ANOVA (pdf)
Lecture 8: Mixed (a.k.a. Split Plot) ANOVA (pdf)
Lecture 9: Analysis of covariance (pdf)
Lecture 10: Multivariate Analysis of Variance & Discriminant Functions Analysis (pdf)
Lecture 11: Revision

Semester 2:

Lecture 1: Regression/correlations (theory)
Lecture 2: Regression/correlations (practice))
Lecture 3: Exploratory factor analysis (theory)
Lecture 4: Exploratory factor analysis (practice)
Lecture 5: Revision of lectures 1 to 4
Lecture 6: Philosophy of science and ethics
Lecture 7: Reliability and validity (questionnaire design)
Lecture 8: Quasi-experiments
Lecture 9: Verbal techniques
Lecture 10: Revision lectures 6 to 9
Lecture 11: Revision (student lead)
Lecture 12: Revision (student lead)

Second year Analysis of Variance and Experimental Design (Semester 1: lectures 1 to 10) - Some basic Multivariate techniques.

This part of the course builds on the parametric statistical techniques introduced in the first year. Analysis of variance is a flexible statistical tool which can be used to test for differences between means for a wide variety of experimental designs, within and between, and, one independent variable or more. It has been extended to deal with the situation where a statistical control is required or when there are multiple dependent variables.

Lecture 1: Experimental design and analysis

This lectures presents some of the basics of experimental design and hypothesis testing. (Additional notes)

Lecture 2: Analysis of variance (ANOVA)

This lecture presents some of the basic concepts that underlie the analysis of variance. The assumptions that need to be met before conducting an ANOVA (analysis of variance) are explained. The meaning of the F statistic, as applied in analysis of variance is discussed. Additional notes are available that provide a more detailed discussion of how these assumptions arise. (Additional notes)

Lecture 3: Comparisons between means

This lecture introduces the calculations required to perform a one-way between groups analysis of variance. It demonstrates how partitioning the variability in the data into different components allows the researcher to test an overall hypothesis concerning the differences between means. Further, the lecture introduces the problem of identifying which means are statistically different. A technique for performing planned (a priori) comparisons is introduced (Additional notes)

Lecture 4: Testing the assumptions of ANOVA

This lecture introduces post hoc comparisons and then moves onto testing the assumptions that underlie the analysis of variance for a one-way between groups analysis of variance. Post hoc comparisons are an important part of the ANOVA technique. When a significant omnibus F is obtained and no a priori predictions have been made it is important to establish which pairs of means differ significantly to correctly interpret the data. Although it seems odd to present this here, it is important to make sure that the ANOVA is the appropriate technique to use given the data that has been collected. A number of techniques are presented for dealing with the situation when the data does not meet ANOVA's assumptions. (Additional notes)

Lecture 5: Statistical Power

This lecture discusses the importance and implications of statistical power both in general and with specific reference to the analysis of variance. A discussion publication is available for reading which provides very good guidance on the use of statistical power in the calculation of effective sample sizes (Effective Sample Size Determination). Also a computer package, GPower is available for downloading by going to the following website: www.psycho.uni-duesseldorf.de/aap/projects/gpower/

Lecture 6: Factorial design and analysis

This lecture introduces factorial designs. A factorial design is when there is more than one independent variable. This lecture is restricted, however, to the situation where there is only one dependent variable. Multiple dependent variables will be covered in the multivariate analysis of variance (manova) lecture later in the course. The basics of partitioning the variability for a between groups design are given and the analysis of interactions through simple main effects analysis is explained. It is expected that students will familiarise themselves with the Experstat computer program (see later under worksheets) to conduct two-way ANOVAs (Additional notes)

Lecture 7: Within subjects ANOVA

This lecture introduces within subject single factor and factorial designs. The advantages and disadvantages of within subject (or repeated measures) designs are discussed relative to between groups designs. The importance of the subject variable is discussed in terms of the reduction in the size of the error estimates for the main effects and interactions. Examples are given of both a single factor and two-way between groups design analysis using ANOVA. The additional assumptions that apply with within subject designs are introduced. (Additional notes)

Lecture 8: Mixed (a.k.a. Split Plot) ANOVA

This lecture introduces mixed (or split plot) designs. A mixed design is when there is at least one between group independent variable and one within subject independent variable. Some of the problems that arise in the analysis of mixed designs are discussed. For example, deciding which is the most appropriate error term is considered a thorny issue for this design.

Lecture 9: Analysis of covariance

This lecture introduces the analysis of covariance (ancova) and how it can be used to achieve statistical control when experimental control is not available. The assumptions that underlie ancova are discussed and a couple of examples are presented. It is important that students should familiarise themselves with SPSS and it's approach to ancova using the general linear model (GLM). Extensive help files are available with SPSS. SPSS runs on both the PC and Apple computers within the School of Psychology

Lecture 10: Multivariate analysis of variance

This lectures introduces the multivariate analysis of variance (manova) and its statistical counterpart, discriminant functions analysis (dfa). The assumptions that underlie both techniques are presented and an example manova and an example dfa are presented. Both these techniques are available using SPSS so it is important that students should familiarise themselves with the approach that SPSS takes. Extensive help files are available with SPSS. SPSS runs on both the PC and Apple computers within the School of Psychology

Worksheets

Alongside the lectures for this course are worksheets which show example analyses. You can either choose to try to complete the worksheet and then check the answers or you can simply use them as guidelines for how to write up ANOVAs. There are five worksheets in total which cover the following designs:

(1) One-way between groups
(2) Transforming data for a one-way between groups
(3) Two-way between groups
(4) Two-way within subjects (or repeated measures)
(5) Two-way mixed (or split plot)

To complete these worksheets it is useful to be able to use statistical packages. A guide to using Experstat (a program available on the Apple computers in the Apple computer lab in the School of Psychology) to complete both worksheet 1 and worksheet 3 is available here. An extensive help file comes with Experstat. Other computer packages, such as SPSS do support analysis of variance as a technique but do not always allow the user to conduct all the different analyses that are required.

Handout

Lecture 2: MLR examples

Worked examples in class
Tabachnick, B., & Fidell, L. (1989) 2nd edition chapter 5
Tabachnick, B., & Fidell, L. (1996) 3rd edition chapter 5

Lecture 3: Exploratory Factor Analysis (EFA)

This lecture will examine one technique designed to uncover 'groupings' of variables within a multiple correlation matrix. After the lecture the students should know about (1) the basic factor model, (2) pre-analysis checks, (3) extraction procedures (K1, Scree and Parallel analysis), (4) factor rotation (orthogonal vs. oblique) and (5) problems of factor naming.
**Ferguson, E & Cox, T. (1992). Exploratory factor analysis: a user guide. International Journal of Selection and Assessment, 1, 84-94. (A rather exceptional piece)

Comrey, A. (1978). Common methodological problems in factor analytical studies. Journal of Clinical and Consulting Psychology, 46, 648 - 659.
Gorsuch, R. (1983) Factor Analysis. LEA Lon. (Good text, but only for those who really like stats and EFA in particular. It is quite heavy going)
Kim, J. and Mueller, (1987). Factor Analysis: Statistical Methods and Practical Issues. Longman NY..
Zwick, W., & Velicer, W. (1986) Comparison of five rules for the determining the number of components to retain. Psychological Bulletin, 99, 432 - 4 42. (Worth reading, but again may be heavy going).
An empirical example from the literature
Ferguson, E. (1993) Rotor's locus of control scale: a ten-item two-factor model. Psychological Reports, 73, 1267-1278 (Short loan GG library)
Ferguson , E., & Daniel, E. (1995) The Illness Attitudes Scale (IAS): A psychometric analysis in a non-clinical population. Personality and Individual Differences, 18, 463-469 (Short loan GG library)
Ferguson, E., & Patterson, F. (1998) The five factor model of personality: Openness a distinct but related construct. Personality and Individual Differences, 24, 789-796 (Short loan GG library)

Handout

Lecture 4 : EFA examples

Worked examples in the class
Tabachnick, B., & Fidell, L. (1989) 2nd edition chapter 12
Tabachnick, B., & Fidell, L. (1996) 3rd edition chapter 13

Lecture 5: Revision of lecture 1 to 4

I will go over the main learning points from lectures 1 to 4. This is also a chance to revisit the ideas and concept discussed in lectures 1 to 4. Students should, therefore, come to this lecture with specific question and queries that can be addressed in the class
Second year Applied Research Methods (lectures 6 to 10) - some issue in non-experimental designs
This aspect of the course aims to introduce you to some basic concepts in the philosophy of science, some basic quasi-experimental designs, ethics, reliability & validity and free-response methods.

Lecture 6: The philosophy of science and ethics

This lecture will examine the nature of scientific enquiry and examine what is understood by scientific fact. This lecture will examine the social aspects of science. The student should know something about: (1) a definition of science, (2) understandings of causality, (3) nature of scientific ‘truth’ (realist vs. anti-realist), (4) scientific fraud and some of the basic ethical considerations when conducting experiments on human subjects
Philosophy of science
**Derksen, M. (1997). Are we not experimenting then? The rhetorical demarcation of psychology and common sense. Theory & Psychology, 7, 435-456
**Gergen, K. (1973) Social psychology as history. Journal of Personality and Social Psychology, 26, 309 - 320.
**Manicas, P., & Secord, P. (1983) Implications for psychology of the new philosophy of science. American Psychologist, 38, 399 - 413. (Heavy going but worth it).
**Mook, D. (1983) In defence of external invalidity. American Psychologist, 38, 379 - 387.
**Gergen, K. (1984) The social constructionist movement in modern psychology. American Psychologist, 40, 266 - 275
Kimble, G. (1994). A frame of reference for psychology. American Psychologist, 49, 510-519
Scarr, S. (1985). Constructing psychology: making facts and fables for our times. American Psychologist, 40, 499 - 512.

Ethics**Adair, J., Dushenko, T., & Lindsay, R. (1985) Ethical regulations and their impact on research practice. American Psychologist. 40, 59 - 72.
**British Psychological Society. (1978) Ethical principals for research with human subjects. Bulletin of the British Psychological Society, 31, 48 - 49
**Kendler, H. (1993) Psychology and the ethics of social policy. American Psychologist, 48, 1046-1053

Handout

Lectures 7: Reliability and validity.

Different types of scales will be briefly discussed, as will methods of test construction, with pitfalls noted and ways to avoid common mistakes examined. Students should understand (1) the concepts of reliability and validity (being able to distinguish different types of reliability and validity), (2) the basics of question writing and (3) how to avoid biases when developing a questionnaires
**Anastasi, A (1988) Psychological Testing. 6th Edition.N.Y. MacMillan
**Campbell, D., & Fiske, D (1959) Convergent and divergent validation by the multitrait-multimethod matrix. Psychological Bulletin, 56, 81 - 105
**Cone, J. (1977) The relevance of reliability and validity for behavioral assessment. Behavior Therapy, 8, 411 - 426. (Short loan GG library)
**Kline. P. (1986) A Handbook of Test Construction: Introduction to Psychometric Design. London, Methuen and Co.
**Roberson, M.., & Sundstrom, E. (1990) Questionnaire design, return rates, and response favorableness in an employee attitude questionnaire. Journal of Applied Psychology, 75, 354 - 357.
Cox, T., Thirlaway, M., Gotts, G., & Cox, S. (1983) The nature and measurement of general well-being. Journal of Psychosomatic Research, 27, 353 - 360.
Nunnally Jnr. J. (1978) Psychometric Theory. NY, McGraw-Hill.
Steinberg, L. (1994) Context and serial order effects in personality measurement: limits on the generality of measuring changes the measure. Journal of Personality and Social Psychology, 66, 341-349.
An empirical example from the literature
Ferguson, E. & Cox, T. (1997) The functional dimensions of coping scale: theory, reliability and validity. British Journal of Health Psychology, 2 109-129. (Short loan GG library)
Ferguson, E., Cox, T., Irving, K., Leiter, M., & Farnsworth, W. (1995) A measure of medical and non-medical students' knowledge and confidence in knowledge of HIV and AIDS: reliability and validity. AIDS Care, 7, 211-228 (Short loan GG library
Robson (1995) pp 66-75

Handout

Lectures 8: Quasi-experimental designs

This lecture will examine what differentiates true experiments from quasi-experiments (random allocation to groups) and explore 1 type of quasi-experimental design (the interrupted times series design). Problems with the generalizability of research findings will be discussed, as will problems with interpreting findings when random allocation to groups is not possible. Students should understand: (1) the difference between experimental and quasi-experimental design (random allocation to groups), (2) threats to internal, external reliability/validity of all types of experiments, (3) interrupted times series design and (4) Mook’s position on generalizability
**Campbell, D. (1978). Reforms as experiments. In. Bynner, J. and Stribley, K. (Eds.). Social research: principles and procedures. Open University Press.
**Eysenck, H. (1975) Who needs a random sample? The Psychologist: Bulletin of the British Psychological Society, 28, 195 - 198.
**Kish, L (1978) Some statistical problems in research design. In. Bynner, J. and Stribley, K. (Eds.). Social research: principles and procedures. Milton Keynes, Open University Press.
**Mook, D. (1983) In defence of external invalidity. American Psychologist, 38, 379 - 387
**Orne, M. T. (1962) On the social psychology of the psychology experiment with particular reference to demand characteristics and their implications. American Psychologist, 17, 776 - 783.
**Overall, J., & Woodward, A. (1977) Nonrandom assignment and the analysis of covariance. Psychological Bulletin, 84, 588 - 594.
**Vaught, R. (1977) What if subjects can't be randomly assigned? Human Factors, 19, 227 - 234
Robson (1995) Chapter 4
An empirical example from the literature
Ferguson, E., Dodds, A., Craig, D., Flannigan, H., & Yates, L. (1994) The changing face of adjustment to sight loss: a longitudinal evaluation of rehabilitation. Journal of Social Behavior and Personality, 9, 287-306 (Short loan GG library
Ferguson, E., Singh, A. & Cunningham-Snell, N. (1997) Stress and blood donation: effects of music and previous donation experience. British Journal of Psychology, 88, 277-294

Handout

Lecture 9: Free response/diary methods.

This lecture will explore other techniques for gathering data. Students should understand the major issues (i.e., the pitfalls to avoid and the basic processes involved in these methods) relating to (1) interviews, (2) participant observation, (3) content analysis, (4) discourse analysis, (5) diary studies and (6) verbal protocols.
**Ericsson, K., & Simon, H. (1980) Verbal reports as data. Psychological Review, 87, 215-251
**Potter, J., & Wetherall, M. (1987) Discourse and social psychology: beyond attitudes and behaviour. London. Sage (In particular chapter 1)
**Wheeler, L., & Reis, H. (1991) Self-recording of everyday life events: origins, types and uses. Journal of Personality, 59, 339-354
Banaji, M., & Crowder, R. (1989) The bankruptcy of everyday memory. American Psychologist., 44, 1185 - 1193.
Krippendorff, K. (1981) Content analysis: an introduction to its methodology. London. Sage
Maurer, T., Palmer, J., & Ashe, D. (1993). Diaries, checklists, evaluations, and contrast effects in measurement of behavior. Journal of Applied Psychology, 78, 226-231
An empirical example from the literature
Silvester, J., Ferguson, E. & Patterson, F. (1997) Comparing spoken attributions by German and British engineers: Evaluating a culture change programme. European Journal of Work and Organizational Psychology, 6, 103-117. (Short loan GG library
Ferguson, E. & Cox, T. (1997) The functional dimensions of coping scale: theory, reliability and validity. British Journal of Health Psychology, 2 109-129 (Short loan GG library)
Robson (1995) Chapters 5-6

Handout

Lecture 10: Revision lectures 6 to 9

I will go over the main learning points from lectures 6 to 9. This is also a chance to revisit the ideas and concept discussed in lectures 6 to 9. Students should, therefore, come to this lecture with specific question and queries that can be addressed in the class

Lecture 11: Revision (student lead)

Both lecturers will be present to answer questions on any aspect of the course materials. Again students should come prepared with questions.

Lecture 12: Revision (student lead)

Both lecturers will be present to answer further questions on any aspect of the course materials. Again students should come prepared with questions.Journals If you wish to keep up to date with developments then look at: Psychological Bulletin, The British Journal of Mathematical and Statistical Psychology, Psychometricka, Psychological Methods, Theory & Psychology, American Psychologist.

General References

Semester 1:

For those lectures that focus on ANOVA:

Keppel, G., Saufley, W.H.,Tokunaga, H. (1992) Introduction to Design and Analysis. This book can be found in the library. It is rather expensive to buy.

For those lectures that focus on ANCOVA and MANOVA:

Tabachnick, B., & Fidell, L.S. (2001). Using Multivariate Statistics (4th ed.).
Earlier editions are fine for ANCOVA and MANOVA.

Semester 2:

General information on references:

Key texts and references are marked with an (**). Students should read these prior to the relevant lecture. The lectures will cover quite complex material and reading prior to the lecture will aid your understanding of each lecture and the course as a whole.

• Ferguson, E., & Bibby, P. (2003). The design and analysis of quasi-experimental field research. In G Breakwell (Ed.) Doing Social Psychology Research. BPS/Blackell, Oxford (pp 93-127). (short loan)

This book chapter covers most of the material to be addressed in this course and should act as a good general overview of the ideas and themes in the course. You will need to read the other recommended texts for a full understanding of the material, but this chapter should provide you with the necessary framework for integrating the material.

Good text for lectures 1-5:

Dancey, C., & Reidy, J. (1999). Statistics without maths for psychology: Using SPSS for Windows. Prentice Hall, London
Green, S., Salkins, N., & Akey, T. (2000). Using SPSS for windows: Analyzing and understanding data (2nd edition). Prentice Hall, London
Howitt, D., & Cramer D. (2000). An introduction to statistics in Psychology: A complete guide for students (2nd edition). Pearson Education, Prentice Hall, London.
Tabachnick, B., & Fidell, L. (1996). Using multivariate statistics. Harper and Row. (copies also in the George Green and Medical school libraries)

Good references for lectures 6-10:

Robson, C. (1995). Real world research. Blackwell: Oxford. (copies in the George Green, Hallwood and Medical school libraries)
Rosenthal, R., & Rosnow, R. (1991). Essential of behavioral research: method and data analysis (2nd Edition). New York, McGraw-Hill. (copies in the George Green, Hallwood and Medical school libraries)

Method and Frequency of Class

One hour lecture per week.

Assessment

This will be in terms of a single 3-hour exam at the end of the course in semester 2. The exam format is in 4 sections. You must answer questions from all four sections. Sections 1 and 2 will relate to the semesters 1 and 2, section 3 will relate to work covered in semester 1 and 4 primarily to the work covered in semester 2. Students are recommended to spend 45 minute on each section. Each section is equally weighed in terms of the overall mark for the paper.

• Sections 1 and 2 will consist of multiple-choice questions. Section 1 will focus on semester 1 and section 2 on semester 2.
• Section 3 will require you to
  • EITHER
  • write a results section based on a computer printout focusing on the techniques presented in semester 1.
  • OR
  • answer an essay based question on the statistics and method discussed in semester 1
• Section 4 (covering work in semester 2) will provide you with a choice between
  • EITHER
  • (1) reading a method section from a journal and writing an evaluative summary of the methods and statistics used. You will be given the abstract and the method,.
    OR
  • (2) answering an essay based question on the statistics and method discussed in semester two.

While the exam is split into these sections to reflect the nature of the course the students are reminded that this is a year long module and that they should integrate ideas across the two semesters especially in essay and data response style questions (i.e., section 3 and 4).