Say hi to everyone on your table and brainstorm …

• Which statistical tests do you remember and when do you use them?

Wouldn’t it be nice to have one approach that can capture most (all?) of our data problems?

• Provide a unified set of advanced statistical techniques that covers a wider range of data-analysis problems: multilevel generalised linear models
• General framework encapsulating a range of widely used techniques including linear regression, ANOVA, ANCOVA, MANCOVA, logistic regression, Poisson regression, log-linear, random effects / mixed-effects models etc.
• These models arise as special cases of a single underlying general principle.
• Apply this general principle to a wider range of data analysis problems.

• Multilevel generalised linear models will be introduce as sequence of consecutively more general models, all of which build on linear regression.
• Linear regression: review of multiple linear regression and factorial ANOVA.
• General linear models: certain problems, which are poorly handled by ANOVA, can be easily accommodated (e.g. varying slope models).
• Generalised linear models: transformations applied to linear models allows modelling of data-types including categorical, ordinal, discrete frequency data.
• Multi-level models: data with inherently hierarchical structure, which have often been inadequately dealt with.

By the end of this module, you should be able to:

1. Apply advanced statistics to real-world data-analysis problems.
2. Use rational and principled arguments to justify the choice of statistical methods.
3. Engage in peer-to-peer debate about methods and practices of data-analysis.
4. Demonstrate a range of transferable skills, including data-analysis, data-preparation, computer programming, graphical presentation of quantitative evidence, reporting of data-analysis results.

• Why did you choose Statistics III?
• What do you expect to get out off this module?
• How confident do you feel about RStudio; how about stats?
• Is there anything you’re worried about with this module?

• Career opportunities! Stats and statistical software skills transfer to many different areas in academia and industry.
• You will be able to show-off your data analysis skill in your final year project, unless you are using qualitative methods.
• Solid understanding of statistical methods is relevant for planning data collections and making sense of quantitative data.
• Data analysis can be efficient, flexible, reliable, and fast once you have had enough R practice.
• You have the opportunity to improve your data analysis and R skills with three experts.

• 2 \(\times\) 2-hours workshop each week.
• Mixture of theory and practical exercises.
• Together, we will work through statistics problems using R.
• For each topic, there will be detail accompanying lecture notes.
• To engage successfully with this module, attend all workshops, and read the lecture notes.
• For excellent results, you will need to demonstrate independent learning that goes beyond what we cover in class.

Using data-sets of your own choice, perform and report analyses using the tools in 1 – 4 to address a set of theoretical questions to address a research question of relevance to psychology.

1. Logistic regression for binomial data
2. Regression models for count data
3. Multilevel regression models
4. A new methods that was not explicitly covered in class

Psychological relevance: address some non-trivial question of some psychological relevance using your chosen data.

• Very wide range of topics and sub-fields, many of which overlap with many other disciplines.
• Consider the data-set described here published in

Bertrand, M. and Mullainathan, S. (2004). Are Emily and Greg More Employable Than Lakisha and Jamal? A Field Experiment on Labor Market Discrimination. American Economic Review, 94, 991–1013.

• Published in an economics journal but it addresses implicit racial bias, and is obviously related to psychology.

• Choose a different data set per each question.
• 4 separate data analyses reported on no more than 4 pages each.
• For all questions, provide full technical details, and graphical analysis.
• Theoretical model (assumed data-generative process) needs to be motivated.

• Deadline for submission via Dropbox: Jan 12th 2026
• Individual written feedback (by Feb 2nd 2026) to help you how to best carry out and report statistical analyses.
• We are looking for evidence of
  • understanding and knowledge of the theoretical basis.
  • how and why to apply certain statistical models.
  • practical skills in data manipulation and analysis.
• For high or exceptional grades, display learning that goes beyond the content explicitly taught in class.
• See Grading Matrix on NOW for details.

• Work must be submitted as single zip archive with
  • One RMarkdown file
  • PDF document generated from RMarkdown
  • RStudio project file
  • Data and supplementary files (e.g. bibliography, custom R function)
  • For an example see demo on NOW.
• Work must be reproducible using RMarkdown file.
• Your analysis, plots, descriptions, for each question will be contained in RMarkdown file, and this will reference all relevant data files.

• Where do I find data sets:
  • Journals such as Journal of Open Psychology Data, Nature: Scientific data, Bahavior Research Methods, PLOS, Psychonomic Bulletin & Review
  • ONS
  • R data sets
  • OSF, GitHub, figshare
• Pick a topic that has psychological relevance (maybe related to your final project).
• Only restriction: no confidential data.

For all tasks, provide …

• descriptive statistics and graphical visualizations of the data.
• full details of the statistical model that you are using (multiple predictors incl. categorical predictors, interaction terms).
• full statistical details of model fit and comparisons with alternative models.
• full statistical details of the inferred model parameter value estimates.
• analysis, including graphical analysis, of the predictions of the model (model checks).

• Y3 modules require you to go beyond the class contents.
• Look for text books and online tutorials, e.g. my tutorial for mixture models.
• Examples: time series, structural equation modelling (SEM), auto-regression models, non-linear regression, signal detection theory, mixture models, categorical models, multi-nominal models, multi-variate models, diffusion models, Bayesian models …
• For example you could apply a Bayesian ordinal regression as described in Bürkner and Vuorre (2019).
• Tip: keep the analysis simple and focus on demonstrating your understanding of the method used.
• Talk to your supervisor / us re advanced analyses relevant for your project.

• Practice how to write a the kind of report we expect from you.
• Data-analysis report using linear regression to address a psychologically relevant question.
• Support in workshops.
• Just one data analysis hence 4 pages max.
• Submit single zip archive via Dropbox until 24th October 2025, 2pm.
• Feedback on what you did well and what you can improve.
• It does not (directly) affect your grade.

• MS Teams channel for R, stats, assessment-related questions, and useful resources.
• Because our answers will be of interest to everyone / easy code sharing, tagging.
• Also you will receive an answer faster.
• We might refer emails to the forum so everyone can benefit from our answer.
• Help each other!
• Online support will stop at Dec 20 2025.
• For confidential questions contact ML Jens Roeser: jens.roeser@ntu.ac.uk

• How will this module be taught?
• What’s the assessment like?
• How will you be supported?
• What’s expected of you?