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Understanding Quantitative Methods: A Comprehensive Guide for Researchers

Explore essential quantitative methods for researchers, focusing on statistical arguments, hypothesis testing, and the importance of prediction. This guide covers comparison of distributions, the implications of gold and silver standard arguments, and the pitfalls of bad science practices like "fishing" for significant results. Learn about choosing the right statistical tests, including parametric and non-parametric methods, effect sizes, ANOVA, and multivariate analysis. Gain insights into crafting an effective abstract and communicating your research findings.

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Understanding Quantitative Methods: A Comprehensive Guide for Researchers

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  1. Quantitative Methods for Researchers Paul Cairns paul.cairns@york.ac.uk

  2. Objectives • Statistical argument • Comparison of distributions • A fly-by of approaches

  3. How are the abstracts? • Questions? • Problems? • Restarts?

  4. Statistical Argument • Inference is an argument form • Prediction is essential • Alternative hypothesis • “X causes Y” • No prediction – measuring noise

  5. Gold standard argument • Collect data • Data variation could be chance (null) • Predict the variations (alternative) • Statistics give probabilities • Unlikely predictions “prove” your case

  6. Implications • Must have an alt hyp • No multiple testing • No post hoc analysis • Need multiple experiments

  7. Silver standard argument • Collect data • Data variations could be chance (null) • Are there “real” patterns in the data? • Use statistics to suggest (unlikely) patterns • Follow up findings with gold standard work

  8. Fishing: This is bad science • Collect lots of data • DVs and IVs • Data variations could be chance • Test until a significant result appears • Report the tests that were significant • Claim the result is important

  9. Statistical inference • Model comparison: • Single distribution (null) • Multiple distributions (alternative) • From samples, which model is better? • From samples, is null likely?

  10. What terms do you know? • The statistical zoo!

  11. Choosing a test • What’s the data type? • Do you know the distribution? • Within or between • What are you looking for?

  12. Distributions • Theoretical stance • Must have this! • Not inferred from samples

  13. Parametric tests • Normal distribution • Two parameters • Null = one underlying normal distribution • Differences in location (mean)

  14. t-test models

  15. t-test • Two samples • Two means • Are means showing natural variation? • Compare difference to natural variation

  16. Effect size • How interesting is the difference? • 2s difference in timings • Significance is not same as importance • Cohen’s d

  17. ANOVA • Parametric • Multiple groups • Why not do pairwise comparison? • Get an F value • Follow up tests

  18. ANOVA++ • Multiple IV • So more F values! • Within and between • Effect size, η2 • Amount of variance predicted by IV

  19. Non-parametric tests • Unknown underlying distribution • Heterogeneity of variance • Non-interval data • Usually test location • Effect size is tricky!

  20. Wilcoxon test • See sheet

  21. Seeing location • Boxplots • Median, IQR, • “Range” • Outliers

  22. Multivariate • Multiple DV • Multivariate normal distribution • Normal no matter how you slice • MANOVA • Null = one underlying (mv) normal distribution

  23. Issues • Sample size • Assumptions • Interpretation • Communication

  24. Your abstract • What sort of data will you produce? • Can you theorise about the distribution? • What sort of test do you think you will need?

  25. Health warnings • Craft skill • Simpler is better • Doing it • Interpreting it • Communicating it • Experiments as evidence • Software packages are deceptively easy

  26. Q & A • Any question about any aspect • Very general or very specific • Any research method!

  27. Useful Reading • Cairns, Cox, Research Methods for HCI: chaps 6 • Rowntree, Statistics Without Tears • Howell, Fundamental Statistics for the Behavioural Sciences, 6thedn. • Abelson, Statistics as Principled Argument • Silver, The Signal and the Noise

  28. Monte Carlo • Process but not distribution • Generate a really large sample • Compare to your sample • Still theoretically driven!

  29. Example • Event = 4 heads in a row from a set of 20 flips of a coin • You have sample of 30 sets • 18 events • How likely? • Get flipping!

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