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

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

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

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

5. 5 Gold standard argument 1.Collect data 2.Data variation could be chance (null) 3.Predict the variations (alternative) 4.Statistics give probabilities 5.Unlikely predictions “prove” your case

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

7. 7 Silver standard argument 1.Collect data 2.Data variations could be chance (null) 3.Are there “real” patterns in the data? 4.Use statistics to suggest (unlikely) patterns 5.Follow up findings with gold standard work

8. 8 Fishing: This is bad science 1.Collect lots of data – DVs and IVs 2.Data variations could be chance 3.Test until a significant result appears 4.Report the tests that were significant 5.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? 9

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

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

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

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

14. t-test models 14

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

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

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

18. ANOVA++  Multiple IV – So more F values!  Within and between  Effect size, η 2 – Amount of variance predicted by IV 18

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

20. Wilcoxon test  See sheet 20

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

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23. Multivariate  Multiple DV  Multivariate normal distribution – Normal no matter how you slice  MANOVA  Null = one underlying (mv) normal distribution 23

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25. Issues  Sample size  Assumptions  Interpretation  Communication 25

26. 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? 26

27. Health warnings  Craft skill  Simpler is better – Doing it – Interpreting it – Communicating it  Experiments as evidence  Software packages are deceptively easy 27

28. Q & A  Any question about any aspect  Very general or very specific  Any research method! 28

29. Useful Reading  Cairns, Cox, Research Methods for HCI: chaps 6  Rowntree, Statistics Without Tears  Howell, Fundamental Statistics for the Behavioural Sciences, 6 th edn.  Abelson, Statistics as Principled Argument  Silver, The Signal and the Noise 29

30. Monte Carlo  Process but not distribution  Generate a really large sample  Compare to your sample  Still theoretically driven! 30

31. 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! 31