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

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Objectives Statistical argument Safe designs A whizz through some stats Time for questions 2

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

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4 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

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5 Implications Must have an alt (testable) hyp No multiple testing No post hoc analysis Need multiple experiments

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6 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

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7 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

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Statistical pit… … is bottomless! Safe designs – One (or two) IV – Two (or three) conditions – One primary DV Other stuff is not severely tested 8

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Choosing a test What’s the data type? Do you know the distribution? Within or between What are you looking for? 9

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Seeing location Boxplots Median, IQR, “Range” Outliers 10

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

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

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t-test: null vs alternate 14

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

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

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

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

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

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Basic tests Mann-Whitney Wilcoxon Kruskal-Wallis Friedman No accepted two-way tests 20

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Choosing a test For your fantasy abstract, what test would you choose? Why? Would you change your design? 21

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Questions Specific problems Specific tests Other tests? 22

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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 23

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Multivariate Multiple DV Multivariate normal distribution – Normal no matter how you slice MANOVA Null = one underlying (mv) normal distribution 24

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Issues Sample size Assumptions Interpretation Communication 26

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Monte Carlo Process but not distribution Generate a really large sample Compare to your sample Still theoretically driven! 27

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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! 28

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