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Lord William Thomson, 1st Baron Kelvin

“ I often say that when you can measure what you are speaking about, and express it in numbers, you know something about it ”. Lord William Thomson, 1st Baron Kelvin. Statistics =. “getting meaning from data”. (Michael Starbird ). measures of central values, measures of variation,

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Lord William Thomson, 1st Baron Kelvin

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  1. “I often say that when you can measure what you are speaking about, and express it in numbers, you know something about it” Lord William Thomson,1st Baron Kelvin

  2. Statistics = “getting meaningfrom data” (Michael Starbird)

  3. measures of central values, measures of variation, visualization descriptivestatistics “inferential”statistics beatingchance!

  4. “inferential”statistics beatingchance!

  5. “inferential”statistics Population beatingchance! PARAMETERS ESTIMATES Sample inference

  6. But what’s the valueof inferential statisticsin our field?? 1. More explicit theories 2. More constraints on theory 3. (Limited) generalizability

  7. The (twisted) logic of hypothesis testing H0 = there is no difference, or there is no correlation Ha = there is a difference; there is a correlation

  8. The (twisted) logic of hypothesis testing Type I error = behind bars… … but not guilty Type II error = guilty… … but not behind bars

  9. p < 0.05 What doesit really mean?

  10. p < 0.05 = Given that H0 is true,this data would befairly unlikely

  11. One-sample t-test Pairedt-test Unpairedt-test ANOVA Regression DiscrimantFunction Analysis ANCOVA MANOVA χ2 test

  12. One-sample t-test Pairedt-test Unpairedt-test ANOVA Regression DiscrimantFunction Analysis ANCOVA MANOVA χ2 test

  13. Linear Model

  14. General Linear Model

  15. General Linear Model Generalized Linear Model GeneralizedLinearMixed Model

  16. General Linear Model Generalized Linear Model GeneralizedLinearMixed Model

  17. “response” what you measure RT ~ Noise “predictor” what you manipulate

  18. best fitting line(least squares estimate)

  19. the slope the intercept

  20. Same intercept, different slopes

  21. Positive vs. negative slope

  22. Same slope, different intercepts

  23. Different slopes and intercepts

  24. The Linear Model response ~ intercept + slope * predictor

  25. The Linear Model Y ~ b0 + b1*X1 coefficients

  26. The Linear Model Y ~ b0 + b1*X1 intercept slope

  27. The Linear Model Y ~ 300 + 9*X1 intercept slope

  28. With Y ~ 300 + 9 *x,what is the response time for anoise level of x = 10? 300 + 9*10 = 390 10 300

  29. “fitted values” Deviation from regression line= residual

  30. The Linear Model Y ~ b0 + b1*X1+ error

  31. The Linear Model Y ~ b0 + b1*X1 + error

  32. is continuous is continuous, too!

  33. men RT ~ Noise women

  34. men RT ~ Noise + Gender women

  35. The Linear Model Y ~ b0 + b1*X1 + b2*X2 noise(continuous) gender(categorical) coefficient ofintercept coefficientsof slopes

  36. The Linear Model “Response” ~ Predictor(s) Can be one thingor many things Has to be onething “multiple regression”

  37. The Linear Model “Response” ~ Predictor(s) Has to becontinuous Can be of any data type (continuous or categorical) (we’ll relaxthat constraint later)

  38. The Linear Model examples RT ~ noise + gender pitch ~ polite vs. informal Word Length ~ Word Frequency

  39. Correlation is (still) not causation Edwards & Lambert (2007); Bohrnstedt& Carter (1971); Duncan(1975); Heise(1969); in Edwards & Lambert (2007)

  40. Correlation is (still) not causation “Response” ~ Predictor(s) Assumed directionof causality

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