2. “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

4. Statistics = “getting meaning from data” (Michael Starbird)

5. descriptive statistics “inferential” statistics measures of central values, measures of variation, visualization beating chance!

6. “inferential” statistics beating chance!

7. “inferential” statistics beating chance! Sample Population inference PARAMETERS ESTIMATES

8. But what’s the value of inferential statistics in our field?? 1. More explicit theories 2. More constraints on theory 3. (Limited) generalizability

9. H 0 = there is no difference, or there is no correlation H a = there is a difference; there is a correlation The (twisted) logic of hypothesis testing

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

11. p < 0.05 What does it really mean?

12. p < 0.05 = Given that H 0 is true, this data would be fairly unlikely

13. One- sample t-test Unpaired t-test ANOVA ANCOVA Regression MANOVA χ 2 test Discrimant Function Analysis Paired t-test

14. One- sample t-test Unpaired t-test ANOVA ANCOVA Regression MANOVA χ 2 test Discrimant Function Analysis Paired t-test

15. Linear Model

16. General Linear Model General Linear Model

17. General Linear Model General Linear Model Generalized Linear Model Generalized Linear Model Generalized Linear Mixed Model

18. General Linear Model General Linear Model Generalized Linear Model Generalized Linear Model Generalized Linear Mixed Model

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

22. best fitting line (least squares estimate)

23. the intercept the slope

24. Same intercept, different slopes

25. Positive vs. negative slope

26. Same slope, different intercepts

27. Different slopes and intercepts

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

29. The Linear Model Y ~ b 0 + b 1 *X 1 coefficients

30. The Linear Model Y ~ b 0 + b 1 *X 1 slopeintercept

31. The Linear Model Y ~ 300 + 9*X 1 slopeintercept

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

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

34. The Linear Model Y ~ b 0 + b 1 *X 1 + error

35. The Linear Model Y ~ b 0 + b 1 *X 1 + error

36. is continuous is continuous, too!

37. RT ~ Noise men women

38. men women RT ~ Noise + Gender

39. The Linear Model Y ~ b 0 + b 1 *X 1 + b 2 *X 2 coefficients of slopes coefficient of intercept noise (continuous) gender (categorical)

40. The Linear Model “Response” ~ Predictor(s) Has to be one thing Can be one thing or many things “multiple regression”

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

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

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

44. “Response” ~ Predictor(s) Assumed direction of causality Correlation is (still) not causation