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Jan 14, 2023 •145 likes •681 views

Welcome to the co u rse ! FOU N DATION S OF IN FE R E N C E Jo Hardin Instr u ctor What is statistical inference ? The process of making claims abo u t a pop u lation based on information from a sample FOUNDATIONS OF INFERENCE What is

  1. Welcome to the co u rse ! FOU N DATION S OF IN FE R E N C E Jo Hardin Instr u ctor

  2. What is statistical inference ? The process of making claims abo u t a pop u lation based on information from a sample FOUNDATIONS OF INFERENCE

  3. What is statistical inference ? FOUNDATIONS OF INFERENCE

  4. What is statistical inference ? FOUNDATIONS OF INFERENCE

  5. What is statistical inference ? FOUNDATIONS OF INFERENCE

  6. What is statistical inference ? FOUNDATIONS OF INFERENCE

  7. Ass u me t w o pop u lations prefer cola at same rate FOUNDATIONS OF INFERENCE

  8. The sample data FOUNDATIONS OF INFERENCE

  9. The sample data ( take 2) FOUNDATIONS OF INFERENCE

  10. Vocab u lar y N u ll h y pothesis ( H ) : The claim is not that interesting 0 Alternati v e h y pothesis ( H ) : The claim corresponding to the research h y pothesis A The " goal " is to dispro v e the n u ll h y pothesis FOUNDATIONS OF INFERENCE

  11. E x ample : cheetah speed Compare speed of t w o di � erent s u bspecies of cheetah H : Asian and African cheetahs r u n the same 0 speed , on a v erage H : African cheetahs are faster than Asian A cheetahs , on a v erage FOUNDATIONS OF INFERENCE

  12. E x ample : election From a sample , the researchers w o u ld like to claim that Candidate X w ill w in H : Candidate X w ill get half the v otes 0 H : Candidate X w ill get more than half the A v otes FOUNDATIONS OF INFERENCE

  13. Let ' s practice ! FOU N DATION S OF IN FE R E N C E

  14. Randomi z ed distrib u tions FOU N DATION S OF IN FE R E N C E Jo Hardin Instr u ctor

  15. Logic of inference FOUNDATIONS OF INFERENCE

  16. Logic of inference FOUNDATIONS OF INFERENCE

  17. Logic of inference FOUNDATIONS OF INFERENCE

  18. Logic of inference FOUNDATIONS OF INFERENCE

  19. Logic of inference FOUNDATIONS OF INFERENCE

  20. Logic of inference FOUNDATIONS OF INFERENCE

  21. Understanding the n u ll distrib u tion Generating a distrib u tion of the statistic from the n u ll pop u lation gi v es information abo u t w hether the obser v ed data are inconsistent w ith the n u ll h y pothesis FOUNDATIONS OF INFERENCE

  22. Understanding the n u ll distrib u tion Original data Location Cola Orange East 28 6 West 19 7 ^ east = 28/(28 + 6) = 0.82 p ^ west = 19/(19 + 7) = 0.73 p FOUNDATIONS OF INFERENCE

  23. Understanding the n u ll distrib u tion First sh u� e , same as original Location Cola Orange East 28 6 West 19 7 FOUNDATIONS OF INFERENCE

  24. Understanding the n u ll distrib u tion Second sh u� e Location Cola Orange East 27 7 West 20 6 FOUNDATIONS OF INFERENCE

  25. Understanding the n u ll distrib u tion Third sh u� e Location Cola Orange East 28 8 West 21 5 FOUNDATIONS OF INFERENCE

  26. Understanding the n u ll distrib u tion Fo u rth sh u� e Location Cola Orange East 25 9 West 22 4 FOUNDATIONS OF INFERENCE

  27. Understanding the n u ll distrib u tion Fi � h sh u� e Location Cola Orange East 29 5 West 18 8 FOUNDATIONS OF INFERENCE

  28. Understanding the n u ll distrib u tion Fi � h sh u� e Location Cola Orange East 29 5 West 18 8 FOUNDATIONS OF INFERENCE

  29. Understanding the n u ll distrib u tion FOUNDATIONS OF INFERENCE

  30. Understanding the n u ll distrib u tion FOUNDATIONS OF INFERENCE

  31. Understanding the n u ll distrib u tion FOUNDATIONS OF INFERENCE

  32. Understanding the n u ll distrib u tion FOUNDATIONS OF INFERENCE

  33. Understanding the n u ll distrib u tion FOUNDATIONS OF INFERENCE

  34. Understanding the n u ll distrib u tion FOUNDATIONS OF INFERENCE

  35. One random perm u tation soda %>% library(infer) group_by(location) %>% soda %>% specify(drink ~ location, summarize(prop_cola = success = "cola") %>% mean(drink == "cola")) %>% hypothesize(null = "independence") %>% summarize(diff(prop_cola)) generate(reps = 1, type = "permute") %>% calculate(stat = "diff in props", order = c("west","east")) # A tibble: 1 x 1 `diff(prop_cola)` <dbl> # A tibble: 1 x 2 1 -0.09276018 replicate stat <int> <dbl> 1 1 -0.02488688 FOUNDATIONS OF INFERENCE

  36. Man y random perm u tations soda %>% specify(drink ~ location, success = "cola") %>% hypothesize(null = "independence") %>% generate(reps = 5, type = "permute") %>% calculate(stat = "diff in props", order = c("west", "east")) # A tibble: 5 x 2 replicate stat <int> <dbl> 1 1 0.04298643 2 2 -0.09276018 3 3 0.11085973 4 4 0.17873303 5 5 -0.16063348 FOUNDATIONS OF INFERENCE

  37. Random distrib u tion FOUNDATIONS OF INFERENCE

  38. Let ' s practice ! FOU N DATION S OF IN FE R E N C E

  39. Using the randomi z ation distrib u tion FOU N DATION S OF IN FE R E N C E Jo Hardin Instr u ctor

  40. Understanding the n u ll distrib u tion FOUNDATIONS OF INFERENCE

  41. Understanding the n u ll distrib u tion FOUNDATIONS OF INFERENCE

  42. Understanding the n u ll distrib u tion FOUNDATIONS OF INFERENCE

  43. Understanding the n u ll distrib u tion FOUNDATIONS OF INFERENCE

  44. Understanding the n u ll distrib u tion FOUNDATIONS OF INFERENCE

  45. Data consistent w ith n u ll ? table(soda) soda %>% group_by(location) %>% summarize(mean(drink == "cola")) location drink East West # A tibble: 2 × 2 cola 28 19 location `mean(drink == "cola")` orange 6 7 <fctr> <dbl> 1 East 0.8235294 2 West 0.7307692 FOUNDATIONS OF INFERENCE

  46. Significance FOUNDATIONS OF INFERENCE

  47. Ho w e x treme are the obser v ed data ? # A tibble: 1 x 1 diff_orig <- soda %>% proportion group_by(location) %>% <dbl> summarize(prop_cola = mean(drink == "cola")) %>% 1 0.380 summarize(diff(prop_cola)) %>% pull() soda_perm <- soda %>% specify(drink ~ location, success = "cola") %>% hypothesize(null = "independence") %>% generate(reps = 100, type = "permute") %>% calculate(stat = "diff in props", order = c("west", "east")) soda_perm %>% summarize(proportion = mean(diff_orig >= stat)) FOUNDATIONS OF INFERENCE

  48. Let ' s practice ! FOU N DATION S OF IN FE R E N C E

  49. St u d y concl u sions FOU N DATION S OF IN FE R E N C E Jo Hardin Instr u ctor

  50. Significance We fail to reject the n u ll h y pothesis : There is no e v idence that o u r data are inconsistent w ith the n u ll h y pothesis FOUNDATIONS OF INFERENCE

  51. NHANES : random sample Representati v e sample of US pop u lation Concl u sions from sample ma y appl y to pop u lation Nothing to report in this case FOUNDATIONS OF INFERENCE

  52. Let ' s practice ! FOU N DATION S OF IN FE R E N C E

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