Statistics

1. Statistics Or How to make the numbers say whatever you want.

2. Announcements Free Pizza Lunch with Faculty – Jordan Hall 4th floor lounge Congrats to the four individuals who were successful in the syllabus challenge

3. Manipulating Numbers “There are lies, damned lies, and statistics” -- Disraeli

4. Why use statistics? Anecdotal evidence is unreliable Why does the phone always ring when you’re in the shower?

5. Why use statistics? Determining the difference between chance and real effects

6. Signal and Noise Data = Signal + Noise Signal = What we’re trying to measure Noise = Error in our measurement If noise is random, then as the sample size increases, noise tends to cancel, leaving only signal.

7. The elusive 'average' Mean – arithmetic average = x/n Median – the halfway point Mode – the most common answer

8. The elusive 'average' 1 2 2 2 3 3 Mean = 4.8 Median = 3 Mode = 2 4 4 27

9. The elusive 'average' 0 1 2 3 4 5 Mean = 7.5 Median = 4 Mode = 27 6 27 27

10. The elusive 'average' 1 1 1 2 2 23 Mean = 10.7 Median = 2 Mode = 1 24 26 27

11. Variability Range – Overall difference between the highest and lowest scores. Variance – Average difference from the mean.

12. Variability Identical Range 1 9 9 9 9 9 11 11 11 11 11 19 • 1 1 • 1 1 • 1 1 • 19 19 • 19 19 • 19 19

13. Variability Identical Variance 1 9 9 9 9 9 11 11 11 11 11 19 • 6 6 • 6 6 • 6 7 • 13 14 • 14 14 • 14 14

14. Distributions The Normal Curve

15. Distributions Central Limit Theorem Any time you have a measure which is created by summing several individual trials of data (Signal + Noise) you will end up with a normal curve

16. Signal and Noise Regression to the mean: On any given free throw, Bob has an 80% chance of making it.

17. Distributions Bimodal Distributions

18. Distributions Skewed Distributions

19. Distributions Uniform distributions

20. The P value P value -- The probability that a particular set of data was gained by chance alone. Statistical Significance – Any P value of less than .05

21. The Correlation Correlation measures the strength of a relationship between two variables.

22. The Correlation Positive Correlation 0 < R < 1 Negative Correlation -1 < R < 0 No Correlation R = 0

23. The Correlation Correlation does not imply causation

24. The Correlation Correlations can be misleading!!!

25. The Right Statistic A person wearing red is 129 times more likely to be gored by a charging bull! But what is the base rate?

26. The Right Statistic Mean: 275 minutes Mean: 53 minutes

27. The Right Statistic 98% of Americans have internet access available. The average temperature in Oklahoma City over the past 100 years is 63.4 degrees. (and each year has been within 1 degree of that average)

28. The Right Statistic Consumer spending on prescription drugs has doubled since 1980. 85% of all car accidents occur within 10 miles of the home. 10 times as many people die each year by plane crashes than train crashes.

29. The Right Statistic During the Spanish-American war, the death rate for soldiers was 9 per 1000. The death rate for civilians in New York City was 16 per 1000.

30. Funny Graphs Fluffy O’s Cereal Gives a body Energy!! 10 ?? 5 1 minute 2 minutes

31. Funny Graphs Earnings

32. Funny Graphs Earnings

33. Funny Graphs Even when the scale is fine, graphs can still be deceptive

34. Funny Graphs Even when the scale is fine, graphs can still be deceptive

35. Funny Graphs As you can see, Bob earns substantially more than Joe Joe’s income Bob’s Income

36. Funny Graphs Is it really a two to one ratio that’s being displayed?

37. Funny Graphs Percent of US income going to federal taxes

38. Funny Graphs Percent of US income going to federal taxes

39. Where's the control? Tylenol is used by 90% doctors for their own aches and pains! So are Asprin, Ibuprofen, and Bayer!

40. Semi-attached Numbers When Dewey was elected Governor in 1942, the minimum teacher’s salary in some districts was as low as $900 per year. Upon Governor Dewey’s recommendation… the Legislature in 1947 appropriated $32,000,000 out of state surplus to provide an increase in teacher’s salaries. As a result, the minimum salaries of teachers in New York City range from $2500 to $5325.

41. Semi-attached Numbers 1) Stanford is the #1 program in psychology 2) I am the only (and therefore #1) student at Stanford studying Decision Errors Therefore: I am the top student studying Decision Errors in the country.

42. What drives the data Group A: IIIIIIIVV 6.2 6.4 7.6 6.1 6.2 Group B:IIIIIIIVV 6.1 6.3 2.2 6.0 6.2 Is Group A superior to Group B?

43. Over Precise Numbers The average American sleeps 8 hours a night The average American sleeps 8.2 hours a night The average American sleeps 8.2339 hours a night

44. Interactions Main Effects – Effect of one independent variable on the dependent variable Interactions – When the effectiveness of independent variable X is influenced by another independent variable Y

45. Interactions Curing the Hiccups Cure 1: Standing on Tiptoes Cure 2: Holding Breath Dependent Measure: Number of Hiccups before relief

46. Interactions

47. Interactions

48. Interactions

49. Interactions

50. Interactions Real effect No effect False Positive (Type 1) Find effect Correct Hit False Negative (Type II) Correct Miss Don’t find effect