Statistics
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This document discusses various statistical concepts and ways that numbers and data can be manipulated or misleading. It provides examples of common statistical measures like mean, median, and mode. It also discusses how graphs and scales can be deliberately misleading. The document emphasizes the importance of critically analyzing data and not taking numbers at face value, as statistics can be easily manipulated to portray whatever message is desired.
Statistics
- 1. Or How to make the numbers say whatever you want.
- 2. Free Pizza Lunch with Faculty Jordan Hall 4th floor lounge Congrats to the four individuals who were successful in the syllabus challenge
- 3. There are lies, damned lies, and statistics -- Disraeli
- 4. Anecdotal evidence is unreliable Why does the phone always ring when youre in the shower?
- 5. Determining the difference between chance and real effects
- 6. Data = Signal + Noise Signal = What were 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. Mean arithmetic average = Sx/n Median the halfway point Mode the most common answer
- 8. 1 4 3 2 2 2 3 4 27 Mean = 4.8 Median = 3 Mode = 2
- 9. 0 6 5 1 2 3 4 27 27 Mean = 7.5 Median = 4 Mode = 27
- 10. 1 24 23 1 1 2 2 26 27 Mean = 10.7 Median = 2 Mode = 1
- 11. Range Overall difference between the highest and lowest scores. Variance Average difference from the mean.
- 12. 1 9 9 9 9 9 11 11 11 11 11 19 Identical Range 1 1 1 1 1 1 19 19 19 19 19 19
- 13. 1 9 9 9 9 9 11 11 11 11 11 19 Identical Variance 6 6 6 6 6 7 13 14 14 14 14 14
- 14. The Normal Curve
- 15. 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. Regression to the mean: On any given free throw, Bob has an 80% chance of making it.
- 20. 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. Correlation measures the strength of a relationship between two variables.
- 22. Positive Correlation 0 < R < 1 No Correlation R = 0 Negative Correlation -1 < R < 0
- 23. Correlation does not imply causation
- 24. Correlations can be misleading!!!
- 25. A person wearing red is 129 times more likely to be gored by a charging bull! But what is the base rate?
- 26. Mean: 275 minutes Mean: 53 minutes
- 27. 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. 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. 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. Fluffy Os Cereal Gives a body Energy!! 1 minute 2 minutes 10 5 ??
- 31. 62.5 62 61.5 61 60.5 60 1st Qtr 2nd Qtr 3rd Qtr 4th Qtr Earnings
- 32. 100 90 80 70 60 50 40 30 20 10 0 1st Qtr 2nd Qtr 3rd Qtr 4th Qtr Earnings
- 33. 40 35 30 25 20 15 10 5 0 1st Qtr 2nd Qtr 3rd Qtr 4th Qtr Even when the scale is fine, graphs can still be deceptive
- 34. Even when the scale is fine, graphs can still be deceptive 40 35 30 25 20 15 10 5 0 1st Qtr 2nd Qtr 3rd Qtr 4th Qtr
- 35. As you can see, Bob earns substantially more than Joe Joes income Bobs Income
- 36. Is it really a two to one ratio thats being displayed?
- 37. Percent of US income going to federal taxes
- 38. Percent of US income going to federal taxes
- 39. Tylenol is used by 90% doctors for their own aches and pains! So are Asprin, Ibuprofen, and Bayer!
- 40. When Dewey was elected Governor in 1942, the minimum teachers salary in some districts was as low as $900 per year. Upon Governor Deweys recommendation the Legislature in 1947 appropriated $32,000,000 out of state surplus to provide an increase in teachers salaries. As a result, the minimum salaries of teachers in New York City range from $2500 to $5325.
- 41. 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. Group A: I II III IV V 6.2 6.4 7.6 6.1 6.2 Group B: I II III IV V 6.1 6.3 2.2 6.0 6.2 Is Group A superior to Group B?
- 43. 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. 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. Curing the Hiccups Cure 1: Standing on Tiptoes Cure 2: Holding Breath Dependent Measure: Number of Hiccups before relief
- 46. 30 25 20 15 10 5 0 Control Tiptoe Control Hold Breath
- 47. 30 25 20 15 10 5 0 Control Tiptoe Control Hold Breath
- 48. 30 25 20 15 10 5 0 Control Tiptoe Control Hold Breath
- 49. 30 25 20 15 10 5 0 Control Tiptoe Control Hold Breath
- 50. Real effect No effect Find effect Dont find effect Correct Hit False Positive (Type 1) Correct Miss False Negative (Type II)
- 51. Critical Analysis of psychology in the popular press 2-3 pages (double spaced, normal font/margins) 4 articles to choose from You may discuss the articles with classmates, but under the honor code you must write your own analysis.
- 52. 1) Statistics are useful for figuring out random noise from real effects 2) Numbers are not absolute, and they can be easily manipulated 3) Always scrutinize data closely, and draw your own conclusions. 4) 85% of all statistics are made up on the spot: the rest are all wrong