1. Looking at Data

3. Descriptive Statistics

4. Types of Variables: Overview Categorical Quantitative continuous discrete ordinal nominal binary 2 categories + more categories + order matters + numerical + uninterrupted

13. The first rule of statistics: USE COMMON SENSE! 90% of the information is contained in the graph.

16. Bar Chart: categorical variables no yes

17. Much easier to extract information from a bar chart than from a table! Bar Chart for SI categories Number of Patients Shock Index Category 0.0 16.7 33.3 50.0 66.7 83.3 100.0 116.7 133.3 150.0 166.7 183.3 200.0 1 2 3 4 5 6 7 8 9 10

19. 0.0 0.7 1.3 2.0 SI Box Plot: Shock Index Shock Index Units “ whisker” Q3 + 1.5IQR = .8+1.5(.25)=1.175 75th percentile (0.8) 25th percentile (0.55) maximum (1.7) interquartile range (IQR) = .8-.55 = .25 minimum (or Q1-1.5IQR) Outliers median (.66)

20. Note the “right skew” Bins of size 0.1 0.0 8.3 16.7 25.0 0.0 0.7 1.3 2.0 Histogram of SI SI Percent

21. 100 bins (too much detail)

22. 2 bins (too little detail)

23. Also shows the “right skew” 0.0 0.7 1.3 2.0 SI Box Plot: Shock Index Shock Index Units

24. 0.0 33.3 66.7 100.0 AGE Box Plot: Age Variables Years More symmetric 75th percentile 25th percentile maximum interquartile range minimum median

25. Histogram: Age Not skewed, but not bell-shaped either… 0.0 4.7 9.3 14.0 0.0 33.3 66.7 100.0 AGE (Years) Percent

26. Some histograms from last year’s class (n=18) Starting with politics…

29. Feelings about math and writing…

30. Optimism…

35. Mean of age in Kline’s data The balancing point 0.0 4.7 9.3 14.0 0.0 33.3 66.7 100.0 Percent

36. Mean of Pulmonary Embolism? (Binary variable?) 19.44% (181) 80.56% (750)

41. Median of age in Kline’s data 0.0 4.7 9.3 14.0 0.0 33.3 66.7 100.0 Percent 50% of mass 50% of mass

50. 0.0 4.7 9.3 14.0 0.0 33.3 66.7 100.0 Range of age: 94 years-15 years = 79 years AGE (Years) Percent

54. Interquartile Range: age Median (Q2) maximum minimum Q1 Q3 25% 25% 25% 25% 15 35 49 65 94 Interquartile range = 65 – 35 = 30

58. Calculation Example: Sample Standard Deviation Age data (n=8) : 17 19 21 22 23 23 23 38 n = 8 Mean = X = 23.25

59. 0.0 4.7 9.3 14.0 0.0 33.3 66.7 100.0 AGE (Years) Percent Std. dev is a measure of the “average” scatter around the mean. Estimation method: if the distribution is bell shaped, the range is around 6 SD, so here rough guess for SD is 79/6 = 13

61. 0.0 62.5 125.0 187.5 250.0 0.0 0.5 1.0 1.5 2.0 Std Dev of Shock Index SI Count Estimation method: if the distribution is bell shaped, the range is around 6 SD, so here rough guess for SD is 1.4/6 =.23 Std. dev is a measure of the “average” scatter around the mean.

63. Std. Dev of binary variable, PE Std. dev is a measure of the “average” scatter around the mean. 19.44% 80.56%

68. **The beauty of the normal curve: No matter what  and  are, the area between  -  and  +  is about 68%; the area between  -2  and  +2  is about 95%; and the area between  -3  and  +3  is about 99.7%. Almost all values fall within 3 standard deviations.

69. 68-95-99.7 Rule 68% of the data 95% of the data 99.7% of the data

71. Examples of bad graphics

72. What’s wrong with this graph? from : ER Tufte. The Visual Display of Quantitative Information. Graphics Press, Cheshire, Connecticut, 1983, p.69

73. From: Visual Revelations: Graphical Tales of Fate and Deception from Napoleon Bonaparte to Ross Perot Wainer, H. 1997, p.29. Notice the X-axis

74. Correctly scaled X-axis…

75. Report of the Presidential Commission on the Space Shuttle Challenger Accident , 1986 (vol 1, p. 145) The graph excludes the observations where no O-rings failed.

77. Even better: graph all the data (including non-failures) using a logistic regression model Tappin, L. (1994). "Analyzing data relating to the Challenger disaster". Mathematics Teacher , 87, 423-426

78. What’s wrong with this graph? from : ER Tufte. The Visual Display of Quantitative Information. Graphics Press, Cheshire, Connecticut, 1983, p.74

80. What’s the message here? Diagraphics II , 1994

81. Diagraphics II , 1994

94. Where did the statistics come from? The 15%: Dummer GM, Rosen LW, Heusner WW, Roberts PJ, and Counsilman JE. Pathogenic weight-control behaviors of young competitive swimmers. Physician Sportsmed 1987; 15: 75-84. The “to”: Rosen LW, McKeag DB, O’Hough D, Curley VC. Pathogenic weight-control behaviors in female athletes. Physician Sportsmed . 1986; 14: 79-86. The 62%:Rosen LW, Hough DO. Pathogenic weight-control behaviors of female college gymnasts. Physician Sportsmed 1988; 16:140-146.