1. 1 Economics 240A Power One

2. 2 Outline w Course Organization w Course Overview w Resources for Studying

4. Organization ( Cont.)

5. 5 Course Overview w Topics in Statistics Descriptive Statistics Exploratory Data Analysis Probability and Distributions Proportions Interval Estimation Hypothesis Testing Correlation and Regression Analysis of Variance

6. 6 http://research.stlouisfed.org/fred2/

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12. 12 Resources for Studying w Keller & Warrack Text Readings CDROM PowerPoint Slide Shows Appletns w Instructor Lecture Notes Lab Notes & Exercises Problem Sets PowerPoint Slide Shows

13. 13 http://econ.ucsb.edu

14. 14 Keller & Warrack CDROM

15. 15 http://www.duxbury.com/statistics

16. 16 Student Book Companion Siten

17. 17 Keller & Warrack Slide Show w Excerpts from Ch. 2

18. 18 Graphical Descriptive Techniques Chapter 2

19. 19 2.1 Introduction w Descriptive statistics involves the arrangement, summary, and presentation of data, to enable meaningful interpretation, and to support decision making. w Descriptive statistics methods make use of graphical techniques numerical descriptive measures. w The methods presented apply to both the entire population the population sample

20. 20 2.2Types of data and information w A variable - a characteristic of population or sample that is of interest for us. Cereal choice Capital expenditure The waiting time for medical services w Data - the actual values of variables Interval data are numerical observations Nominal data are categorical observations Ordinal data are ordered categorical observations

21. 21 Types of data - examples Interval data Age - income 5575000 4268000.. Age - income 5575000 4268000.. Weight gain +10 +5. Weight gain +10 +5. Nominal Person Marital status 1married 2single 3single.. Person Marital status 1married 2single 3single.. Computer Brand 1IBM 2Dell 3IBM.. Computer Brand 1IBM 2Dell 3IBM..

22. 22 Types of data - examples Interval data Age - income 5575000 4268000.. Age - income 5575000 4268000.. Nominal data With nominal data, all we can do is, calculate the proportion of data that falls into each category. IBM Dell Compaq OtherTotal 25 11 8 6 5 0 50% 22% 16% 12% IBM Dell Compaq OtherTotal 25 11 8 6 5 0 50% 22% 16% 12% Weight gain +10 +5. Weight gain +10 +5.

23. 23 Types of data – analysis  Knowing the type of data is necessary to properly select the technique to be used when analyzing data.  Type of analysis allowed for each type of data Interval data – arithmetic calculations Nominal data – counting the number of observation in each category Ordinal data - computations based on an ordering process

24. 24 Cross-Sectional/Time-Series Data w Cross sectional data is collected at a certain point in time Marketing survey (observe preferences by gender, age) Test score in a statistics course Starting salaries of an MBA program graduates w Time series data is collected over successive points in time Weekly closing price of gold Amount of crude oil imported monthly

25. 25 2.3 Graphical Techniques for Interval Data w Example 2.1: Providing information concerning the monthly bills of new subscribers in the first month after signing on with a telephone company. Example 2.1 Collect data Prepare a frequency distribution Draw a histogram

26. 26 Largest observation Collect data (There are 200 data points Prepare a frequency distribution How many classes to use? Number of observations Number of classes Less then 505-7 50 - 2007-9 200 - 5009-10 500 - 1,00010-11 1,000 – 5,00011-13 5,000- 50,00013-17 More than 50,00017-20 Class width = [Range] / [# of classes] [119.63 - 0] / [8] = 14.95 15 Largest observation Largest observation Smallest observation Smallest observation Smallest observation Smallest observation Largest observation Example 2.1Example 2.1: Providing information

27. 27 Draw a Histogram Example 2.1Example 2.1: Providing information

28. 28 nnnn 0 20 40 60 80 153045607590 105120 Bills Frequency What information can we extract from this histogram About half of all the bills are small 71+37=108 13+9+10=32 A few bills are in the middle range Relatively, large number of large bills 18+28+14=60 Example 2.1Example 2.1: Providing information

29. 29 w It is generally best to use equal class width, but sometimes unequal class width are called for. w Unequal class width is used when the frequency associated with some classes is too low. Then, several classes are combined together to form a wider and “more populated” class. It is possible to form an open ended class at the higher end or lower end of the histogram. Class width

30. 30 w There are four typical shape characteristics Shapes of histograms

31. 31 Positively skewed Negatively skewed Shapes of histograms

32. 32 A modal class is the one with the largest number of observations. A unimodal histogram The modal class Modal classes

33. 33 Descriptive Statistics w Central Tendency mode median mean w Dispersion standard deviation interquartile range (IQR)

34. 34 http://www.dof.ca.gov/

35. 35 http://research.stlouisfed.org/fred2/

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37. 37 Concepts w What do we mean by central tendency? w Possibilities What is the most likely outcome? What outcome do we expect? What is the outcome in the middle?

38. 38 Moving from Concepts to Measures w Mode: most likely value.

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41. 41 Moving from Concepts to Measures w Mode: most likely value. w Median: sort the data from largest to smallest. The observation with half of the values larger and half smaller is the median.

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43. 43 Moving from Concepts to Measures w Median: sort the data from largest to smallest. The observation with half of the values larger and half smaller is the median. w Mode: most likely value. w Mean or average: sum the values of all of the observations and divide by the number of observations.

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45. 45 Concepts w What do we mean by dispersion? w Possibilities How far, on average are the values from the mean? What is the range of values from the biggest to the smallest?

46. 46 Exploratory Data Analysis w Stem and Leaf Diagrams w Box and Whiskers Plots

47. Males: 140 145 160 190 155 165 150 190 195 138 160 155 153 145 170 175 175 170 180 135 170 157 130 185 190 155 170 155 215 150 145 155 155 150 155 150 180 160 135 160 130 155 150 148 155 150 140 180 190 145 150 164 140 142 136 123 155 Females: 140 120 130 138 121 125 116 145 150 112 125 130 120 130 131 120 118 125 135 125 118 122 115 102 115 150 110 116 108 95 125 133 110 150 108 Weight Data

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50. 50 Box Diagram First or lowest quartile; 25% of observations below Upper or highest quartile 25% of observations above median

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52. 52 Whiskers w The whiskers end with points that are not outliers w Outliers are beyond 1.5 times the interquartile range ( in this case IQR = 31), so 1.5*31 = 46.5 w 1 st quartile – 1.5*IQR = 125 – 46.5 = 78.5,but the minimum is 95 so the lower whisker ends with 95.

53. 3 rd Quartile + 1.5* IQR = 156 + 46.5 = 202.5; 1 st value below =195