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Economics 240A

Economics 240A. Power One. Outline. Course Organization Course Overview Resources for Studying. Organization ( Cont.). Course Overview. Topics in Statistics Descriptive Statistics Exploratory Data Analysis Probability and Distributions Proportions Interval Estimation

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Economics 240A

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  1. Economics 240A Power One

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

  3. Organization ( Cont.)

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

  5. Concepts 1 • Two types of data: • Time series • Cross section

  6. http://research.stlouisfed.org/fred2/ Index 1982-84 =100

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

  8. CPIAUCNS Jan 1921- Aug 2007

  9. Examples of: • Graphical Display of Results • Cross-Section Data • Survey Sample of 12,571 • Men & women • Ages 15-44

  10. What is the Message?

  11. Concepts 2 • Population Versus Sample • Iowa Caucuses, New Hampshire Primary • Population: All eligible voters • Sample: Field poll in California sample Pop

  12. Concepts 3 • Different views of the world (universe) • Deterministic • Stochastic

  13. Statistical Inference and Probability • Deterministic • Newtonian physics: e g. distance = rate*time • Einsteinian(relativistic) physics: E=m*c2 • Stochastic (random) • Quantum mechanics

  14. Statistical Inference and Probability • Probability: A tool to understand chance • What is chancy about the statistical world we will study? • Example: • Suppose I number everyone in the class from 1 to 65? • And draw one number a meeting to ask a question; what is the likelihood I will call on you today?

  15. Keller Text Readings CDROM Applets Instructor Lecture Notes Lab Notes & Exercises Problem Sets PowerPoint Slide Shows Resources for Studying

  16. Keller CDROM

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

  18. Student Book Companion Site

  19. Concepts 4 • Three types of data • Cardinal • Ordinal • Categorical

  20. Keller & Warrack Slide Show • Excerpts from Ch. 2

  21. Chapter 2 Graphical Descriptive Techniques

  22. 2.1 Introduction • Descriptive statistics involves the arrangement, summary, and presentation of data, to enable meaningful interpretation, and to support decision making. • Descriptive statistics methods make use of • graphical techniques • numerical descriptive measures. • The methods presented apply to both • the entire population • the population sample

  23. 2.2 Types of data and information • A variable - a characteristic of population or sample that is of interest for us. • Cereal choice • Capital expenditure • The waiting time for medical services • Data - the actual values of variables • Interval data are numerical observations • Nominal data are categorical observations • Ordinal data are ordered categorical observations

  24. Types of data - examples Interval data Nominal Age - income 55 75000 42 68000 . . . . PersonMarital status 1 married 2 single 3 single . . . . Weight gain +10 +5 . . Computer Brand 1 IBM 2 Dell 3 IBM . . . .

  25. Types of data - examples Interval data Nominal data With nominal data, all we can do is, calculate the proportion of data that falls into each category. Age - income 55 75000 42 68000 . . . . Weight gain +10 +5 . . IBM Dell Compaq Other Total 25 11 8 6 50 50% 22% 16% 12%

  26. 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

  27. Cross-Sectional/Time-Series Data • 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 • Time series data is collected over successive points in time • Weekly closing price of gold • Amount of crude oil imported monthly

  28. 2.3 Graphical Techniques for Interval Data • Example 2.1: Providing information concerning the monthly bills of new subscribers in the first month after signing on with a telephone company. • Collect data • Prepare a frequency distribution • Draw a histogram

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

  30. Draw a Histogram Example 2.1: Providing information

  31. Example 2.1: Providing information nnnn What information can we extract from this histogram Relatively, large number of large bills About half of all the bills are small A few bills are in the middle range 71+37=108 13+9+10=32 80 18+28+14=60 60 Frequency 40 20 0 15 45 75 30 60 90 105 120 Bills

  32. Class width • It is generally best to use equal class width, but sometimes unequal class width are called for. • 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.

  33. Shapes of histograms Symmetry • There are four typical shape characteristics

  34. Shapes of histograms Skewness Negatively skewed Positively skewed

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

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

  37. Concepts 5 • Normal Distribution • Central tendency: mean or average • Dispersion: standard deviation • Non-normal distributions

  38. Concepts 6 • What do we mean by central tendency? • Possibilities • What is the most likely outcome? • What outcome do we expect? • What is the outcome in the middle?

  39. Moving from Concepts to Measures • Mode: most likely value.

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