1 Economics 240A Power One

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

Organization ( Cont.)

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

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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

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14 Keller & Warrack CDROM

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16 Student Book Companion Siten

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

18 Graphical Descriptive Techniques Chapter 2

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

22 Types of data - examples Interval data Age - income Age - income Nominal data With nominal data, all we can do is, calculate the proportion of data that falls into each category. IBM Dell Compaq OtherTotal % 22% 16% 12% IBM Dell Compaq OtherTotal % 22% 16% 12% Weight gain Weight gain

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 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

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 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 , ,000 – 5, , , More than 50, Class width = [Range] / [# of classes] [ ] / [8] = Largest observation Largest observation Smallest observation Smallest observation Smallest observation Smallest observation Largest observation Example 2.1Example 2.1: Providing information

27 Draw a Histogram Example 2.1Example 2.1: Providing information

28 nnnn Bills Frequency What information can we extract from this histogram About half of all the bills are small 71+37= =32 A few bills are in the middle range Relatively, large number of large bills =60 Example 2.1Example 2.1: Providing information

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 w There are four typical shape characteristics Shapes of histograms

31 Positively skewed Negatively skewed Shapes of histograms

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

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

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

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

Males: Females: Weight Data

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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 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.

3 rd Quartile + 1.5* IQR = = 202.5; 1 st value below =195