Economics 240A

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Economics 240A

• Power One

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Outline

• Course Organization
• Course Overview
• Resources for Studying

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Organization ( Cont.)
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Course Overview

• 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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http//research.stlouisfed.org/fred2/
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http//research.stlouisfed.org/fred2/
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Resources for Studying

• Keller Warrack
• Text Readings
• CDROM
• PowerPoint Slide Shows
• Appletns

• Instructor
• Lecture Notes
• Lab Notes Exercises
• Problem Sets
• PowerPoint Slide Shows

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http//econ.ucsb.edu
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Keller Warrack CDROM
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http//www.duxbury.com/statistics
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Student Book Companion Siten
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Keller Warrack Slide Show

• Excerpts from Ch. 2

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Chapter 2
Graphical Descriptive Techniques
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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

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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

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

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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

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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

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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
Smallest observation
Smallest observation
Smallest observation
Largest observation
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Example 2.1 Providing information
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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
7137108
1391032
80
18281460
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Frequency
40
20
0
15
30
45
60
75
90
105
120
Bills
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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.

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Shapes of histograms
Symmetry

• There are four typical shape characteristics

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Shapes of histograms
Skewness
Negatively skewed
Positively skewed
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Modal classes

• A modal class is the one with the largest number
  of observations.
• A unimodal histogram

The modal class
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Descriptive Statistics

• Central Tendency
• mode
• median
• mean
• Dispersion
• standard deviation
• interquartile range (IQR)

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http//www.dof.ca.gov/
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http//research.stlouisfed.org/fred2/
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Concepts

• 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?

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Moving from Concepts to Measures

• Mode most likely value.

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Moving from Concepts to Measures

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

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

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Concepts

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

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Exploratory Data Analysis

• Stem and Leaf Diagrams
• Box and Whiskers Plots

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Weight Data
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
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Box Diagram
median
First or lowest quartile 25 of observations
below
Upper or highest quartile 25 of observations
above
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Whiskers

• The whiskers end with points that are not
  outliers
• Outliers are beyond 1.5 times the interquartile
  range ( in this case IQR 31), so 1.531 46.5
• 1st quartile 1.5IQR 125 46.5 78.5,but
  the minimum is 95 so the lower whisker ends with
  95.

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3rd Quartile 1.5 IQR 156 46.5 202.5 1st
value below 195