Download Lessons 3 and 4: Statistics

Lessons 3 and 4: Statistics
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Working with Stata
Probability Example: CLT in action
Populations have parameters, Samples have
estimators
Estimators & Estimates
Parameters have distributions: From
Probability to Statistics
Confidence Intervals for Parameters
E.g. Pick a digit
Hypothesis Testing: terms
Hypothesis Testing: steps
P-value
Properties of Estimators
Efficiency of Sample Mean
Monte Carlo Demonstration of CLT
1. Probability Example:
Confidence Interval
for sample mean
• Ai - the outcome of
some event for individual i
E.g. p(lefthanded)=.085
• How often should that
happen in a class of this size?
• frequency of “4”s = N x sample mean of “4”s
• Standard error (std. deviation of mean)
- V(Ai) = p(Ai=1)[1-p(Ai=1)]
• Normal approximation
• Confidence interval for sample mean
• Application: Fair bet?
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Calculating Confidence interval for lefties
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2. Populations have parameters,
Samples have estimators
Population
Sample
e.g. U.S. Residents
All coin flips
Parameters
(typically Greek)
e.g. Pop. mean
Pop. Variance
C.P.S.
N coin flips
Estimators
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Sample mean
Sample variance
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3. Estimators and Estimates
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4. Parameters have distributions:
From Probability to Statistics
• Probability: use information from
populations to learn about samples
(Lefthanded example)
• Statistics: use information from samples
to learn about populations
• How to make the transition
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From Probability to Statistics…
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5. Confidence Intervals for parameters:
Pick a number example
• Find the distribution of
estimator
• Interpret as
distribution of
parameter
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Confidence Intervals
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6. Hypothesis testing: terms
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7. Hypothesis Testing: Steps
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8. P-value:
How likely were we to miss by at least that much,
if Ho is true?
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9. Properties of Estimators
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10 Efficiency of Sample Mean
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11. Monte Carlo Demonstration of CLT
• Imagine estimating the mean hourly
wage :, by drawing samples of size N
from the distribution of hourly wages,
say in 1984.
• Stata will do this for us, maybe 10,000
times.
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N=40, 10,000 draws
Fraction
.0705
0
6
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8
m
10
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N=60, 10,000 draws
Fraction
.0786
0
6
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8
m
10
12
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The next two
slides each
present one half
of Figure 3.3.
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Summary - Lessons 3 and 4: Statistics
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
Probability Example: CLT in action
Populations have parameters, Samples have
estimators
Estimators & Estimates
Parameters have distributions: From
Probability to Statistics
Confidence Intervals for Parameters
E.g. Pick a digit
Hypothesis Testing: terms
Hypothesis Testing: steps
P-value
Properties of Estimators
Efficiency of Sample Mean
Monte Carlo Demonstration of CLT
Appendix 3.1
Copyright © 2003 by Pearson Education, Inc.
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