Statistics Review, Lecture 3

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Statistics Review, Lecture 3

• Econ 326
• Eric Bettinger
• (Notes created in part from Woolridge (2000))

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Class Announcement

• Have you opened Weatherhead accounts?
• Have you been able to access the lecture notes on
  the course website?
• First assignment is due tomorrow (1/24/03)

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Review

• Random Variable and Probability
• Probability Density Function
• Expected Value
• Variance
• VaXba 2 VX
• Covariance

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Z-scores

• Suppose that we have a number of variables with
  similar histograms.
• We can Standardize these variables to make them
  comparable
• Suppose X is a variable with mean µ and standard
  deviation s
• Then standardize X by

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Z-scores (cont.)

• What is the expectation of Z?
• What is the variance of Z?
• What is the intuition?
• Bottom line
• Most random events can be modified to appear like
  a normal distribution
• Using standardization, we can make most things
  look like a Normal with mean0 and standard
  deviation1

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T-tests

• T-distribution
• In samples smaller than 120, we may not reach a
  Normal Distribution
• We use the sample mean and std. Deviation to get
  a t-distribution with n degrees of freedom

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2. Hypothesis Testing

• Now we know that we can compare things, what do
  we want to compare?
• Hypothesis Testing
• Null Hypothesis
• Alternative Hypothesis
• Types of Test
• 2-sided test
• 1-sided test

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Hypothesis Testing (cont)

• Example from Class Age Data
• 2 sided-test
• Null Hypothesis Econometrics Students are
  juniors (age 21). Mean age21
• Alternative Hypothesis Age doesnt matter and
  the mean age does not equal 21.
• Well reject the hypothesis if mean is too low
  or too high

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2. Hypothesis Testing (cont)

• Example from Class Age Data (cont.)
• See Excel Worksheet Demonstration

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2. Hypothesis Testing (cont)

• Example from Class Age Data
• 1 sided-test
• Null Hypothesis Most econometrics students are
  older than most students. Mean agegt21
• Alternative Hypothesis Age doesnt matter and
  the mean age is less than 21.
• Well reject the hypothesis if mean is too low

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2. Hypothesis Testing (cont)

• Example from Class Age Data (cont.)
• See Excel Worksheet Demonstration

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2. Hypothesis Testing (cont)

• Example from Colombian Data
• 2 sided-test
• Null Hypothesis The voucher has no effect on
  drop-out rates and voucher winners are equally
  likely to be in school as voucher losers.
  Winners mean Losers mean.
• Alternative Hypothesis The voucher has an
  effect but we dont know which way. Winners
  mean does not equal losers mean.
• Where is the rejection region?

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In-Class Exercise

• In Class Exercise
• http//connection.cwru.edu/econ326/mod2/a/Lecture3
  in class exercise.doc
• In Class Examples and Exercise Answers
• http//connection.cwru.edu/econ326/mod2/a/Lecture
  3 example.xls