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Econ 0160-W, Professor Berkowitz

Econ 0160-W, Professor Berkowitz. Lecture 1 (chapters 1 and 2) For course information click onto www.econ.pitt.edu , go to the faculty pages, click onto Daniel Berkowitz’s page and follow the links.

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Econ 0160-W, Professor Berkowitz

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  1. Econ 0160-W, Professor Berkowitz • Lecture 1 (chapters 1 and 2) • For course information click onto www.econ.pitt.edu, go to the faculty pages, click onto Daniel Berkowitz’s page and follow the links. • For the next class, read over chapter 2, and do all of the problems in chapter 2 listed in problem set 1

  2. This course is about using data to measure causal effects.

  3. In this course you will:

  4. Review of Probability and Statistics(SW Chapters 2, 3)

  5. The California Test Score Data Set

  6. Initial look at the data:(You should already know how to interpret this table) • This table doesn’t tell us anything about the relationship between test scores and the STR.

  7. Do districts with smaller classes have higher test scores? Scatterplot of test score v. student-teacher ratio What does this figure show?

  8. We need to get some numerical evidence on whether districts with low STRs have higher test scores – but how?

  9. Initial data analysis: Compare districts with “small” (STR < 20) and “large” (STR ≥ 20) class sizes: 1. Estimation of  = difference between group means 2. Test the hypothesis that  = 0 3. Construct a confidence interval for 

  10. 1. Estimation

  11. 2. Hypothesis testing

  12. Compute the difference-of-means t-statistic:

  13. 3. Confidence interval

  14. What comes next…

  15. Review of Statistical Theory

  16. (a) Population, random variable, and distribution

  17. Population distribution of Y

  18. (b) Moments of a population distribution: mean, variance, standard deviation, covariance, correlation

  19. Moments, ctd.

  20. 2 random variables: joint distributions and covariance

  21. The covariance between Test Score and STR is negative: so is the correlation…

  22. The correlation coefficient is defined in terms of the covariance:

  23. The correlation coefficient measures linear association

  24. (c) Conditional distributions and conditional means

  25. Conditional mean, ctd.

  26. (d) Distribution of a sample of data drawn randomly from a population: Y1,…, Yn

  27. Distribution of Y1,…, Ynunder simple random sampling

  28. (a) The sampling distribution of

  29. The sampling distribution of , ctd.

  30. The sampling distribution of when Yis Bernoulli (p = .78):

  31. Things we want to know about the sampling distribution:

  32. The mean and variance of the sampling distribution of

  33. Mean and variance of sampling distribution of , ctd.

  34. The sampling distribution of when n is large

  35. The Law of Large Numbers:

  36. The Central Limit Theorem (CLT):

  37. Sampling distribution of when Y is Bernoulli, p = 0.78:

  38. Same example: sampling distribution of :

  39. Summary: The Sampling Distribution of

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