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# Econ 0160-W, Professor Berkowitz - PowerPoint PPT Presentation

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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Presentation Transcript

• 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

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.

Do districts with smaller classes have higher test scores? Scatterplot of test score v. student-teacher ratio

What does this figure show?

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

Initial data analysis: with low STRs have higher test scores – but how? 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 

1. Estimation with low STRs have higher test scores – but how?

2. Hypothesis testing with low STRs have higher test scores – but how?

Compute the difference-of-means with low STRs have higher test scores – but how? t-statistic:

3. Confidence interval with low STRs have higher test scores – but how?

What comes next… with low STRs have higher test scores – but how?

Review of Statistical Theory with low STRs have higher test scores – but how?

(a) Population, random variable, and distribution with low STRs have higher test scores – but how?

Population distribution of Y with low STRs have higher test scores – but how?

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

Moments, ctd. standard deviation, covariance, correlation

2 random variables: joint distributions and covariance standard deviation, covariance, correlation

The covariance between Test Score and STR is negative: standard deviation, covariance, correlation

so is the correlation…

The standard deviation, covariance, correlationcorrelation coefficient is defined in terms of the covariance:

The correlation coefficient measures linear association standard deviation, covariance, correlation

(c) Conditional distributions and conditional means standard deviation, covariance, correlation

Conditional mean, ctd. standard deviation, covariance, correlation

Distribution of Y population: 1,…, Ynunder simple random sampling

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

The sampling distribution of when population: n is large

The population: Law of Large Numbers:

The population: Central Limit Theorem (CLT):

Same example population: : sampling distribution of :