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2004 QE1 Statistics Review. Adam Shrager ashrager@yahoo.com ashrager@princeton.edu April 4, 2004. First, the disclaimer…. I have not seen this year’s exam Everything is subject to change Consider the following direction in the realm of highly probabilistic based on prior (recent) exams.
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2004QE1 Statistics Review Adam Shrager ashrager@yahoo.com ashrager@princeton.edu April 4, 2004
First, the disclaimer… • I have not seen this year’s exam • Everything is subject to change • Consider the following direction in the realm of highly probabilistic based on prior (recent) exams. • In terms of focusing your studying efforts…there are some pretty clear guidelines….
The three types of Statistics Questions on the QE1 • The Regression Question • Explain the model • Calculate something • Analyze or criticize the model • The Hypothesis Testing Question • Often difference of means or proportions • Your choice: Confidence interval or t-test • The Probability Question • On May ’03 exam. • Bayes Rule (Conditional Probability)
The Regression Question • Explain the Regression Equation What are we modeling? Restate dependent and independent variables. What does one additional unit of X do to Y? Get specific. May ’02: “ A one mpg increase in avg. fuel efficiency will lower the per capita oil consumption by 0.38 barrels per person per year.”
The Regression Question • Plug numbers into the model to solve for something. May ’02: 3 mpg increase lowers oil consumption by 1.14 barrels per person per year (0.38 x 3). With 260 million people, change in national oil consumption would be 296 million barrels per year (260,000,000 x 1.14). Question asked for you to explain the 296 million barrel claim.
The Regression Question • Criticize/Analyze/Discuss the model • CORRELATION!!!!!!! • External validity • What else impacts Y? • Use “external” knowledge (or knowledge gleaned from background reading) here.
Hypothesis Testing • Be prepared for: • Difference of Means • Difference of Proportions Have these formulas handy!!!!! Consider: “Do I like confidence intervals or do I like t-tests?”
Hypothesis TestingTIPS FOR SUCCESS • Make and explicitly state your assumptions. Even if wrong, then your answers will logically flow. • Assumptions: • State Null (H0) and Alternative (Ha) hypothesis • Two-sided/one sided test • Level of confidence (often .05) • What test are you using and why?
Hypothesis TestingTIPS FOR SUCCESS • Be sure to explicitly test for (and state that you are testing for) the following: • If confidence interval, is zero in the interval? Why does this matter? (also common: if asking about “majority,” is .50 in the interval?) • If t-test, explicitly state critical value (often 1.96 or 1.68, could be something else). Does your test statistic exceed this value? What does that mean? Even if you screw up the math – by explicitly stating what you’re doing, the grader can follow your logic and may only deduct nominal points. • If you use both tests – do your answers correspond? THEY SHOULD!!!!!!!!!
Probability • What could they ask you? • Conditional Probability • Bayes Rule. • It’s your choice…..
Bayes Rule • The algebraic formulation for Bayes’ Rule • P (A│B) = P (B│A) P (A) / P (B) (plug in the numbers presented to you as appropriate, and solve)
Bayes Rule • Much easier to solve with a tree.