Unit IV -- Sampling, Confidence Intervals, and Hypothesis Testing

• Irregularities In Russian Election ? blog post by Andrew Gelman at The Monkey Cage , showing demonstrators in Moscow, Dec. 2011, with a sign reading "We don't believe in Churov, we believe in Gauss". Churov was the head of the Russian State Electoral Commission, who rigged elections for Putin
  See also, Russian Legislative Elections, 2011 for a more complete analysis of the elections by Anton Nikolenko, with graphs!

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  Review Questions for Unit IV

• Review Questions for Normal Approximation for Probability Distributions Chapter 18 of Freedman, Pisani and Purves.

• Review Questions for Chance Errors in Sampling Chapter 20 of Freedman, Pisani and Purves.
• Wichura handout on Chapter 20

• Review Questions for Accuracy of Percentages Chapter 21 of Freedman, Pisani and Purves.

• Review Questions for Accuracy of Averages Chapter 23 of Freedman, Pisani and Purves.

• Ryan Gosling - Null Hypothesis at biostatistcsryangosling.com

• Hypothesis Testing -- an Introduction

• Statistical Hypothesis Testing from Wikipedia.
• The Earth is Round (p < .05) , by Jacob Cohen, American Psychologist, Dec. 1994.
  Strong critique of Statistical Hypothesis Inference Testing and excessive focus on p-values.

• Wichura handout on Chapter 26 (Hypothesis Testing)

Law of Averages and the Central Limit Theorem

• Berkeley Webcast of Ibser's webcourse. Lectures 23-32 cover Chapters 16-18 (Law of Averages through Normal Approximation for Probability Histograms); Lectures 33-37 cover Chapters 19-23 (Surveys through Confidence Intervals); Lectures 38-4? cover Chapters 26-? (Hypothesis tests)

• The Law of Averages and the Gambler's Fallacy Simulation of the law of averages and introduction to box models.

• Keno Simulation The Wikipedia entry on Keno provides the more elaborate rules that make it more "fun" (and more profitable for the house). Also see a more elaborate discussion of Keno odds by Michael Shackleford. To play a real game, try the Maryland Lottery Keno page

• The Law of Averages Chapter 16 of Freedman, Pisani and Purves.

• The Expected Value and the Standard Error Chapter 17 of Freedman, Pisani and Purves.

• Review Questions for Normal Approximation for Probability Distributions Chapter 18 of Freedman, Pisani and Purves.

Sampling and Confidence Intervals

Review Questions for Chance Errors in Sampling Chapter 20 of Freedman, Pisani and Purves.
• Wichura handout on Chapter 20

• The Mean and Variance of Binomial and Expected Values and Standard Errors of Sums
  Algebraic derivation of the "shortcut formula" used in the text;
  sums o random variables the importance of independence in sampling.

• Review Questions for Accuracy of Percentages Chapter 21 of Freedman, Pisani and Purves.

• Review Questions for Accuracy of Averages Chapter 23 of Freedman, Pisani and Purves.

• Hypothesis Testing -- an Introduction My most recent explanation of the language of hypothesis testing.
• Wichura handout on Chapter 26

• Hypothesis Testing An earlier effort to explain the language of hypothesis testing. Concentrate on the above document, but this may help some.

• Significant by Randall Munro, at xkcd