Review

• Red Sox probability problem: what's the probability that they will win, given that they are 2-0 in the series and assuming that the teams are equally matched?
• Theoretical probability of winning in the double-cheating coin-flip problem.
• Article on tort law facts (to discuss next time):
  • Are the facts on businesses suing businesses relevant? Why or why not?
  • They concentrated on trials in which plaintifff succeeds. Good call?
  • They used the median award and median punitive damage, not the mean. Good call?
  • other observations?
• Other symmetrical distributions: Cauchy, double-exponential
• Examples of Discrete Event simulations
• Confidence Intervals

Two Sample tests

• the logic of statistical tests:
  • determine H0
  • run an experiment and measure M
  • determine the probability P of M under H0
  • reject H0 if P is small
• With more detail:
  • determine null hypothesis (H0) and alternative hypothesis (H1)
  • decide what kind of value you're going to measure
  • determine the sampling distribution under H0
  • determine the rejection region (one tail or two)
  • conduct the experiment and measure M
  • determine the probability P of M under H0, or establish a critical value for M for some conventional significance level
  • reject M if P is too small or M exceeds the critical value
• Type I and Type II errors
• Practical Significance versus Statistical Significance
  • If N is large enough, anything is "significant"
  • If N is too small, even real differences may not show up
• Examples: SAT scores and pain scores
• Testing using the Bootstrap
• Testing using the z test
• Testing using the t test (next time)