Statistics: Unlocking the Power of DataLock5Section 4.2Measuring Evidence with p-values

5Paul the Octopus•In 2008, Paul the Octopus predicted 8 World Cup games, and predicted them all correctly •Is this evidence that Paul’s chance of guessing correctly, p, is really greater than 50%?•What are the null and alternative hypotheses?

Statistics: Unlocking the Power of DataLock5Key QuestionIf it is very unusual, we have statistically significantevidence against the null hypothesisToday’s Question: How do we measure how unusual a sample statistic is, if H0is true?How unusual is it to see a sample statistic as extreme as that observed, if H0is true?

Statistics: Unlocking the Power of DataLock5To see if a statistic provides evidence against H0,we need to see what kind of sample statistics we would observe, just by random chance, if H0were trueMeasuring Evidence against H0

Statistics: Unlocking the Power of DataLock5Paul the OctopusWe need to know what kinds of statistics we would observe just by random chance, if the null hypothesis were trueHow could we figure this out???Simulate many samples of size n = 8 with p = 0.5

Statistics: Unlocking the Power of DataLock5Simulate!•We can simulate this with a coin!•Each coin flip = a guess between two teams (Heads = correct, Tails = incorrect)•Flip a coin 8 times, count the number of heads, and calculate the sample proportion of heads•Come to the board to add your sample proportion to a class dotplot•How extreme is Paul’s sample proportion of 1?•We just created our first randomization distribution!

Statistics: Unlocking the Power of DataLock5Randomization DistributionA