Apr. 8 Stat 100

To do Read Chapter 21, try problems 1-6 Skim Chapter 22

Significance Test Data used to decide between two competing statements (hypotheses) about the population Statements are called null hypothesis and alternative hypothesis

Notation H 0 represents null hypothesis H A represents alternative hypothesis

College performance and SAT relationship H 0 : No relationship between college performance and SAT H A : college performance and SAT scores are related

Memorization skills of men and women H 0 : No difference in memorization skills of men and women H A : There is a difference between men and women

Thought question Consider coin flipping. Null hypothesis: chance of heads =.5 Which is stronger evidence against this null hypothesis - 3 heads in 3 flips, or 30 heads in 30 flips?

Somewhat obvious answer = 30 heads in 30 flips What about this that would make us reject the hypothesis that chance of heads =.5 It seems almost impossible to get this many heads if the coin flipping is “fair” Chance of 30 heads in a row is about 1 in a billion

Statistically Significant A result is called statistically significant when a null hypothesis is rejected Basis for deciding is a probability called the “p-value”

Finding the p-value P-value = probability that the observed data would have occurred if the null hypothesis were true. Example: data = 30 heads in 30 flips null hyp = flipping is random p-value = chance of 30 heads if flipping is random

Using the p-value to make decisions The smaller the p-value, the stronger the evidence against the null (and for the alternative) Why? Small p-value means the observed data not likely to happen if the null really is true. Example - it would not be very likely that we’d get 100 straight heads

Usual borderline for decision If p-value less than.05 (5%), pick alternative hypothesis If p-value larger than.05 (5%), pick null hypothesis

Typical research paper statement “We found a significant difference between treatment success rates (p <.05).” p-value of a test was less than.05 so the researchers rejected a null hypothesis. The null would be that there is no difference between treatments observed difference was large enough to be “unlikely” if we believed the null to be true

Another typical statement The difference between means for the two treatments was not significant (p =.42). This means the researchers could not reject a null hypothesis; the p-value =.42. Null: no difference in treatment means p-value=.42 means the observed difference would be quite likely to happen if the null were true

Book Ch. 22 Thought Question 1 Imagine a jury decision in a murder trial. It is a mistake if the jury claims the suspect is guilty when in fact he or she is innocent. What is the other type of mistake a jury can make? Which type of mistake is more serious?

Statistical Errors Type 1: rejecting the null hypothesis when you should not (like convicting a person who’s not guilty) Type 2: not rejecting the null hypothesis when you should (like not convicting a guilty person)

Example Experiment is done to see if new treatment for depression is better than old treatment null hyp: new treatment not better alternative hyp: new treatment is better Type I error: deciding new treatment is better when it is not Type 2 error: deciding new treatment is not better when it actually is

Biggest cause of Type II error Not getting enough evidence In statistical problems, small sample size