1. More about tests and intervals CHAPTER 21

2. Do not state your claim as the null hypothesis, instead make what you’re trying to prove the alternative. The p-value is NOT the probability that the null hypothesis is true. The p-value is the conditional probability of the observed statistic, if the null hypothesis is true. Large p-values just tell us that what we have observed isn’t surprising, so we don’t reject the null. We arbitrarily set the alpha level (or significance level) for a test to decide at what p-value we will reject the null. Always report the p-value with your results. Significant does not necessarily mean important. A confidence interval with C% level of confidence corresponds to a two- sided hypothesis test with (100-C)% alpha level. A confidence interval with C% level of confidence corresponds to a one- sided hypothesis test with ½(100- C)% alpha level.

3. Errors: Type 1 Error – the null is true but we reject it (false positive) Type 2 Error – The null is false but we fail to reject (false negative) A healthy person diagnosed with a disease is a false positive, a sick person diagnosed as disease free is a false negative. The probability of a type one error is equal to the alpha level of the test. The probability of a type two error is called its beta level. We can reduce β by increasing α. We can reduce both by increasing the sample size. The power of a test is the probability that it correctly rejects a false null. The power is equal to 1-β. The distance between the null hypothesis value and the truth is the effect size.