2. Final project questions Review sessions tomorrow: 1:00-2:00 pm, 3:30-5:00 pm, 6:30-7:30 pm… all in SSC 107 You can start the exam as early as 8:30 am, if you want Study resources: I posted videos, extra practice problems/solutions, Moodle quiz solutions Logistics

3. The “p” in “p-value” stands for “probability,” which means that it ALWAYS is between 0 and 1. “p-value low, null must go.” Rejecting a null (using any method) shows statistical significance, not practical significance. You never “prove” anything in hypothesis testing. Never “accept” the null; either reject it or fail to reject it. Starred values get looked up on a chart; statistics (t and z) are calculated with an equation. Important points!!!

4. You CAN do this It’s not about who you are or whether you think you’re a “math” person; ANYONE can learn this material, but it does take… Discipline Reviewing your mistakes Seeking help when you have questions *Images by Gettyimages, Steven Johnson, Dr.Chromo Common Mistake: Thinking that your brain just isn’t wired this way and giving up.

5. Type I vs. Type II errors Type I – rejecting H 0 when, actually, H 0 is true. Type II – failing to reject H 0 when, actually, H 0 is false. With any null hypothesis test, there’s always a possibility that you made exactly one of the errors; but you typically never know if you made one. Which is worse? Typically we protect against Type I error more, but in any given situation, ask yourself what would happen if H 0 is true and you reject it… and then ask what would happen if H 0 is false but you fail to reject it.

6. Is it a confidence interval or a null hypothesis t-test? One sample or two samples? (Tip: A matched pairs t- test is statistically the same as a one sample t-test.) If it’s a t-test, is it one-sided (one-tailed) or two- sided (two-tailed)? Three Important t-Questions Big Tip: When using a critical value to set up a rejection region, color in only ONE tail for a one-tailed test and BOTH tails for a two-tailed test.

7. Know the variables Big Tip: Understand the difference between critical values and test statistics

8. Argh!!! Which formula do I use??? t-testConfidence interval One- sample Two- sample

9. Use this for your standard deviation when working with 1-sample tests. Replace σ with s when doing t-tests or t- confidence intervals. Formula for two- sample confidence interval Formula for two- sample t-test

10. Tips on using Table C Degrees of freedom are (n-1) for 1-sample tests and the lower of the two sample sizes, minus 1, for 2- sample tests. If your degree of freedom isn’t there, go up to the next available one (e.g., df = 47 goes up to df = 40). For confidence intervals or 2-sided tests, you can use the labels across the top, or the TWO-sided row at bottom. For 1-sided tests, you must use the ONE-sided row at bottom. Big Tip: Don’t use the numbers across the top for a 1-sided (1- tailed) t test.

12. Tips on calculating Big Tip: Know the order in which the calculator that you are using does math operations.

14. Tips on deciding about H 0 * * One-tailed test Two-tailed test Reject H 0 Fail to reject H 0 * Big Tip: Never compare a test statistic to an alpha level!

15. Tips on “Plain English” If you reject H 0 : Our study suggests that ****** does help #######. If you fail to reject H 0 : We were not able to find convincing evidence that ********** does help #######. Big Tip: There’s always a chance that you made an error. Don’t sound TOO certain! Big Tip: You never accept H 0 so don’t make it sound like you showed H 0 to be true even if you fail to reject it.

16. Using a confidence interval for a two-tailed test Lower limit of CI Upper limit of CI

17. Hypothesis Test Comparisons p-value to alpha level (α) z statistic to z* t statistic to t* Measured in % of the Distribution Measured in Number of Standard Errors *