2. Introduction to Statistics for the Social Sciences SBS200, COMM200, GEOG200, PA200, POL200, or SOC200 Lecture Section 001, Fall 2015 Room 150 Harvill Building 10:00 - 10:50 Mondays, Wednesdays & Fridays. http://courses.eller.arizona.edu/mgmt/delaney/d15s_database_weekone_screenshot.xlsx

4. By the end of lecture today 10/26/15 Hypothesis testing Doing everything right – but still being wrong Type I versus Type II Errors

5. Before next exam (November 20 th ) Please read chapters 1 - 11 in OpenStax textbook Please read Chapters 2, 3, and 4 in Plous Chapter 2: Cognitive Dissonance Chapter 3: Memory and Hindsight Bias Chapter 4: Context Dependence

6. Homework Assignment Go to D2L - Click on “Interactive Online Homework Assignments” Complete Assignment 15: HW15-Hypothesis Testing, Type I versus Type II Errors Due: Wednesday, October 28 th

7. Confidence Interval of 99% Has and alpha of 1% α =.01 Confidence Interval of 90% Has and alpha of 10% α =. 10 Confidence Interval of 95% Has and alpha of 5% α =.05 99%95%90% Area outside confidence interval is alpha Area in the tails is called alpha Area associated with most extreme scores is called alpha Critical z -2.58 Critical z 2.58 Critical z -1.96 Critical z 1.96 Critical z -1.64 Critical z 1.64

8. Confidence interval uses SEM

9. Upper boundary raw score x = mean + (z)(standard deviation) x = 55 + (+ 2.58)(10) x = 80.8 Lower boundary raw score x = mean + (z)(standard deviation) x = 55 + (- 2.58)(10) x = 29.2 29.2 80.8 29.2 80.8

10. Upper boundary raw score x = mean + (z)(standard error mean) x = 55 + (+ 2.58)(1.42) x = 58.7 Lower boundary raw score x = mean + (z)(standard error mean) x = 55 + (- 2.58)(1.42) x = 51.3 29.2 80.8 51.3 58.7 10 49 1.42 51.3 58.7

11. 29.2 80.8 58.7 8.02 8.6 9.18 7.8 8.6 9.4 51.3 10.2 29.8 23.1 16.9 4.09 13.11 9.18 8.02 2.67 14.5 9.4 7.8

12. How do we know how rare is rare enough? Critical z: A z score that separates common from rare outcomes and hence dictates whether the null hypothesis should be retained (same logic will hold for “critical t”) The degree of rarity required for an observed outcome to be “weird enough” to reject the null hypothesis Which alpha level would be associated with most “weird” or rare scores? Level of significance is called alpha ( α ) If the observed z falls beyond the critical z in the distribution (curve) then it is so rare, we conclude it must be from some other distribution 99%95%90% α =.01 α =.05 α =.10 Area in the tails is alpha

13. Rejecting the null hypothesis The result is “statistically significant” if: the observed statistic is larger than the critical statistic (which can be a ‘z” or “t” or “r” or “F” or x 2 ) observed stat > critical stat If we want to reject the null, we want our t (or z or r or F or x 2 ) to be big!! the p value is less than 0.05 (which is our alpha) p < 0.05 If we want to reject the null, we want our “p” to be small!! we reject the null hypothesis then we have support for our alternative hypothesis

14. How would the critical z change? α = 0.05 Significance level =.05 α = 0.01 Significance level =.01 -1.96 or +1.96 -2.58 or +2.58 What if our observed z = 2.0? Reject the null Do not Reject the null Remember, reject the null if the observed z is bigger than the critical z Deciding whether or not to reject the null hypothesis.05 versus.01 alpha levels p < 0.05 Yes, Significant difference Not a Significant difference

15. How would the critical z change? α = 0.05 Significance level =.05 α = 0.01 Significance level =.01 -1.96 or +1.96 -2.58 or +2.58 What if our observed z = 1.5? Do Not Reject the null Do Not Reject the null Remember, reject the null if the observed z is bigger than the critical z Deciding whether or not to reject the null hypothesis.05 versus.01 alpha levels Not a Significant difference

16. How would the critical z change? α = 0.05 Significance level =.05 α = 0.01 Significance level =.01 -1.96 or +1.96 -2.58 or +2.58 What if our observed z = -3.9? Reject the null Remember, reject the null if the observed z is bigger than the critical z Deciding whether or not to reject the null hypothesis.05 versus.01 alpha levels p < 0.05 Yes, Significant difference p < 0.01 Yes, Significant difference

17. How would the critical z change? α = 0.05 Significance level =.05 α = 0.01 Significance level =.01 -1.96 or +1.96 -2.58 or +2.58 What if our observed z = -2.52? Reject the null Do not Reject the null Remember, reject the null if the observed z is bigger than the critical z Deciding whether or not to reject the null hypothesis.05 versus.01 alpha levels p < 0.05 Yes, Significant difference Not a Significant difference

18. Critical Values What percent of the distribution will fall in region of rejection Measurements that occur outside this middle ranges are suspicious, may be an error or belong elsewhere Measurements that occur within the middle part of the curve are ordinary (typical) and probably belong there For scores that fall into the regions of rejection, we reject the null 90% For scores that fall into the middle range, we do not reject the null 5% Moving from descriptive stats into inferential stats…. http://www.youtube.com/watch?v=0r7NXEWpheg http://today.msnbc.msn.com/id/33411196/ns/today-today_health/ Critical z -1.64 Critical z 1.64

19. Rejecting the null hypothesis The result is “statistically significant” if: the observed statistic is larger than the critical statistic observed stat > critical stat If we want to reject the null, we want our t (or z or r or F or x 2 ) to be big!! the p value is less than 0.05 (which is our alpha) p < 0.05 If we want to reject the null, we want our “p” to be small!! we reject the null hypothesis then we have support for our alternative hypothesis A note on decision making following procedure versus being right relative to the “TRUTH”

20. . Decision making: Procedures versus outcome Best guess versus “truth” What does it mean to be correct? Why do we say: “innocent until proven guilty” “not guilty” rather than “innocent” Is it possible we got a verdict wrong?

21. .. We make decisions at Security Check Points

22. .. Type I or Type II error? Does this airline passenger have a snow globe? Null Hypothesis means she does not have a snow globe (that nothing unusual is happening) – Should we reject it???!! As detectives, do we accuse her of brandishing a snow globe?

23. . Decision made by experimenter Status of Null Hypothesis (actually, via magic truth-line) Reject H o “yes snow globe, stop!” Do not reject H o “no snow globe move on” True H o No snow globe False H o Yes snow globe You are right! Correct decision You are wrong! Type I error (false alarm) You are right! Correct decision You are wrong! Type II error (miss) Are we correct or have we made a Type I or Type II error? Does this airline passenger have a snow globe? Note: Null Hypothesis means she does not have a snow globe (that nothing unusual is happening) – Should we reject it???!!

24. . Type I or type II error? Does this airline passenger have a snow globe? Type I error: Rejecting a true null hypothesis Saying the she does have snow globe when in fact she does not (false alarm) Type II error: Not rejecting a false null hypothesis Saying she does not have snow globe when in fact she does (miss) What would null hypothesis be? This passenger does not have any snow globe Two ways to be correct: Say she does have snow globe when she does have snow globe Say she doesn’t have any when she doesn’t have any Two ways to be incorrect: Say she does when she doesn’t (false alarm) Say she does not have any when she does (miss) Which is worse? Decision made by experimenter Reject H o Do not Reject H o True H o False H o You are right! Correct decision You are wrong! Type I error (false alarm) You are right! Correct decision You are wrong! Type II error (miss)

25. . Type I or type II error Does advertising affect sales? Type I error: Rejecting a true null hypothesis Saying the advertising would help sales, when it really wouldn’t help people (false alarm) Type II error: Not rejecting a false null hypothesis Saying the advertising would not help when in fact it would (miss) What would null hypothesis be? This new advertising has no effect on sales Two ways to be correct: Say it helps when it does Say it does not help when it doesn’t help Two ways to be incorrect: Say it helps when it doesn’t Say it does not help when it does Which is worse? Decision made by experimenter Reject H o Do not Reject H o True H o False H o You are right! Correct decision You are wrong! Type I error (false alarm) You are right! Correct decision You are wrong! Type II error (miss)

26. . What is worse a type I or type II error? What if we were looking at a new HIV drug that had no unpleasant side affects Type I error: Rejecting a true null hypothesis Saying the drug would help people, when it really wouldn’t help people (false alarm) Type II error: Not rejecting a false null hypothesis Saying the drug would not help when in fact it would (miss) What would null hypothesis be? This new drug has no effect on HIV Two ways to be correct: Say it helps when it does Say it does not help when it doesn’t help Two ways to be incorrect: Say it helps when it doesn’t Say it does not help when it does Which is worse? Decision made by experimenter Reject H o Do not Reject H o True H o False H o You are right! Correct decision You are wrong! Type I error (false alarm) You are right! Correct decision You are wrong! Type II error (miss)

27. . Type I or type II error What if we were looking to see if there is a fire burning in an apartment building full of cute puppies Type I error: Rejecting a true null hypothesis (false alarm) Type II error: Not rejecting a false null hypothesis (miss) What would null hypothesis be? No fire is occurring Two ways to be correct: Say “fire” when it’s really there Say “no fire” when there isn’t one Two ways to be incorrect: Say “fire” when there’s no fire (false alarm) Say “no fire” when there is one (miss) Which is worse?

28. . Type I or type II error What if we were looking to see if an individual were guilty of a crime? Type I error: Rejecting a true null hypothesis Saying the person is guilty when they are not (false alarm) Sending an innocent person to jail (& guilty person to stays free) Type II error: Not rejecting a false null hypothesis Saying the person in innocent when they are guilty (miss) Allowing a guilty person to stay free What would null hypothesis be? This person is innocent - there is no crime here Two ways to be correct: Say they are guilty when they are guilty Say they are not guilty when they are innocent Two ways to be incorrect: Say they are guilty when they are not Say they are not guilty when they are Which is worse?

29. . people taking drug people not taking drug people taking drug people not taking drug Null Hypothesis Null is TRUE Null is FALSE No effect of drug Nothing going on Drug does have effect Something going on The null hypothesis is typically that something is not present, that there is no effect, that there is no difference between population and sample or between treatment and control. There is no difference between the groups There is a difference between the groups (There are two distributions here, they are just on top of each other) (overlapping) A measure of sickness

30. . critical stat Score should fall in this region Score should fall in one of these regions Null is TRUE Null is FALSE No effect of drug Nothing going on Drug does have effect Something going on Score should fall in one of these regions people taking drug people not taking drug people taking drug people not taking drug Null is TRUE Null is FALSE A measure of sickness (There are two distributions here, they are just on top of each other) (overlapping) Remember: “procedure” vs “TRUTH”