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Introduction to Statistics for the Social Sciences

This course provides an introduction to statistics for the social sciences, covering topics such as hypothesis testing, type I and type II errors, confidence intervals, and more. Students will learn how to analyze and interpret data in order to make informed decisions.

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Introduction to Statistics for the Social Sciences

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  1. Introduction to Statistics for the Social SciencesSBS200, COMM200, GEOG200, PA200, POL200, or SOC200Lecture Section 001, Fall 2015Room 150 Harvill Building10:00 - 10:50 Mondays, Wednesdays & Fridays. Welcome http://courses.eller.arizona.edu/mgmt/delaney/d15s_database_weekone_screenshot.xlsx

  2. By the end of lecture today10/26/15 Hypothesis testing Doing everything right – but still being wrong Type I versus Type II Errors

  3. Before next exam (November 20th) 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

  4. 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 28th

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

  6. Homework Worksheet: Confidence interval uses SEM

  7. Homework Worksheet: Problem 1 29.2 Upper boundary raw score x = mean + (z)(standard deviation) x = 55 + (+ 2.58)(10) x = 80.8 80.8 Lower boundary raw score x = mean + (z)(standard deviation) x = 55 + (- 2.58)(10) x = 29.2 Standard deviation = 10 Mean = 55 2.58 sd 2.58 sd .99 55 ? ? 80.8 29.2

  8. Homework Worksheet: Problem 1 29.2 Upper boundary raw score x = mean + (z)(standard error mean) x = 55 + (+ 2.58)(1.42) x = 58.7 80.8 51.3 58.7 Lower boundary raw score x = mean + (z)(standard error mean) x = 55 + (- 2.58)(1.42) x = 51.3 Standard deviation = 10 Mean = 55 10 49 2.58 sem 2.58 sem 1.42 .99 55 ? ? 58.7 51.3

  9. Homework Worksheet: Problem 5 29.2 80.8 51.3 58.7 10.2 29.8 8.02 8.6 9.18 16.9 23.1 4.09 13.11 8.02 9.18 2.67 7.8 7.8 8.6 9.4 14.5 9.4

  10. How do we know how rare is rare enough? Area in the tails is alpha α = .01 α = .10 α = .05 99% Level of significance is called alpha (α) • 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? 95% 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”) 90% 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 Review

  11. 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 x2) • observed stat > critical stat If we want to reject the null, we want our t (or z or r or F or x2) 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 Review

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

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

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

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

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

  17. 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 x2) 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”

  18. . 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?

  19. We make decisions at Security Check Points . .

  20. . Type I or Type II error? . Does this airline passengerhave 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?

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

  22. . Type I or type II error? True Ho False Ho You are right! Correct decision You are wrong! Type II error(miss) Do notReject Ho Decision madeby experimenter You are wrong! Type I error(false alarm) You are right! Correct decision Reject Ho Does this airline passenger have a 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? What would null hypothesis be? This passenger does not have any 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)

  23. . Type I or type II error True Ho False Ho You are right! Correct decision You are wrong! Type II error(miss) Do notReject Ho Decision madeby experimenter You are wrong! Type I error(false alarm) You are right! Correct decision Reject Ho Does advertising affect sales? • Two ways to be correct: • Say it helps when it does • Say it does not help when it doesn’t help Which is worse? • Two ways to be incorrect: • Say it helps when it doesn’t • Say it does not help when it does What would null hypothesis be? This new advertising has no effect on 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)

  24. . What is worse a type I or type II error? True Ho False Ho You are right! Correct decision You are wrong! Type II error(miss) Do notReject Ho Decision madeby experimenter You are wrong! Type I error(false alarm) You are right! Correct decision Reject Ho What if we were lookingat a new HIV drug that had no unpleasant side affects • 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? What would null hypothesis be? This new drug has no effect on HIV 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)

  25. . Type I or type II error Which is worse? What if we were looking to see if there is a fire burning in an apartment building full of cute puppies • 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) What would null hypothesis be? No fire is occurring Type I error: Rejecting a true null hypothesis (false alarm) Type II error: Not rejecting a false null hypothesis (miss)

  26. . Type I or type II error Which is worse? What if we were looking to see if an individualwere guilty of a crime? • 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 What would null hypothesis be? This person is innocent - there is no crime here 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

  27. . 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. Null Hypothesis A measure of sickness people taking drugpeople not taking drug (There are two distributions here, they are just on top of each other) (overlapping) people taking drug people not taking drug A measure of sickness A measure of sickness Null is FALSE Null is TRUE Drug does have effect Something going on Nothing going on No effect of drug There is no difference between the groups There is a difference between the groups

  28. Remember: “procedure” vs “TRUTH” . (There are two distributions here, they are just on top of each other) (overlapping) A measure of sickness people taking drug people not taking drug people taking drugpeople not taking drug A measure of sickness A measure of sickness Null is FALSE Null is TRUE Score should fall in this region critical stat critical stat critical stat critical stat Score should fall in one of these regions 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

  29. Thank you! See you next time!!

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