Introduction to Statistics for the Social Sciences SBS200 - Lecture Section 001, Spring 2017 Room 150 Harvill Building 9:00 - 9:50 Mondays, Wednesdays & Fridays. Welcome http://www.youtube.com/watch?v=oSQJP40PcGI http://www.youtube.com/watch?v=oSQJP40PcGI

A note on doodling

Lab sessions Everyone will want to be enrolled in one of the lab sessions Project 2 Presentations continue

By the end of lecture today 3/6/17 Introduction to hypothesis testing Interpreting Alpha levels p values Type I and Type II Errors

Before next exam (April 7th) 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

No class on Friday Have a safe and happy spring break . No homework over spring break

Whether or not feed had corn oil No, feed had no corn oil Yes, the feed had corn oil Weight of eggs 60 grams if no corn oil 63 grams if corn oil weight of eggs based on corn oil in food weight of eggs based on corn oil in food true experiment between nominal ratio 200 100 100 198 99 99

-3.35 1.97 Yes Yes Yes 0.0009638 Yes 0.05 The weights of eggs for chickens who received the corn oil was 63 grams, while the weights of the eggs for chickens who did not receive the corn oil was 60 grams. A t-test found this to be a significant difference t(198) = -3.35; p < 0.05

Whether or not offered incentive Was offered incentive Was not offered incentive Grade point average 2.3 for incentive group 2.1 for no incentive group GPA based on incentive GPA based on incentive true experiment between nominal interval 500 250 250 498 249 249

3.64 1.964 Yes Yes Yes 0.000297947 Yes 0.05 The average GPA was 2.3 for students who were offered an incentive and was 2.1 for students who were not offered an incentive. A t-test was completed and we found this to be a significant difference t(498) = 3.64; p < 0.05

Whether or not video included sound Video with no sound Video with sound Number of items correctly recalled 3.7 for video with no sound 3.3 items for video with sound number of items recalled number of items recalled true experiment between nominal ratio 40 20 20 38 19 19

1.17 2.02 No No No 0.248 No 0.05 The average number of items recalled was 3.7 for the students who watched the ads with no sound, and was 3.3 for students who watched video with sound. A t-test was completed and we found no significant difference t(38) = 1.17; p < 0.05

Location of air conditioner plant Japan United States Turnover rate 3.12% turnover rate for Japan 6.56% turnover rate for USA turnover rates between Japan and USA turnover rates between Japan and USA quasi between nominal ratio 10 5 5 8 4 4

-4.46 2.31 Yes Yes Yes 0.0021 Yes 0.05 The average turnover rate in the Japanese plants is 3.12 while the average turnover rated in the American plants is 6.56. A t-test showed a significant difference, t(8) = -4.46; p < 0.05

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

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 in the tails is called alpha Critical z -1.96 Critical z 1.96 Confidence Interval of 95% Has and alpha of 5% α = .05 95% Critical Z separates rare from common scores Critical z -1.64 Critical z 1.64 Confidence Interval of 90% Has and alpha of 10% α = . 10 90%

Deciding whether or not to reject the null hypothesis. 05 versus 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? α = 0.05 Significance level = .05 α = 0.01 Significance level = .01 -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 not Reject the null

Deciding whether or not to reject the null hypothesis. 05 versus 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? α = 0.05 Significance level = .05 α = 0.01 Significance level = .01 -1.96 or +1.96 Do Not Reject the null Not a Significant difference 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

90% Moving from descriptive stats into inferential stats…. 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% Measurements that occur within the middle part of the curve are ordinary (typical) and probably belong there 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/ http://www.youtube.com/watch?v=0r7NXEWpheg

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”

Procedures versus outcome Best guess versus “truth” . 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?

Thank you! See you next time!!