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Introduction to Statistics for the Social Sciences SBS200 - Lecture Section 001, Fall 2017 Room 150 Harvill Building 10:00 - 10:50 Mondays, Wednesdays.

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Presentation on theme: "Introduction to Statistics for the Social Sciences SBS200 - Lecture Section 001, Fall 2017 Room 150 Harvill Building 10:00 - 10:50 Mondays, Wednesdays."— Presentation transcript:

1 Introduction to Statistics for the Social Sciences SBS200 - Lecture Section 001, Fall 2017 Room 150 Harvill Building 10: :50 Mondays, Wednesdays & Fridays. Welcome

2 Lecturer’s desk Projection Booth Screen Screen Harvill 150 renumbered
Row A 15 14 Row A 13 3 2 1 Row A Row B 23 20 Row B 19 5 4 3 2 1 Row B Row C 25 21 Row C 20 6 5 1 Row C Row D 29 23 Row D 22 8 7 1 Row D Row E 31 23 Row E 23 9 8 1 Row E Row F 35 26 Row F 25 11 10 1 Row F Row G 35 26 Row G 25 11 10 1 Row G Row H 37 28 27 13 Row H 12 1 Row H 41 29 28 14 Row J 13 1 Row J 41 29 Row K 28 14 13 1 Row K Row L 33 25 Row L 24 10 9 1 Row L Row M 21 20 19 Row M 18 4 3 2 1 Row M Row N 15 1 Row P 15 1 Harvill 150 renumbered table 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 Projection Booth Left handed desk

3 A note on doodling

4 Schedule of readings Before next exam (November 17th)
Please read chapters 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

5

6 Labs continue this week
Lab sessions Everyone will want to be enrolled in one of the lab sessions Labs continue this week Presentations

7 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 < 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

8 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 Review

9 How would the critical z change?
One versus two tail test of significance: Comparing different critical scores (but same alpha level – e.g. alpha = 5%) One versus two tailed test of significance 1.64 95% 95% 5% 2.5% 2.5% How would the critical z change? Pros and cons… Review

10 One versus two tail test of significance 5% versus 1% alpha levels
What if our observed z = 2.45? How would the critical z change? One-tailed Two-tailed α = 0.05 Significance level = .05 α = 0.01 Significance level = .01 -1.64 or +1.64 -1.96 or +1.96 Remember, reject the null if the observed z is bigger than the critical z Reject the null Reject the null -2.33 or +2.33 -2.58 or +2.58 Reject the null Do not Reject the null Review

11 90% Moving from descriptive stats into inferential stats….
For scores that fall into the middle range, we do not reject the null Measurements that occur within the middle part of the curve are ordinary (typical) and probably belong there Critical z 1.64 Critical z -1.64 90% Measurements that occur outside this middle ranges are suspicious, may be an error or belong elsewhere 5% 5% 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

12 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 < 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” Review

13 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? Review

14 We make decisions at Security Check Points
. We make decisions at Security Check Points .

15 Does this airline passenger have a snow globe?
. 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?

16 Does this airline passenger have a snow globe?
. 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? True Ho No snow globe False Ho Yes snow globe You are wrong! Type II error (miss) Do not reject Ho “no snow globe move on” You are right! Correct decision Decision made by 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???!!

17 Type I error (false alarm)
Type I or type II error? . Decision made by experimenter Reject Ho Do not Reject Ho True Ho False Ho You are right! Correct decision You are wrong! Type I error (false alarm) Type II error (miss) 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)

18 Type I error (false alarm)
Type I or type II error . Decision made by experimenter Reject Ho Do not Reject Ho True Ho False Ho You are right! Correct decision You are wrong! Type I error (false alarm) Type II error (miss) 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)

19 What is worse a type I or type II error?
. Decision made by experimenter Reject Ho Do not Reject Ho True Ho False Ho You are right! Correct decision You are wrong! Type I error (false alarm) Type II error (miss) What if we were looking at 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)

20 Which is worse? Type I or type II error
. Which is worse? 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 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)

21 Which is worse? Type I or type II error
. Which is worse? Type I or type II error What if we were looking to see if an individual were 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

22 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

23 -3.35 1.97 Yes Yes Yes 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

24 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

25 3.64 1.964 Yes Yes Yes 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

26 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

27 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

28 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

29 -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 A t-test showed a significant difference, t(8) = ; p < 0.05

30

31

32 Thank you! See you next time!!

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