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MGMT 276: Statistical Inference in Management Spring , 2013

MGMT 276: Statistical Inference in Management Spring , 2013. Welcome. Statistical Inference in Management. Instructor: Suzanne Delaney, Ph.D. Office: 405 “N” McClelland Hall. Phone: 621-2045. Email: delaney@u.arizona.edu. Office hours: 2:00 – 3:30 Mondays and Fridays and by appointment.

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MGMT 276: Statistical Inference in Management Spring , 2013

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  1. MGMT 276: Statistical Inference in ManagementSpring, 2013 Welcome

  2. Statistical Inference in Management Instructor:Suzanne Delaney, Ph.D. Office:405 “N” McClelland Hall Phone:621-2045 Email:delaney@u.arizona.edu Office hours:2:00 – 3:30Mondays and Fridays and by appointment

  3. Please click in My last name starts with a letter somewhere between A. A – D B. E – L C. M – R D. S – Z Hand in your homework

  4. Please read before our next exam (March 19th) - Chapters 5 - 11 in Lind book - Chapters 10, 11, 12 & 14 in Plous book: Lind Chapter 5: Survey of Probability Concepts Chapter 6: Discrete Probability Distributions Chapter 7: Continuous Probability Distributions Chapter 8: Sampling Methods and CLT Chapter 9: Estimation and Confidence Interval Chapter 10: One sample Tests of Hypothesis Chapter 11: Two sample Tests of Hypothesis Plous Chapter 10: The Representativeness Heuristic Chapter 11: The Availability Heuristic Chapter 12: Probability and Risk Chapter 14: The Perception of Randomness

  5. Exam 2 – Tuesday (3/19/13) Study guide online Bring 2 calculators (remember only simple calculators,we can’t use calculators with programming functions) Bring 2 pencils (with good erasers) Bring ID

  6. Use this as your study guide By the end of lecture today3/5/13 Logic of hypothesis testing Steps for hypothesis testing Levels of significance (Levels of alpha) One-tailed versus Two-tailed test Examples of t-tests

  7. Homework due – Thursday (March 7th) On class website: Please print and complete homework worksheet #12 Confidence intervals and Type I versus Type II Errors

  8. 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 95% Critical Z separates rare from common scores 90% Critical z 1.64 Critical z -1.64 Confidence Interval of 90% Has and alpha of 10% α = . 10

  9. 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

  10. 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

  11. 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

  12. 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

  13. 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

  14. 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 95% 95% 2.5% 5% 2.5% How would the critical z change? Pros and cons…

  15. One versus two tail test of significance5% versus 1% alpha levels How would the critical z change? 2.5% .5% 5% 2.5% 1% .5% -1.64 or +1.64 -1.96 or +1.96 -2.33 or +2.33 -2.58 or +2.58

  16. One versus two tail test of significance5% versus 1% alpha levels What if our observed z = 2.0? How would the critical z change? -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 Do notReject the null Do notReject the null

  17. One versus two tail test of significance5% versus 1% alpha levels What if our observed z = 1.75? How would the critical z change? -1.64 or +1.64 -1.96 or +1.96 Do not Reject the null Remember, reject the null if the observed z is bigger than the critical z Reject the null -2.33 or +2.33 -2.58 or +2.58 Do notReject the null Do notReject the null

  18. One versus two tail test of significance5% versus 1% alpha levels What if our observed z = 2.45? How would the critical z change? -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 Do notReject the null Reject the null

  19. Five steps to hypothesis testing Step 1: Identify the research problem (hypothesis) Describe the null and alternative hypotheses Step 2: Decision rule • Alpha level? (α= .05 or .01)? • One or two tailed test? • Balance between Type I versus Type II error • Critical statistic (e.g. z or t or F or r) value? Step 3: Calculations Step 4: Make decision whether or not to reject null hypothesis If observed z (or t) is bigger then critical z (or t) then reject null Step 5: Conclusion - tie findings back in to research problem

  20. 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”

  21. . 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) 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)

  22. . Type I or type II error? Who is taller men or women? What would null hypothesis be? No difference in the height between men and women Type I error: Rejecting a true null hypothesis Saying that there is a difference in height when in fact there is not (false alarm) Type II error: Not rejecting a false null hypothesis Saying there is no difference in height when in fact there is a difference (miss) This is an example of a _____. a. correlation b. t-test c. one-way ANOVA d. two-way ANOVA t-test

  23. . Type I or type II error? Curly versus straight hair – which is more “dateable”? What would null hypothesis be? No difference in the dateability between curly and straight hair Type I error: Rejecting a true null hypothesis Saying that there is a difference in dateability when in fact there is not (false alarm) Type II error: Not rejecting a false null hypothesis Saying there is no difference in dateability when in fact there is a difference (miss) This is an example of a _____. a. correlation b. t-test c. one-way ANOVA d. two-way ANOVA t-test

  24. Writing Assignment Please watch this video describing a series of t-tests What is the independent variable? How many different dependent variables did they use? (They would conduct a different t-test for every dependent variable) http://www.everydayresearchmethods.com/2011/09/curly-or-straight-.html http://www.youtube.com/watch?v=z7kfiA2SXMY http://www.youtube.com/watch?v=n4WQhJHGQB4

  25. Writing Assignment Worksheet Design two t-tests http://www.youtube.com/watch?v=z7kfiA2SXMY http://www.youtube.com/watch?v=n4WQhJHGQB4

  26. Thank you! See you next time!!

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