2. Modern Languages 14131211109 87 6 54321 111098765 43 2 Row A Row B Row C Row D Row E Row F Row G Row H Row J Row K Row L Row M 212019181716 1514 13 12111098 212019181716 13 12111098 141312 table 7 6 54321 Row C Row D Row E Row F Row G Row H Row J Row K Row L Row M 321 21 1413 Projection Booth 212019181716 1514 13 12111098 212019181716 1514 13 12111098 212019181716 1514 13 12111098 212019181716 1514 13 12111098 212019181716 1514 13 12111098 212019181716 1514 13 12111098 212019181716 1514 13 12111098 212019181716 1514 13 12111098 7 6 5432 1 765 43 2 1 7 6 5432 1 765 43 2 1 7 6 54321 765 43 2 1 7 6 54321 765 43 2 1 7 6 54321 table Row C Row D Row E Row F Row G Row H Row J Row K Row L Row M 321 28 27 26252423 22 282726 2524 23 22 282726 2524 23 22 28 27 26252423 22 282726 2524 23 22 282726 2524 23 22 28 27 26252423 22 282726 2524 23 22 282726 2524 23 22 282726 2524 23 22 R/L handed broken desk Stage Lecturer’s desk Screen 1

3. MGMT 276: Statistical Inference in Management Spring 2015

5. Before our next exam (April 14 th ) Lind (10 – 12) Chapter 10: One sample Tests of Hypothesis Chapter 11: Two sample Tests of Hypothesis Chapter 12: Analysis of Variance Plous (2, 3, & 4) Chapter 2: Cognitive Dissonance Chapter 3: Memory and Hindsight Bias Chapter 4: Context Dependence Schedule of readings

6. Logic of hypothesis testing Steps for hypothesis testing Levels of significance (Levels of alpha) what does p < 0.05 mean? what does p < 0.01 mean? Hypothesis testing with t-scores (two independent samples) Analysis of Variance (ANOVA) Constructing brief, complete summary statements By the end of lecture today 4/2/15

7. On class website: Please print and complete homework worksheet #13 & 14 Hypothesis testing using t-tests Homework due – Tuesday (April 7 th ) Please note: Because this homework is longer than most, it is worth two assignments Please note: Because this homework is longer than most, it is worth two assignments On class website: Please print and complete homework worksheet #15 Hypothesis testing using ANOVAs Homework due – Thursday (April 9 th )

8. .. A note on z scores, and t score: Difference between means Numerator is always distance between means (how far away the distributions are) Denominator is always measure of variability (how wide or much overlap there is between distributions) Variability of curve(s)

9. 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)? 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 Critical statistic (e.g. z or t) value? How is a single sample t-test different than two sample t-test? Single sample standard deviation versus average standard deviation for two samples How is a single sample t-test most similar to the two sample t-test? Single sample has one “n” while two samples will have an “n” for each sample

10. What happened? We ran more subjects: Increased n So, we decreased variability Easier to find effect significant even though effect size didn’t change Big sampleSmall sample This is variance for each sample (Remember, variance is just standard deviation squared) This is variance for each sample (Remember, variance is just standard deviation squared)

11. If this is less than.05 (or whatever alpha is) it is significant, and we the reject null df = (n 1 – 1) + (n 2 – 1) = (165 - 1) + (120 -1) = 283

12. A survey was conducted to see whether men or women superintendents make more money 1.The independent variable is ________________ 2.The dependent variable is _________________ 3. Who made more money men or women? 4. Identify the two means and the observed t score 5. Identify the p value and state whether it is less than.05

13. A survey was conducted to see whether men or women superintendents make more money 1.37834 E-05 Equals.00001378 4 zeros 6.8917 E-06 Equals.0000068917 5 zeros Are both p values less than 0.05?

14. A survey was conducted to see whether men or women superintendents make more money 1.37834 E-05 Equals.00001378 4 zeros 6.8917 E-06 Equals.0000068917 5 zeros A note on scientific notation: “E-05” means move the decimal to the left 5 places E-06” means move the decimal to the left 6 places

15. A survey was conducted to see whether men or women superintendents make more money. The independent variable is a. nominal level of measurement b. ordinal level of measurement c. interval level of measurement d. ratio level of measurement correct

16. A survey was conducted to see whether men or women superintendents make more money. The dependent variable is a. nominal level of measurement b. ordinal level of measurement c. interval level of measurement d. ratio level of measurement correct

17. A survey was conducted to see whether men or women superintendents make more money. The independent variable is a. continuous and qualitative b. continuous and quantitative c. discrete and qualitative d. discrete and quantitative correct

18. A survey was conducted to see whether men or women superintendents make more money. The dependent variable is a. continuous and qualitative b. continuous and quantitative c. discrete and qualitative d. discrete and quantitative correct

19. A survey was conducted to see whether men or women superintendents make more money. This is a a. quasi, between subject design b. quasi, within subject design c. true, between subject design d. true, within subject design correct

20. A survey was conducted to see whether men or women superintendents make more money. This is a a. one-tailed test b. two-tailed test c. three-tailed test d. not enough information correct

21. A survey was conducted to see whether men or women superintendents make more money. The null hypothesis is a. men make more money b. women make more money c. no difference between amount of money made d. there is a difference between the amount of money made correct

22. A survey was conducted to see whether men or women superintendents make more money. If the null hypothesis was rejected we will conclude that a. men make more money b. women make more money c.no difference between amount of money made d. there is a difference between the amount of money made correct

23. A survey was conducted to see whether men or women superintendents make more money. A Type I error would be a. claiming men make more money, when they don’t b. claiming women make more money, when they don’t c.claiming no difference between amount of money made, when there is a difference d. claiming there is a difference between the amount of money made, when there is no difference correct

24. A survey was conducted to see whether men or women superintendents make more money. A Type II error would be a. claiming men make more money, when they don’t b. claiming women make more money, when they don’t c.claiming no difference between amount of money made, when there is a difference d. claiming there is a difference between the amount of money made, when there is no difference correct

25. An t-test was conducted, there were ___ men in the study and ___ women. a. 18; 21 b. 21; 18 c. 19; 19 d. 38; 38 Let’s try one correct

26. A t-test was conducted, which of the following best describes the results: a. t(37) = 2.02; p < 0.05 b. t(21) = 2.02; n.s. c. t(37) = 5.0; p < 0.05 d. t(21) = 5.0; n.s Let’s try one correct

27. A t-test was conducted, with a two tail test was there a significant difference? a. No, because 5.0 is not bigger than 6.89 b. Yes, because 5.0 is bigger than 1.68. c. Yes, because 5.0 is bigger than 1.37 d. Yes, because 5.0 is bigger than 2.02 Let’s try one correct

28. Which is true a. p < 0.05 b. p < 0.01 c. p < 0.001 d. All of the above Let’s try one correct

29. A survey was conducted to see whether women superintendents make more money than men. This is a a. one-tailed test b. two-tailed test c. three-tailed test d. not enough information Note the change in the problem correct

30. A survey was conducted to see whether women superintendents make more money than men. A t-test was conducted, which of the following best describes the results: Note the results were in the unpredicted direction a. reject the null b. do not reject the null c. not enough information Let’s try one correct

31. A survey was conducted to see whether women superintendents make more money than men. A t-test was conducted, which of the following best describes the results: Note the results were in the unpredicted direction a. t(21) = 2.02; p < 0.05 b. t(21) = 2.02; n.s. c. t(37) = 5.0; p < 0.05 d. t(37) = 5.0; n.s Let’s try one correct

33. Study Type 2: t-test Study Type 3: One-way Analysis of Variance (ANOVA) Comparing more than two means We are looking to compare two means

34. Single Independent Variable comparing more than two groups Study Type 3: One-way ANOVA Single Dependent Variable (numerical/continuous) Independent Variable: Type of incentive Levels of Independent Variable: None, Bike, Trip to Hawaii Dependent Variable: Number of cookies sold Levels of Dependent Variable: 1, 2, 3 up to max sold Between participant design Causal relationship: Incentive had an effect – it increased sales Ian was interested in the effect of incentives for girl scouts on the number of cookies sold. He randomly assigned girl scouts into one of three groups. The three groups were given one of three incentives and looked to see who sold more cookies. The 3 incentives were 1) Trip to Hawaii, 2) New Bike or 3) Nothing. This is an example of a true experiment Used to test the effect of the IV on the DV How could we make this a quasi-experiment?

35. Single Independent Variable comparing more than two groups Study Type 3: One-way ANOVA Single Dependent Variable (numerical/continuous) Ian was interested in the effect of incentives for girl scouts on the number of cookies sold. He randomly assigned girl scouts into one of three groups. The three groups were given one of three incentives and looked to see who sold more cookies. The 3 incentives were 1) Trip to Hawaii, 2) New Bike or 3) Nothing. This is an example of a true experiment Used to test the effect of the IV on the DV None New Bike Sales per Girl scout Trip Hawaii None New Bike Trip Hawaii Dependent variable is always quantitative In an ANOVA, independent variable is qualitative (& more than two groups) Sales per Girl scout

36. Be careful you are not designing a Chi Square One-way ANOVA versus Chi Square None New Bike Sales per Girl scout Trip Hawaii This is an ANOVA None New Bike Total Number of Boxes Sold Trip Hawaii This is a Chi Square If this is just frequency you may have a problem These are means These are just frequencies

37. One-way ANOVA One-way ANOVAs test only one independent variable - although there may be many levels “Factor” = one independent variable “Level” = levels of the independent variable treatment condition groups “Main Effect” of independent variable = difference between levels Note: doesn’t tell you which specific levels (means) differ from each other A multi-factor experiment would be a multi-independent variables experiment Number of cookies sold Incentives None Bike Hawaii trip

38. Comparing ANOVAs with t-tests Similarities still include: Using distributions to make decisions about common and rare events Using distributions to make inferences about whether to reject the null hypothesis or not The same 5 steps for testing an hypothesis The three primary differences between t-tests and ANOVAS are: 1. ANOVAs can test more than two means 2. We are comparing sample means indirectly by comparing sample variances 3. We now will have two types of degrees of freedom t(16) = 3.0; p < 0.05 F(2, 15) = 3.0; p < 0.05 Tells us generally about number of participants / observations Tells us generally about number of groups / levels of IV

39. A girlscout troop leader wondered whether providing an incentive to whomever sold the most girlscout cookies would have an effect on the number cookies sold. She provided a big incentive to one troop (trip to Hawaii), a lesser incentive to a second troop (bicycle), and no incentive to a third group, and then looked to see who sold more cookies. Troop 1 (Hawaii) 6 5 9 4 6 Troop 2 (bicycle) 6 8 5 4 2 Note: 5 girls in each troop Troop 3 (nada) 0 4 0 1 0 x = 6 x = 5 x = 1 What if we want to compare 3 means? One independent variable with 3 means

40. A girl scout troop leader wondered whether providing an incentive to whomever sold the most girl scout cookies would have an effect on the number cookies sold. She provided a big incentive to one troop (trip to Hawaii), a lesser incentive to a second troop (bicycle), and no incentive to a third group, and then looked to see who sold more cookies. n = 5 x = 10 n = 5 x = 12 n = 5 x = 14 Troop 1 (nada) 10 8 12 7 13 Troop 2 (bicycle) 12 14 10 11 13 Troop 3 (Hawaii) 14 9 19 13 15 What is Independent Variable? How many groups? What is Dependent Variable? How many levels of the Independent Variable?

41. Main effect of incentive: Will offering an incentive result in more girl scout cookies being sold? If we have a “effect” of incentive then the means are significantly different from each other we reject the null we have a significant F p < 0.05 We don’t know which means are different from which …. just that they are not all the same To get an effect we want: Large “F” - big effect and small variability Small “p” - less than 0.05 (whatever our alpha is)

42. Hypothesis testing: Step 1: Identify the research problem Describe the null and alternative hypotheses Is there a significant difference in the number of cookie boxes sold between the girlscout troops that were given the different levels of incentive?

43. Hypothesis testing: Decision rule =.05 Critical F (2,12) =3.98 Degrees of freedom (between) = number of groups - 1 Degrees of freedom (within) = # of scores - # of groups = 3 - 1 = 2 = (15-3) = 12* *or = (5-1) + (5-1) + (5-1) = 12.

44. α =.05 Critical F (2,12) = 3.89 F (2,12) Appendix B.4 (pg.518)

45. ANOVA table ? dfMS F ? ? ? Source Between Within Total ? ? SS ? ? ? We’ll start here next time We’ll start here next time