2. Lecturer’s desk INTEGRATED LEARNING CENTER ILC 120 Screen 11 10 2 1 98 7 6 5 13 12 15 14 17 16 19 18 4 3 Row A Row B Row C Row D Row E Row F Row G Row H Row I Row J Row K Row L Computer Storage Cabinet Cabinet Table 20 11 10 2 1 9 8 7 6 5 21 20 23 22 25 24 27 26 4 3 28 13 12 14 16 15 17 18 19 11 10 2 1 9 8 7 6 5 21 20 23 22 25 24 26 4 3 13 12 14 16 15 17 18 19 11 10 2 1 9 8 7 6 5 21 20 23 22 25 24 26 4 3 13 12 14 16 15 17 18 19 11 10 2 1 9 8 7 6 5 21 20 23 22 25 24 27 26 4 3 28 13 12 14 16 15 17 18 19 29 11 10 2 1 9 8 7 6 5 21 20 23 22 25 24 27 26 4 3 28 13 12 14 16 15 17 18 19 11 10 2 1 9 8 7 6 5 21 20 23 22 25 24 27 26 4 3 13 12 14 16 15 17 18 19 11 10 2 1 9 8 7 6 5 21 20 23 22 25 24 26 4 3 13 12 14 16 15 17 18 19 11 10 2 1 9 8 7 6 5 21 20 23 22 25 24 4 3 13 12 14 16 15 17 18 19 11 10 2 1 9 8 7 6 5 21 20 23 22 24 4 3 13 12 14 16 15 17 18 19 11 10 2 1 9 8 7 6 5 21 20 23 22 4 3 13 12 14 16 15 17 18 19 11 10 9 8 7 6 5 4 3 13 12 14 16 15 17 18 19 broken desk

3. Introduction to Statistics for the Social Sciences SBS200, COMM200, GEOG200, PA200, POL200, or SOC200 Lecture Section 001, Fall, 2014 Room 120 Integrated Learning Center (ILC) 10:00 - 10:50 Mondays, Wednesdays & Fridays. http://www.youtube.com/watch?v=oSQJP40PcGI

4. Reminder A note on doodling

5. Schedule of readings Before next exam (November 21 st ) Please read chapters 7 – 11 in Ha & Ha Please read Chapters 2, 3, and 4 in Plous Chapter 2: Cognitive Dissonance Chapter 3: Memory and Hindsight Bias Chapter 4: Context Dependence

6. Use this as your study guide Logic of hypothesis testing with t-tests Steps for hypothesis testing for t-tests Levels of significance (alpha) what does alpha of.05 mean? what does p < 0.05 mean? what does alpha of.01 mean? what does p < 0.01 mean? Using Excel to complete t-tests By the end of lecture today 10/31/14

7. Homework due Assignment 17 Two-sample t-tests Due date : Monday, November 3 rd

8. Labs continue this week with Project 2

10. Questions from the homework assignment?

11. mean + z σ = 30 ± (1.96)(2) mean + z σ = 30 ± (2.58)(2) 26.08 < µ < 33.92 24.84 < µ < 35.16 95% 99%

12. Melvin Mark Melvin Difference not due sample size because both samples same size Difference not due population variability because same population Yes! Difference is due to sloppiness and random error in Melvin’s sample Melvin

13. Ho: µ = 5 Ha: µ ≠ 5 Bags of potatoes from that plant are not different from other plants Bags of potatoes from that plant are different from other plants Two tailed test (α =.05) 1.96 6 – 5.25 = 4.0 1 16 √ =.25 4.0 1.96 -1.96 1 4 = z- score : because we know the population standard deviation

14. Yes These three will always match Probability of Type I error is always equal to alpha.05 Because the observed z (4.0 ) is bigger than critical z (1.96) 1.64 No Because observed z (4.0) is still bigger than critical z (1.64) 2.58 there is a difference No Because observed z (4.0) is still bigger than critical z(2.58) there is no difference there is not there is 1.96 2.58

15. Two tailed test (α =.05) Critical t(15) = 2.131 89 - 85 6 16 √ 2.667 t- score : because we don’t know the population standard deviation n – 1 =16 – 1 = 15 2.13 -2.13

16. Yes These three will always match Probability of Type I error is always equal to alpha.05 Because the observed z (2.67) is bigger than critical z (2.13) 1.753 No Because observed t (2.67) is still bigger than critical t (1.753) 2.947 consultant did improve morale Yes Because observed t (2.67) is not bigger than critical t(2.947) consultant did not improve morale she did not she did 2.131 2.947 No These three will always match

17. The average weight of bags of potatoes from this particular plant is 6 pounds, while the average weight for population is 5 pounds. A z-test was completed and this difference was found to be statistically significant. We should fix the plant. (z = 4.0; p<0.05) Start summary with two means (based on DV) for two levels of the IV Describe type of test (z-test versus t-test) with brief overview of results Finish with statistical summary z = 4.0; p < 0.05 Or if it *were not* significant: z = 1.2 ; n.s. Value of observed statistic n.s. = “not significant” p<0.05 = “significant”

18. The average job-satisfaction score was 89 for the employees who went On the retreat, while the average score for population is 85. A t-test was completed and this difference was found to be statistically significant. We should hire the consultant. (t(15) = 2.67; p<0.05) Start summary with two means (based on DV) for two levels of the IV Describe type of test (z-test versus t-test) with brief overview of results Finish with statistical summary t(15) = 2.67; p < 0.05 Or if it *were not* significant: t(15) = 1.07; n.s. df Value of observed statistic n.s. = “not significant” p<0.05 = “significant”

19. .. A note on z scores, and t score: Difference between means Variability of curve(s) 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)

20. 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

21. Independent samples t-test Donald is a consultant and leads training sessions. As part of his training sessions, he provides the students with breakfast. He has noticed that when he provides a full breakfast people seem to learn better than when he provides just a small meal (donuts and muffins). So, he put his hunch to the test. He had two classes, both with three people enrolled. The one group was given a big meal and the other group was given only a small meal. He then compared their test performance at the end of the day. Please test with an alpha =.05 Big Meal 22 25 Small meal 19 23 21 Mean= 24 Mean= 21 t = x 1 – x 2 variability t = 24 – 21 variability Got to figure this part out: We want to average from 2 samples - Call it “pooled” Are the two means significantly different from each other, or is the difference just due to chance?

22. Hypothesis testing Step 1: Identify the research problem Step 2: Describe the null and alternative hypotheses Did the size of the meal affect the learning / test scores? Step 3: Decision rule α =.05 Two tailed test Degrees of freedom total (df total ) = (n 1 - 1) + (n 2 – 1) = (3 - 1) + (3 – 1) = 4 n 1 = 3; n 2 = 3 Critical t (4) = 2.776 Step 4: Calculate observed t score Notice: Two different ways to think about it

23. α =.05 (df) = 4 Critical t (4) = 2.776 two tail test

24. 3 4 Mean= 24 Squared Deviation 4 0 Σ = 8 Big Meal 22 25 Small meal 19 23 21 Big Meal Deviation From mean -2 1 Squared deviation 4 1 Mean= 21 Small Meal Deviation From mean -2 2 0 Σ = 6 = 3.5 S 2 pooled = (n 1 – 1) s 1 2 + (n 2 – 1) s 2 2 n 1 + n 2 - 2 S 2 pooled = (3 – 1) (3) + (3 – 1) (4) 3 1 + 3 2 - 2 6 2 1 8 2 1 2 2 Notice: s 2 = 3.0 Notice: s 2 = 4.0 Notice: Simple Average = 3.5

25. Mean= 24 Squared Deviation 4 0 Σ = 8 Participant 1 2 3 Big Meal 22 25 Small meal 19 23 21 Big Meal Deviation From mean -2 1 Squared deviation 4 1 Mean= 21 Small Meal Deviation From mean -2 2 0 Σ = 6 = 24 – 21 1.5275 = 1.964 S 2 p = 3.5 24 - 21 3.5 33 Observed t 1.964 is not larger than 2.776 so, we do not reject the null hypothesis t(4) = 1.964; n.s. Observed t = 1.964 Critical t = 2.776 Conclusion: There appears to be no difference between the groups

26. How to report the findings for a t-test One paragraph summary of this study. Describe the IV & DV. Present the two means, which type of test was conducted, and the statistical results. Observed t = 1.964 df = 4 Mean of big meal was 24 Mean of small meal was 21 We compared test scores for large and small meals. The mean test scores for the big meal was 24, and was 21 for the small meal. A t-test was calculated and there appears to be no significant difference in test scores between the two types of meals t(4) = 1.964; n.s. Start summary with two means (based on DV) for two levels of the IV Describe type of test (t-test versus anova) with brief overview of results Finish with statistical summary t(4) = 1.96; ns Or if it *were* significant: t(9) = 3.93; p < 0.05 Type of test with degrees of freedom Value of observed statistic n.s. = “not significant” p<0.05 = “significant” n.s. = “not significant” p<0.05 = “significant”

27. We compared test scores for large and small meals. The mean test scores for the big meal was 24, and was 21 for the small meal. A t-test was calculated and there appears to be no significant difference in test scores between the two types of meals, t(4) = 1.964; n.s. Start summary with two means (based on DV) for two levels of the IV Describe type of test (t-test versus anova) with brief overview of results Finish with statistical summary t(4) = 1.96; ns Or if it *were* significant: t(9) = 3.93; p < 0.05 Type of test with degrees of freedom Value of observed statistic n.s. = “not significant” p<0.05 = “significant”

28. Mean= 24 Participant 1 2 3 Big Meal 22 25 Small meal 19 23 21 Mean= 21 Complete a t-test

29. Mean= 24 Participant 1 2 3 Big Meal 22 25 Small meal 19 23 21 Mean= 21 Complete a t-test

30. Mean= 24 Participant 1 2 3 Big Meal 22 25 Small meal 19 23 21 Mean= 21 Complete a t-test If checked you’ll want to include the labels in your variable range If checked, you’ll want to include the labels in your variable range

31. Finding Means

32. This is variance for each sample (Remember, variance is just standard deviation squared) Please note: “Pooled variance” is just like the average of the two sample variances, so notice that the average of 3 and 4 is 3.5

33. This is “n” for each sample (Remember, “n” is just number of observations for each sample) df = “degrees of freedom” Remember, “degrees of freedom” is just (n-1) for each sample. So for sample 1: n-1 =3-1 = 2 And for sample 2: n-1=3-1 = 2 Then, df = 2+2=4 This is “n” for each sample (Remember, “n” is just number of observations for each sample)

34. Finding degrees of freedom

35. Finding Observed t

36. Finding Critical t

38. Finding p value (Is it less than.05?)

40. We compared test scores for large and small meals. The mean test scores for the big meal was 24, and was 21 for the small meal. A t-test was calculated and there appears to be no significant difference in test scores between the two types of meals, t(4) = 1.964; n.s. Start summary with two means (based on DV) for two levels of the IV Describe type of test (t-test versus anova) with brief overview of results Finish with statistical summary t(4) = 1.96; ns Or if it *were* significant: t(9) = 3.93; p < 0.05 Type of test with degrees of freedom Value of observed statistic n.s. = “not significant” p<0.05 = “significant”

41. Hypothesis testing α =.05 Step 4: Make decision whether or not to reject null hypothesis Reject when: observed stat > critical stat 1.96396 is not bigger than 2.776 “p” is less than 0.05 (or whatever alpha is) p = 0.121 is not less than 0.05 Step 5: Conclusion - tie findings back in to research problem There was no significant difference, there is no evidence that size of meal affected test scores

42. The mean test score for participants who ate the big meal was 24, while the mean test score for participants who ate the small meal was 21. A t-test was completed and there appears to be no significant difference in the test scores as a function of the size of the meal, t(4) = 1.96; n.s. Start summary with two means (based on DV) for two levels of the IV Describe type of test (t-test versus anova) with brief overview of results Finish with statistical summary t(4) = 1.96; ns Type of test with degrees of freedom Value of observed statistic n.s. = “not significant” p<0.05 = “significant”

43. Graphing your t-test results

45. Graphing your t-test results Chart Layout

46. Graphing your t-test results Fill out titles

48. Is there a difference in mpg between these two cars There is no difference in mpg between these two cars There is a difference in mpg between these two cars

49. 2-tail 18 0.05 2.101 0.05

50. α =.05 (df) = 18 Critical t (18) = 2.101 two tail test

51. 2-tail 18 0.05 2.101 0.05 S 2 pooled = (n 1 – 1) s 1 2 + (n 2 – 1) s 2 2 n 1 + n 2 - 2 =.82 S 2 pooled = (10 – 1) (.80) 2 + (10 – 1) (1) 2 10 1 + 10 2 - 2 = 3.704 t = 17 – 18.5.82/10 +.82/10 = 1.5.4049691

52. Yes There is a difference There is no difference there is no difference there is a difference

53. The average mpg is 18.5 for the Ford Explorer and 17.0 for the Expedition. A t-test was conducted and found this difference to be significantly different, t(18) = 3.70; p < 0.05 Expedition Explorer Type of Car Miles per gallon 18.6 18.3 18.0 17.7 17.4 17.1 16.8 0

54. . Homework Is there an increase in foot size from 1960 to 1980 Is there no difference (or a decrease) in foot size from 1960 to 1980 There is an increase in foot size from 1960 to 1980 1-tail 22 0.05 1.717

55. α =.05 (df) = 22 Critical t (22) = 1.717 one tail test

56. . Homework Yes =.6201 =.4502 =.2936 S 2 pooled = (12 – 1) (.6201) 2 + (12 – 1) (4502) 2 12 1 + 12 2 - 2 = 2.26 t = 8.208 – 7.708.2936/12 +.2936/12 = 0.5.2212 Yes The average foot size for women in 1960 is 7.7, while the average foot size for women in 1980 is 8.2. A t-test was conducted and found that the increase in foot size is statistically significant, t(22) = 2.26; p < 0.05

57. . 1980 1960 Year of birth Shoe Size 8.6 8.3 8.0 7.7 7.4 0 Homework

58. . Homework – same problem using excel The average foot size for women in 1960 is 7.7, while the average foot size for women in 1980 is 8.2. A t-test was conducted and found that the increase in foot size is statistically significant, t(22) = 2.26; p < 0.05 Shoe Size 1-tail 22 0.05 7.7 8.2 Yes.017014309 1.7170 2.26 Year of Birth