2. Introduction to Statistics for the Social Sciences SBS200, COMM200, GEOG200, PA200, POL200, or SOC200 Lecture Section 001, Spring 2015 Room 150 Harvill Building 8:00 - 8:50 Mondays, Wednesdays & Fridays.

4. Schedule of readings Before next exam (April 10 th ) 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

5. By the end of lecture today 4/1/15 Use this as your study guide Logic of hypothesis testing Steps for hypothesis testing Levels of significance (Levels of alpha) Hypothesis testing with t-scores (two independent samples) Constructing brief, complete summary statements Using Excel for completing t-tests

6. Homework due Assignment 16 Analysis of Variance Due: Monday, April 6 th

7. Labs continue this week Project 2

8. 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 Are the two means significantly different from each other, or is the difference just due to chance?

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

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

11. 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

12. Finding Means

13. 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

14. 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

15. 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)

16. Finding Observed t

17. Finding Critical t

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

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”

22. 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

23. 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”

24. Graphing your t-test results

26. Graphing your t-test results Chart Layout

27. Graphing your t-test results Fill out titles

28. 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 What if we ran more subjects? Big Meal 22 25 22 25 22 25 Small meal 19 23 21 19 23 21 19 23 21 Mean= 24 Mean= 21

29. We compared test scores for large and small meals. The mean test score for the big meal was 24, and was 21 for the small meal. A t-test was calculated and there was a significant difference in test scores between the two types of meals t(16) = 3.928; p < 0.05 Let’s run more subjects using our excel!

30. 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 the sample size

31. 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)

32. Another format option Independent samples t-test Big Meal versus Small Meal Will use the sort function

33. Another format option Independent samples t-test Big Meal versus Small Meal Will use the sort function

34. Independent samples t-test Male versus Female Students Another format option Will use the sort function

35. Independent samples t-test Male versus Female Students Another format option Will use the sort function

36. The mean test score for female participants was 22.2, while the mean test score for male participants was 22.7. A t-test was completed and there appears to be no significant difference in the test scores as a function of gender, t(16) = -0.523; n.s. Type of test with degrees of freedom Value of observed statistic n.s. = “not significant” p<0.05 = “significant”

37. One paragraph summary of this study. Describe the IV & DV. Present the two means, which type of test was conducted, and the statistical results. We compared productivity for men and women. The mean productivity level for men was 3.65 and the mean productivity for women was 3.43. A t-test was calculated and there appears to be a significant difference in productivity between the two groups t(298) = 3.64; p < 0.05 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 Type of test with degrees of freedom Value of observed statistic p<0.05 = “significant” Sample size150150

38. 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

40. . Homework

41. .

42. . Type of instruction Exam score 50 0.05 2-tail 2.66 2.02 40 38 p = 0.0113 yes CAUTION This is significant with alpha of 0.05 BUT NOT WITH alpha of 0.01 The average exam score for those with instruction was 50, while the average exam score for those with no instruction was 40. A t-test was conducted and found that instruction significantly improved exam scores, t(38) = 2.66; p < 0.05

43. . Homework Type of Staff Travel Expenses 142.5 0.05 2-tail 1.53679 2.2 130.29 11 p = 0.153 no The average expenses for sales staff is 142.5, while the average expenses for the audit staff was 130.29. A t-test was conducted and no significant difference was found, t(11) = 1.54; n.s.

44. . Homework Location of lot Number of cars 86.24 0.05 2-tail -0.88 2.01 92.04 51 p = 0.38 no The average number of cars in the Ocean Drive Lot was 86.24, while the average number of cars in Rio Rancho Lot was 92.04. A t-test was conducted and no significant difference between the number of cars parked in these two lots, t(51) = -.88; n.s. Fun fact: If the observed t is less than one it will never be significant

45. . Please hand in your homework – they must be stapled