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1. Introduction to Statistics for the Social SciencesSBS200, COMM200, GEOG200, PA200, POL200, or SOC200Lecture Section 001, Spring 2015Room 150 Harvill Building8:00 - 8:50 Mondays, Wednesdays & Fridays. Welcome

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

4. Use this as your study guide By the end of lecture today4/1/15 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

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

6. Lab sessions Labs continue this week Project 2

7. Independent samples t-test Are the two means significantly different from each other, or is the difference just due to chance? 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 Small meal 19 23 21 Big Meal 22 25 25 Mean= 21 Mean= 24

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

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

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

11. Finding Means Finding Means

12. 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

13. Mean= 21 Mean= 24 Big Meal Deviation From mean -2 1 1 Small Meal Deviation From mean -2 2 0 SquaredDeviation 4 4 0 Squared deviation 4 1 1 Big Meal 22 25 25 Small meal 19 23 21 Σ = 6 Σ = 8 6 3 Notice: s2 = 3.0 1 2 1 Notice: Simple Average = 3.5 8 4 Notice: s2 = 4.0 2 2 2 (n1 – 1) s12 + (n2 – 1) s22 S2pooled = n1 + n2 - 2 (3 – 1) (3)+ (3 – 1) (4) = 3.5 S2pooled = 31+ 32- 2

14. This is “n” for each sample (Remember, “n” is just number of observations for each sample) This is “n” for each sample (Remember, “n” is just number of observations for each sample) 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 df = “degrees of freedom”

15. Finding Observed t

16. Finding Critical t

17. Finding Critical t

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

20. 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. Type of test with degrees of freedom n.s. = “not significant” p<0.05 = “significant” Value of observed statistic Start summary with two means (based on DV) for two levels of the IV Finish with statistical summaryt(4) = 1.96; ns Describe type of test (t-test versus anova) with brief overview of results Or if it *were* significant: t(9) = 3.93; p < 0.05

21. 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

22. 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. Type of test with degrees of freedom n.s. = “not significant” p<0.05 = “significant” Value of observed statistic 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 summaryt(4) = 1.96; ns

23. Graphing your t-test results

24. Graphing your t-test results

25. Graphing your t-test results Chart Layout

26. Graphing your t-test results Fill out titles

27. Independent samples t-test What if we ran more subjects? 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 Small meal 19 23 21 19 23 21 19 23 21 Big Meal 22 25 25 22 25 25 22 25 25 Mean= 21 Mean= 24

28. 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!

29. What happened? We ran more subjects: Increased n So, we decreased variability Easier to find effect significant even though effect size didn’t change This is the sample size This is the sample size Big sample Small sample

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 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) Big sample Small sample

31. Another format option Independent samples t-test Big Meal versus Small Meal Will use the sortfunction

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

33. Another format option Independent samples t-test Male versus Female Students Will use the sortfunction

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

35. 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 n.s. = “not significant” p<0.05 = “significant” Value of observed statistic

36. Sample size 150 150 One paragraph summary of this study. Describe the IV & DV. Present the two means, which type of test was conducted, and the statistical results. Start summary with two means (based on DV) for two levels of the IV 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 Type of test with degrees of freedom Describe type of test (t-test versus anova) with brief overview of results Value of observed statistic p<0.05 = “significant”

37. If this is less than .05 (or whatever alpha is) it is significant, and we the reject null df = (n1 – 1) + (n2 – 1) = (165 - 1) + (120 -1) = 283

38. Homework review

39. . Homework

40. . Homework

41. . Homework Type of instruction Exam score 50 40 2-tail 0.05 CAUTION This is significant with alpha of 0.05 BUT NOT WITH alpha of 0.01 2.66 2.02 38 p = 0.0113 yes 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

42. . Homework Type of Staff Travel Expenses 142.5 130.29 2-tail 0.05 1.53679 2.2 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.

43. . Homework Location of lot Number of cars 86.24 92.04 2-tail 0.05 -0.88 2.01 51 p = 0.38 no Fun fact: If the observed t is less than one it will never be significant 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.

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

45. Thank you! See you next time!!