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My last name starts with a letter somewhere between A. A – D B. E – L C. M – R D. S – Z

Please click in. Set your clicker to channel 41. My last name starts with a letter somewhere between A. A – D B. E – L C. M – R D. S – Z .

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My last name starts with a letter somewhere between A. A – D B. E – L C. M – R D. S – Z

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  1. Please click in Set your clicker to channel 41 My last name starts with a letter somewhere between A. A – D B. E – L C. M – R D. S – Z

  2. Introduction to Statistics for the Social SciencesSBS200, COMM200, GEOG200, PA200, POL200, SOC200Lecture Section 001, Fall, 2011Room 201 Physics-Atmospheric Sciences (PAS)10:00 - 10:50 Mondays & Wednesdays + Lab Session Welcome Please double check – All cell phones other electronic devices are turned off and stowed away http://www.youtube.com/watch?v=oSQJP40PcGI

  3. Please read: Chapters 10 – 11 in Lind book and Chapters 2 – 4 in Plous book: Lind Chapter 10: One sample Tests of Hypothesis Chapter 11: Two sample Tests of Hypothesis Chapter 12: Analysis of Variance Plous Chapter 2: Cognitive Dissonance Chapter 3: Memory and Hindsight Bias Chapter 4: Context Dependence Chapter 12: Analysis of Variance WILL NOT appear on Exam 3 Exam 3 is a week from today – Study Guide is online

  4. Exam 3 – This Monday (11/7/11) Study guide is posted online Bring 2 calculators (remember only simple calculators,we can’t use calculators with programming functions) Bring 2 pencils (with good erasers) Bring ID

  5. No Homework Just study for Exam 3 Monday – November 7, 2011 No Class on Wednesday -Nov. 9, 2011 Use time to meet with group and/or gather data for lab project Please double check – All cell phones other electronic devices are turned off and stowed away

  6. Use this as your study guide By the end of lecture today11/2/11 Logic of hypothesis testing Steps for hypothesis testing for t-tests Two-sample t-tests using Excel

  7. . . A note on z scores, and t score: • 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) Difference between means Difference between means Difference between means Variabilityof curve(s) Variabilityof curve(s) Variabilityof curve(s)

  8. Independent samples t-test Are the two means significantly different from each other, or is the difference just due to chance? 24 – 21 t = variability 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 Got to figure this part out: We want to average from 2 samples - Call it “pooled” x1 – x2 t = variability

  9. Hypothesis testing Step 1: Identify the research problem Did the size of the meal affect the learning / test scores? Step 2: Describe the null and alternative hypotheses Ho: The size of the meal has no effect on test scores H1: The size of the meal does have an effect on test scores Step 3: Decision rule α= .05 One tail or two tail test?

  10. Hypothesis testing Step 3: Decision rule α= .05 n1 = 3; n2 = 3 Degrees of freedom total (df total) = (n1 - 1) + (n2 – 1) = (3 - 1) + (3 – 1) = 4 Degrees of freedom total (df total) = (n total - 2) two tailed test Notice: Two different ways to think about it Critical t(4) = 2.776

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

  12. 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 = 1.732 6 Notice: s2 = 3.0 1 2 1 Notice: Simple Average = 3.5 = 2.0 8 Notice: s2 = 4.0 2 2 2 (n1 – 1) s12 + (n2 – 1) s22 S2pooled = n1 + n2 - 2 (3 – 1) (1.732) 2 + (3 – 1) (2)2 = 3.5 S2pooled = 31+ 32- 2

  13. 24 – 21 = 1.5275 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 Participant 1 2 3 Σ = 6 Σ = 8 S2p= 3.5 24 - 21 = 1.964 3.5 3.5 3 3 Observed t

  14. Hypothesis testing Step 5: Make decision whether or not to reject null hypothesis Observed t = 1.964 Critical t = 2.776 1.964 is not farther out on the curve than 2.776 so, we do not reject the null hypothesis t(4) = 1.964; n.s. Step 6: Conclusion: There appears to be no difference in test scores between the two groups

  15. How to report the findingsfor a t-test Mean of small meal was 21 Mean of big meal was 24 One paragraph summary of this study. Describe the IV & DV. Present the two means, which type of test was conducted, and the statistical results. Finish with statistical summaryt(4) = 1.96; ns Observed t = 1.964 Start summary with two means (based on DV) for two levels of the IV df = 4 Or if it *were* significant: t(9) = 3.93; p < 0.05 Describe type of test (t-test versus anova) with brief overview of results 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. n.s. = “not significant” p<0.05 = “significant” n.s. = “not significant” p<0.05 = “significant” Type of test with degrees of freedom Value of observed statistic

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

  17. 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

  18. Finding Means Finding Means

  19. Finding degrees of freedom

  20. Finding Observed t

  21. Finding Critical t

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

  23. 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

  24. 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

  25. Hypothesis testing Notice: Additional participants don’t affect this part of the problem Step 1: Identify the research problem Did the size of the meal affect the test scores? Step 2: Describe the null and alternative hypotheses Ho: The size of the meal has no effect on test scores H1: The size of the meal does have an effect on test scores One tail or two tail test?

  26. Hypothesis testing Step 3: Decision rule α= .05 n1 = 9; n2 = 9 Degrees of freedom total (df total) = (n1 - 1) + (n2 – 1) = (9 - 1) + (9 – 1) = 16 Degrees of freedom total (dftotal) = (n total - 2) = 18 – 2 = 16 two tailed test Notice: Two different ways to think about it Critical t(16) = 2.12

  27. two tail test α= .05 (df) = 16 Critical t(16) = 2.12

  28. Mean= 21 Mean= 24 Big Meal Deviation From mean 2 -1 -1 2 -1 -1 2 -1 -1 Small Meal Deviation From mean 2 -2 0 2 -2 0 2 -2 0 SquaredDeviation 4 4 0 4 4 0 4 4 0 Squared deviation 4 1 1 4 1 1 4 1 1 Big Meal 22 25 25 22 25 25 22 25 25 Small meal 19 23 21 19 23 21 19 23 21 Σ = 18 Σ = 24 = 1.50 18 Notice: s2 = 2.25 1 8 1 Notice: Simple Average = 2.625 = 1.732 24 Notice: s2 = 3.0 2 8 2

  29. Mean= 21 Mean= 24 Big Meal 22 25 25 22 25 25 22 25 25 Small meal 19 23 21 19 23 21 19 23 21 Sp = 2.625 S22 = 3.00 S21 = 2.25 S2 = 1.732 S1 = 1.5 (n1 – 1) s12 + (n2 – 1) s22 S2pooled = n1 + n2 - 2 (9 – 1) (1.50)2 + (9 – 1) (1.732)2 = 2.625 S2pooled = 9 + 9 - 2

  30. 24 – 21 = 0.7638 Mean= 21 Mean= 24 Big Meal 22 25 25 22 25 25 22 25 25 Small meal 19 23 21 19 23 21 19 23 21 Sp = 2.625 S2 = 1.732 S1 = 1.5 24 - 21 = 3.928 2.625 2.625 9 9

  31. Hypothesis testing Step 5: Make decision whether or not to reject null hypothesis Observed t = 3.928 Critical t = 2.120 3.928 is farther out on the curve than 2.120 so, we do reject the null hypothesis t(16) = 3.928; p < 0.05 Step 6: Conclusion: There appears to be a difference in hearing sensitivity between the two groups

  32. How to report the findingsfor a t-test Mean of small meal was 21 Mean of big meal was 24 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 Observed t = 3.928 Finish with statistical summaryt(9) = 3.93; p < 0.05 Describe type of test (z-test versus t-test) with brief overview of results df = 16 p < 0.05 n.s. = “not significant” p<0.05 = “significant” Type of test with degrees of freedom Value of observed statistic 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

  33. Let’s run more subjects using our excel!

  34. Let’s run more subjects using our excel! Finding Means Finding Means

  35. Let’s run more subjects using our excel! Finding degrees of freedom Finding degrees of freedom

  36. Let’s run more subjects using our excel! Finding Observed t

  37. Let’s run more subjects using our excel! Finding Critical t

  38. Let’s run more subjects using our excel! Finding p value (Is it less than .05?)

  39. 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!

  40. Homework Review

  41. Writing Assignment

  42. Review for Exam 3

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