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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. Homework #11 (Due November 2nd) Complete Homework Hypothesis testing 2-sample t-scores Available on class website Exam 3 - November 7th Study guide is available online

  4. Use this as your study guide By the end of lecture today10/31/11 Logic of hypothesis testing Steps for hypothesis testing for t-tests How are t-tests similar to z-tests How are t-tests different from z tests Levels of significance (Levels of 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? How is a two-tailed t-test different from a one-tailed t-test

  5. 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

  6. Review of Homework

  7. Finish with statistical summaryt(15) = 2.67; p < 0.05 Or if it *were not* significant: t(15) = 1.07; n.s. 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 n.s. = “not significant” p<0.05 = “significant” 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) Value of observed statistic df

  8. . . 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)

  9. Five steps to hypothesis testing Step 1: Identify the research problem (hypothesis) How is a single sample t-test different than two sample t-test? Describe the null and alternative hypotheses How is a single sample t-test most similar to the two sample t-test? Step 2: Decision rule • Alpha level? (α= .05 or .01)? • Critical statistic (e.g. z or t) value? 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 Single sample standard deviation versus average standard deviation for two samples Single sample has one “n” while two samples will have an “n” for each sample Step 5: Conclusion - tie findings back in to research problem

  10. 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

  11. 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?

  12. 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

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

  14. 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

  15. 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

  16. 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

  17. 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

  18. Thank you! See you next time!!

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