1. Chapter 1 Jan. 8, 20081 Chapter 1 Where Do Data Come From?

2. Chapter 1 Jan. 8, 20082 Thought Question 1 From a recent study, researchers concluded that high levels of alcohol consumption resulted in lower graduation rates at colleges. How do you think this study was carried out in order to get these results? Do you think the conclusion is correct? Is there a more reasonable conclusion?

3. Chapter 1 Jan. 8, 20083 Thought Question 2 It is popular knowledge that for similar jobs men earn more money on average than women, and yet there are cases where some women make more money than some men. Therefore, to determine if men really do earn more, you would need to sample many people of each sex. Suppose we also want to know if, on average, men stay at their current jobs for a longer time period than women. How could you go about trying to determine this? Would it be sufficient to collect data for one member of each sex?... two members of each sex? What information about men’s and women’s measurements would help you decide how many people to measure?

4. Chapter 1 Jan. 8, 20084

5. 5 What is STATISTICS ?  Using “data” to draw a conclusion about something unknown.  Decision making in the presence of uncertainty.

6. Chapter 1 Jan. 8, 20086 Statistics- Meaning ? MMethod of analysis a collection of methods for planning experiments or observational studies, obtaining data, and then organizing, summarizing, presenting, analyzing, interpreting, and drawing conclusions based on the data.

7. 7 Statistics- Meaning ? OOur Book: Statistics is the science (or ‘art’) of data.

8. 8 Common Language

9. Chapter 1 Jan. 8, 20089 Population TThe complete collection of all subjects or objects (scores, people, measurements, and so on) that are being studied. TThe collection is complete in the sense that it includes all subjects to be studied.

10. 10  Census: The collection of data from every element in a population.  Sample : A subset of elements drawn from a population from which we collect data.  The sample must be a good representative of the entire population.

11. Chapter 1 Jan. 8, 200811 Population individuals

12. Chapter 1 Jan. 8, 200812 Sampling Frame Individuals that could possibly be selected for the sample (not necessarily the same as the population)

13. Chapter 1 Jan. 8, 200813 List of Individuals 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 Census 1 9 2 345 6 7 8 10 17 16 15 13 14 12 11 1 9 2 345 6 7 8 10 17 16 15 13 14 12 11 Census

14. Chapter 1 Jan. 8, 200814 Sampling Frame 1 9 2 345 6 7 8 10 17 16 15 13 14 12 11 List of Individuals 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 Sample

15. Chapter 1 Jan. 8, 200815 Example  Suppose we are interested in the average age of all Malaspina students.  The relevant population is all Malaspina students (including students in all campuses).  Sampling Frame: List of Malaspina students at the Nanaimo campus.

16. Chapter 1 Jan. 8, 200816 Example Cont. AA sample can be students in this Math 161 class, or, 50 randomly selected Malaspina students at the Nanaimo campus. IIf we use the ages of all Malaspina students, then we have a census.

17. Chapter 1 Jan. 8, 200817 _____________________________________ ______________________________________ What is Statistics?

18. Chapter 1 Jan. 8, 200818 Descriptive & Inferential Statistics

19. Chapter 1 Jan. 8, 200819 Descriptive Statistics Consists of the collection, organization, summarization, and presentation of data.

20. Chapter 1 Jan. 8, 200820 Inferential Statistics Consists of generalizing from samples to populations, performing estimations and hypothesis tests, determining relationships among variables, and making predictions.

21. Chapter 1 Jan. 8, 200821 What Is “Data”? (better: What are “data”?)  Pieces of information.  Numbers.  The above are data only if the information has a meaning attached.

22. Chapter 1 Jan. 8, 200822 Data Data are observations that have been collected. The observation may be numerical (example: age, height, GPA) or non-numerical (example: gender, eye colour, province of residence) The Nature of Data

23. Chapter 1 Jan. 8, 200823 Two Types of Data Quantitative or Numeric Data Numbers representing counts or measurements. Qualitative or Categorical Data Data can be separated into different categories that are distinguished by some non-numeric characteristics. The Nature of Data

24. Chapter 1 Jan. 8, 200824 Examples Quantitative (numerical) data the ________________ of college graduates the ________________ between home and school Qualitative (or categorical) data the ___________ of college graduates (F, M) the ___________ of a product (best, good, bad)

25. Chapter 1 Jan. 8, 200825 Two Types of Quantitative Data  Discrete: Data values that can be counted such as 0, 1, 2, 3,... Example: Number of students in a Stat. class.  Continuous: Data that can assume an infinite number of values between any two specific values. - Usually results from measurements. 23

26. Chapter 1 Jan. 8, 200826 Classify as discrete or continuous: 1. The number of eggs that hens lay; for example, 3 eggs a day________. Examples 2. The height of College students. ___________________

27. Chapter 1 Jan. 8, 200827

28. Chapter 1 Jan. 8, 200828 1. Nominal: characterized by data that consist of names, labels, or categories only. The data cannot be arranged in an ordering scheme (such as low to high) Example: Survey responses may be yes, no, or undecided. Eye colour, gender etc. Levels of Measurements

29. Chapter 1 Jan. 8, 200829 2. Ordinal: involves data that may be arranged in some order, but differences between data values either cannot be determined or are meaningless Example: Course grades: A, B, C, D, or F Dress size: small, medium, large, XL

30. Chapter 1 Jan. 8, 200830 3. Interval: like the ordinal level, with the additional property that the difference between any two data values is meaningful. However, there is no natural zero starting point (where none of the quantity is present) Example: Years 1000, 2000, 1776, and 1492 Temperature in 0 C - 0 0 C does not mean no temperature.

31. Chapter 1 Jan. 8, 200831 4. Ratio: the interval level modified to include the natural zero starting point (where zero indicates that none of the quantity is present). For values at this level, differences and ratios are meaningful. Example: Prices of college textbooks.

32. Chapter 1 Jan. 8, 200832 Levels of Measurement _________________ - categories only _________________- categories with some order _________________- differences but no natural starting point _________________- differences and a natural starting point

33. Chapter 1 Jan. 8, 200833 SummaryData Categorical NominalOrdinal Numerical IntervalRatio

34. Chapter 1 Jan. 8, 200834 How Data are Obtained  Observational Study –Observes individuals and measures variables of interest but does not attempt to influence the responses. –Describes some group or situation. –Sample Surveys are a type of observational study.  Experiment –Deliberately imposes some treatment on individuals in order to observe their responses. –Studies whether the treatment causes change in the response.

35. Chapter 1 Jan. 8, 200835 Experiments vs. observational studies for comparing the effects of treatments: EExperiment –e–experimenter determines which units receive which treatments (ideally using some form of random allocation) OObservational study –c–compare units that happen to have received each of the treatments –o–often useful for identifying possible causes of effects, but cannot reliably establish causation OOnly properly designed and executed experiments can reliably demonstrate causation.

36. Chapter 1 Jan. 8, 200836 Data Sources Data Sources PrimarySecondary Experiment Survey Observation

37. Chapter 1 Jan. 8, 200837 Case Study The Effect of Hypnosis on the Immune System reported in Science News, Sept. 4, 1993, p. 153

38. Chapter 1 Jan. 8, 200838 Case Study The Effect of Hypnosis on the Immune System Objective: To determine if hypnosis strengthens the disease-fighting capacity of immune cells.

39. Chapter 1 Jan. 8, 200839 Case Study  65 college students. –33 easily hypnotized –32 not easily hypnotized  white blood cell counts measured  All students viewed a brief video about the immune system.

40. Chapter 1 Jan. 8, 200840 Case Study  Students randomly assigned to one of three conditions –subjects hypnotized, given mental exercise –subjects relaxed in sensory deprivation tank –control group (no treatment)

41. Chapter 1 Jan. 8, 200841 Case Study  white blood cell counts re-measured after one week  the two white blood cell counts are compared for each group  Results –hypnotized group showed larger jump in white blood cells –“easily hypnotized” group showed largest immune enhancement

42. Chapter 1 Jan. 8, 200842 Case Study The Effect of Hypnosis on the Immune System What is the population? What is the sample?

43. Chapter 1 Jan. 8, 200843 Case Study The Effect of Hypnosis on the Immune System What data were collected?  Easy or difficult to achieve hypnotic trance  Group assignment  Pre-study white blood cell count  Post-study white blood cell count

44. Chapter 1 Jan. 8, 200844 Case Study The Effect of Hypnosis on the Immune System Is this an experiment or an observational study?

45. Chapter 1 Jan. 8, 200845 Case Study The Effect of Hypnosis on the Immune System Do hypnosis and mental exercise affect the immune system?

46. Chapter 1 Jan. 8, 200846 Case Study Weight Gain Spells Heart Risk for Women “Weight, weight change, and coronary heart disease in women.” W.C. Willett, et al., vol. 273(6), Journal of the American Medical Association, Feb. 8, 1995. (Reported in Science News, Feb. 18, 1995, p. 108)

47. Chapter 1 Jan. 8, 200847 Case Study Weight Gain Spells Heart Risk for Women Objective: To recommend a range of body mass index (a function of weight and height) in terms of coronary heart disease (CHD) risk in women.

48. Chapter 1 Jan. 8, 200848 Case Study  Study started in 1976 with 115,818 women aged 30 to 55 years and without a history of previous CHD.  Each woman’s weight (body mass) was determined.  Each woman was asked her weight at age 18.

49. Chapter 1 Jan. 8, 200849 Case Study  The cohort of women were followed for 14 years.  The number of CHD (fatal and nonfatal) cases were counted (1292 cases).  Results were adjusted for other variables.

50. Chapter 1 Jan. 8, 200850 Case Study  Results: compare those who gained less than 11 pounds from age 18 to current age to the others. –11 to 17 lbs: 25% more likely to develop heart disease –17 to 24 lbs: 64% more likely –24 to 44 lbs: 92% more likely –more than 44 lbs: 165% more likely

51. Chapter 1 Jan. 8, 200851 Case Study Weight Gain Spells Heart Risk for Women What is the population? What is the sample?

52. Chapter 1 Jan. 8, 200852 Case Study Weight Gain Spells Heart Risk for Women What data were collected?  Age in 1976  Weight in 1976  Weight at age 18  Incidence of coronary heart disease  Other: smoking, family history, menopausal status, post-menopausal hormone use

53. Chapter 1 Jan. 8, 200853 Case Study Weight Gain Spells Heart Risk for Women Is this an experiment or an observational study?

54. Chapter 1 Jan. 8, 200854 Case Study Weight Gain Spells Heart Risk for Women Does weight gain in women increase their risk for CHD?

55. Chapter 1 Jan. 8, 200855 Key Concepts  Knowing about statistical methods will have practical consequences in your everyday lives.  Experiment versus Observational Study.  Common Terms: –Individuals, Population, Sampling Frame, Sample, Sample Survey, Census, Variable.

56. Chapter 1 Jan. 8, 200856 Conclusion Defined statistics. Distinguished between descriptive & inferential statistics. Summarized the sources of data. Described the types of data & scales. Common Terms: Population, Sampling frame, Census, Sample, Individuals, Variables etc.