Stats 244.3

1. Stats 244.3 Elementary Statistical Concepts

2. Instructor: W.H.Laverty Office: 235 McLean Hall Phone: 966-6096 Lectures: M Tu W Th F 10:30am -11:50amArts 200Lab: Tu W Th 12:00 - 12:50 Arts 200 Evaluation: Assignments, Labs, Term tests - 40% Each Friday – Term TestFinal Examination - 60%

3. Text: Moore, The Basic Practice of Statistics, I will provide lecture notes (power point slides). I will provide tables. The assignments will not come from the textbook. This means that the purchasing of the text is optional.

4. Course Outline

5. Introduction • Populations, samples • Variables • Data Collection • Chapter 1

6. Data Presentation-Exploratory Statistics • Organizing and displaying Data • Numerical measures of Central Tendency an Variability • Describing Bivariate Data • Chapter 2 , Chapter 3 , Chapter 4

7. Probability Theory • Concepts of Probability • Random variables and their distributions • Binomial distribution, Normal distribution • Chapters 9, 10, 11 and 12

8. Inferential Statistics • Estimation, Hypotheses testing • Comparing Samples • Analyzing count data , Contingency Tables • Regression and Correlation • Multiple Regression • Chapters 13 - 23

9. Introduction

10. Questions arise about a phenomenon Conclusion are drawn from the analysis A decision is made to collect data A decision is made as how to collect the data The data is summarized and analyzed The data is collected The circular process of research:

11. What is Statistics? It is the major mathematical tool of scientific inference (research) - the art of drawing conclusion from data. Data that is to some extent corrupted by some component of random variation (random noise)

12. Random variation or (random noise) can be defined to be the variation in the data that is not accounted for by factors considered in the analysis.

13. Example Suppose we are collecting data on Blood Pressure Height Weight Age

14. Suppose we are interested in how Blood Pressure is influenced by the following factors Height Weight Age

15. Blood Pressure will not be perfectly predictable from : • Height • Weight • Age There will departures (random variation) from a perfect prediction because of other factors the could affect Blood pressure (diet, exercise, hereditary factors)

16. Another Example In this example we are interested in the use of: • antidepressants, • mood stabilizing medication, • anxiety medication, • stimulants and • sleeping pills. The data were collected for n = 16383 cases

17. Age 20-29, 30-39,40-49, 50-59, 60-69, 70+ In addition we are interested in how the use these medications is affected by: • Gender Male, female • Education • < Secondary, • Secondary Grad., • some Post-Sec., • Post-Sec. Grad.

18. Income • Low, Low Mid, Up Mid, High • Role • parent, partner , worker • parent, partner • parent, worker • partner, worker • worker only • parent only • partner only • no roles

19. Some questions of interest • How are the dependent variables (antidepressant use, mood stabilizing medication use, anxiety medication use, stimulants use, sleeping pill use) interrelated? • How are the dependent variables (drug use) related to the independent variables (age, gender, income, education and role)?

20. Again the relationships will not be perfect • Because of the effects of other factors (variables) that have not been considered in the experiment • If the data is recollected, the patterns observed at the second collection will not be exactly the same as that observed at the first collection

21. The data appears in the following Excel file drug data.xls

22. In Statistics • Questions • About some scientific, sociological, medical or economic phenomena • Data • The purpose of the data is to find answers to the questions • Answers • Because of the random variation in the data (the noise). Conclusions based on the data will be subject to error.

23. Statistics Statistics In what part of this process does statistics play a role? Questions arise about a phenomenon The circular process of research: Conclusion are drawn from the analysis A decision is made to collect data Experimental Design A decision is made as how to collect the data The data is summarized and analyzed The data is collected

24. Statistical Theory is interested in • The design of the data collection procedures. (Experimental designs, Survey designs). The experiment can be totally lost if it is not designed correctly. • The techniques for analyzing the data.

25. In any statistical analysis it is important to assess the magnitude of the error made by the conclusions of the analysis.

26. Consider the following statement: You can prove anything with Statistics.

27. In fact: One is unable to “prove” anything with Statistics.

28. At the end of any statistical analysis there always is a possibility of an error in any of the decisions that it makes.

29. The success of a research project does not depend on the its conclusions The success of a research project depends on the accuracy of its conclusions

30. If one is testing the effectiveness of a drug There is two possible conclusions: 1. The drug is effective: 2. The drug is not effective:

31. The success of a this project does not depend on the its conclusions The successdepends on the accuracy of its conclusions

32. For this reason: It is extremely important in any study to assess the accuracy of its conclusions

33. Some definitions important to Statistics

34. A population: this is the complete collection of subjects (objects) that are of interest in the study. There may be (and frequently are) more than one in which case a major objective is that of comparison.

35. A case (elementary sampling unit): This is an individual unit (subject) of the population.

36. A variable: a measurement or type of measurement that is made on each individual case in the population.

37. Types of variables Some variables may be measured on a numerical scale while others are measured on a categorical scale. The nature of the variables has a great influence on which analysis will be used. .

38. For Variables measured on a numerical scale the measurements will be numbers. Ex: Age, Weight, Systolic Blood Pressure For Variables measured on a categoricalscale the measurements will be categories. Ex: Sex, Religion, Heart Disease

39. Note Sometimes variables can be measured on both a numerical scale and a categorical scale. In fact, variables measured on a numerical scale can always be converted to measurements on a categorical scale.

40. Example • Cause of the injury (categorical) • Motor vehicle accident • Fall • Violence • other The following variables were evaluated for a study of individuals receiving head injuries in Saskatchewan.

41. Time of year (date) (numerical or categorical) • summer • fall • winter • spring • Sex on injured individual (categorical) • male • female

42. Age (numerical or categorical) • < 10 • 10-19 • 20 - 29 • 30 - 49 • 50 – 65 • 65+ • Mortality (categorical) • Died from injury • alive

43. Types of variables In addition some variables are labeled as dependent variables and some variables are labeled as independent variables.

44. This usually depends on the objectives of the analysis. Dependent variables are output or response variables while the independent variables are the input variables or factors.

45. Usually one is interested in determining equations that describe how the dependent variables are affected by the independent variables

46. Example Suppose we are collecting data on Blood Pressure Height Weight Age

47. Suppose we are interested in how Blood Pressure is influenced by the following factors Height Weight Age

48. Then Blood Pressure is the dependent variable and Height Weight Age Are the independent variables

49. Example – Head Injury study Suppose we are interested in how Mortality is influenced by the following factors Cause of head injury Time of year Sex Age

50. Then Mortality is the dependent variable and Cause of head injury Time of year Sex Age Are the independent variables