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Introduction to Statistical Methods

This course provides an introduction to statistical methods, covering topics such as populations, samples, variables, data collection, and statistical inference. Assignments, labs, and term tests make up 40% of the grade, while the final examination is worth 60%. Lectures are available for download on the course website.

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Introduction to Statistical Methods

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  1. Stats 244.3 Introduction to Statistical Methods

  2. Instructor: W.H.Laverty Office: 235 McLean Hall Phone: 966-6096 Lectures: M T W Th F 11:00am - 12:20pm Geol 261 Lab: M W Th 12:30 - 1:20 Geol 261 Evaluation: Assignments, Labs, Term tests - 40% Every Thursday – Term TestFinal Examination - 60%

  3. Text:

  4. The lectures will be given in Power Point

  5. To download lectures • Go to the stats 244 web site • Through PAWS or • by going to the website of the department of Mathematics and Statistics -> people -> faculty -> W.H. Laverty -> Stats 244-> Lectures. • Then • select the lecture • Right click and choose Save as

  6. To print lectures • Open the lecture using MS Powerpoint • Select the menu item File -> Print Stat 244.3

  7. The following dialogue box appear

  8. In the Print what box, select handouts

  9. Set Slides per page to 6 or 3.

  10. 6 slides per page will result in the least amount of paper being printed 1 2 3 4 5 6

  11. 3 slides per page leaves room for notes. 1 2 3

  12. Course Outline

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

  14. Introduction

  15. 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:

  16. What is Statistics? It is the major mathematical tool of scientific inference (research) – with an interest in drawing conclusion from data. Data that is to some extent corrupted by some component of random variation (random noise)

  17. 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.

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

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

  20. 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)

  21. 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

  22. 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.

  23. 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

  24. 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)?

  25. 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

  26. The data appears in the following Excel file Drug data

  27. 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.

  28. 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

  29. 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.

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

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

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

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

  34. 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

  35. 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:

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

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

  38. Some definitions important to Statistics

  39. 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.

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

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

  42. 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. .

  43. 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

  44. 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.

  45. 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.

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

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