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Quantitative Methods
QMS 102

Session 1 (June 23) Chapter 1 – Introduction and Data Collection I) What is Data? Data Consist of information coming from observations, counts, measurements, or responses. • “People who eat three daily servings of whole grains have been shown to reduce their risk of…stroke by 37%.” (Source: Whole Grains Council) • “Seventy percent of the 1500 U.S. spinal cord injuries to minors result from vehicle accidents, and 68 percent were not wearing a seatbelt.” (Source: UPI) II) What is Statistics? Statistics The science of collecting, organizing, analyzing, and interpreting data in order to make decisions. Summer 2011 Pa1e# III) Data Sets a) Population The collection of all outcomes, responses, measurements, or counts that are of interest. Examples: 1) All the registered voters in Canada; 2) All students registered in CQMS102 at Ryerson University; 3) All people in Ontario who have OHIP. b) Sample A subset of the population. Summer 2011 Pag2# Examples: 1) All the registered voters in Ontario; 2) All students in this class; 3) All people in Ryerson who have OHIP. Example: Identifying Data Sets In a recent survey, 1708 adults in the United States were asked if they think global warming is a problem that requires immediate government action. Nine hundred thirty-nine of the adults said yes. Identify the population and the sample. Describe the data set. (Adapted from: PewResearch Center) • The population consists of the responses of all adults in the U.S. • The sample consists of the responses of the 1708 adults in the U.S. in the survey. Parameter and Statistic c) Parameter A number that describes a population characteristic. Average age of all people in the United States. Summer 2011 Pag3# d) Statistic A number that describes a sample characteristic. Average age of people from a sample of three states Example: Distinguish Parameter and Statistic Decide whether the numerical value describes a population parameter or a sample statistic. 1. A recent survey of a sample of MBAs reported that the average salary for an MBA is more than $82,000. (Source:The Wall Street Journal) Solution: Sample statistic (the average of $82,000 is based on a subset of the population) 2. Starting salaries for the 667 MBA graduates from the University of Chicago Graduate School of Business increased 8.5% from the previous year. Solution: Population parameter (the percent increase of 8.5% is based on all 667 graduates’ starting salaries) IV) Branches of Statistics Summer 2011 Pag4# 1) Descriptive Statistics Involves organizing, summarizing and displaying data. 2) Inferential Statistics Involves using sample data to draw conclusions about a population. The course CQMS102 will discuss Descriptive Statistics, while CQMS202 will discuss Inferential Statistics. Summer 2011 Pa5e# Example: Descriptive and Inferential Statistics Decide which part of the study represents the descriptive branch of statistics. What conclusions might be drawn from the study using inferential statistics? A large sample of men, aged 48, was studied for 18 years. For unmarried men, approximately 70% were alive at age 65. For married men, 90% were alive at age 65. (Source: The Journal of Family Issues) Solution: Descriptive statistics involves statements such as “For unmarried men, approximately 70% were alive at age 65” and “For married men, 90% were alive at 65.” A possible inference drawn from the study is that being married is associated with a longer life for men. Summer 2011 Pag6# V) Data Collection Observational study •A researcher observes and measures characteristics of interest of part of a population. • Researchers observed and recorded the mouthing behavior on nonfood objects of children up to three years old. (Source: Pediatric Magazine) Experiment •A treatment is applied to part of a population and responses are observed. • An experiment was performed in which diabetics took cinnamon extract daily while a control group took none. After 40 days, the diabetics who had the cinnamon reduced their risk of heart disease while the control group experienced no change. (Source: Diabetes Care) Simulation •Uses a mathematical or physical model to reproduce the conditions of a situation or process. • Often involves the use of computers. Summer 2011 Pag7# • Automobile manufacturers use simulations with dummies to study the effects of crashes on humans. Survey • An investigation of one or more characteristics of a population. • Commonly done by interview, mail, or telephone. • A survey is conducted on a sample of female physicians to determine whether the primary reason for their career choice is financial stability. Consider the following statistical studies. Which method of data collection would you use to collect data for each study? 1. A study of the effect of changing flight patterns on the number of airplane accidents. Solution: Simulation (It is impractical to create this situation) 2. A study of the effect of eating oatmeal on lowering blood pressure. Solution: Experiment (Measure the effect of a treatment – eating oatmeal) 3. A study of U.S. residents’ approval rating of the U.S. president Summer 2011 Pa8e# Solution: Survey (Ask “Do you approve of the way the president is president handling his job?”) VI) Data Classification Types of Data 1) Qualitative Data (Categorical Data) consists of attributes, labels, or non-numerical entries. Another example: The responses to some questions such as 1) Are you currently looking for a job? (Yes or No) 2) Which day of the week do you have a class in Ryerson? (M, T, W, TR, F) 3) Where are you living? Summer 2011 Pag9# 4) What’s the postal code of the address where you are living? 2) Quantitative data (Numerical Data) Numerical measurements or counts. Discrete: From a counting process. Continuous: From a measuring process. Another example: The responses to some questions such as Discrete: How many courses are you taking this term? (1, 2, 3, etc. ) How old are you? (5, 20, 30, 45, etc. ) Continuous: How tall are you? How much time do you spend on shopping each week? Summer 2011 Pag10 Levels of Measurement Data can be classified according to the type of measurement scale that is i
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