STA291 Spring 2010 LECTURE 2 Monday, January 25 th Review Consumers Union asked all subscribers whether they had used alternative medical treatments. They found that 20% of all their subscribers said “yes.” Is this number a parameter or statistic? A survey was conducted in a city with 500,000 residents. They contacted 100 people randomly and found that 67% of them thought that businesses should be required to pay for their employees’ health insurance. Is this number a parameter or statistic? Scales of Measurement Quantitative or Numerical Variable with numerical values associated with them Qualitative or Categorical Variables without numerical values associated with them Qualitative Variables Nominal Gender, nationality, hair color, state of residence Nominal variables have a scale of unordered categories It does not make sense to say, for example, that green hair is greater/higher/better than orange hair Ordinal Disease status, company rating, grade in STA 291 Ordinal variables have a scale of ordered categories, they are often treated in a quantitative manner (A = 4.0, B = 3.0, etc.) One unit can have more of a certain property than another unit Quantitative Variables Quantitative Age, income, height Quantitative variables are measured numerically, that is, for each subject a number is observed The scale for quantitative variables is called interval scale Example A study about oral hygiene and periodontal conditions among institutionalized elderly measured the following Nominal (Qualitative): Requires assistance from staff? Yes No Ordinal (Qualitative): Plaque score No visible plaque Small amounts of plaque Moderate amounts of plaque Abundant plaque Interval (Quantitative): Number of teeth Example A birth registry database collects the following information on newborns Birth weight: in grams Infant’s Condition: Excellent Good Fair Poor Number of prenatal visits Ethnic background: African-American Caucasian Hispanic Native American Other What are the appropriate scales? Quantitative (Interval) Qualitative (Ordinal, Nominal) Importance of Different Types of Data Statistical methods vary for quantitative and qualitative variables Methods for quantitative data cannot be used to analyze qualitative data Quantitative variables can be treated in a less quantitative manner Height: measured in cm/in Interval (Quantitative) Can be treated at Qualitative Ordinal: • Short • Average • Tall Nominal: • Greater than 60in? (Yes/No) • Between 60in-72in? (Yes/No) Discrete Variables A variable is discrete if it can take on a finite number of values Gender Nationality Hair color Disease status Grade in STA 291 Favorite MLB team All Qualitative variables are discrete Continuous Variables Continuous variables can take an infinite continuum of possible real number values Time spent studying for STA 291 per day 43 minutes 2 minutes 27.487 minutes 27.48682 minutes Can be subdivided into more accurate values Therefore continuous Discrete or Continuous Quantitative variables can be discrete or continuous Age, income, height? Depends on the scale Age is potentially continuous, but usually measured in years (discrete) The following are examples of quantitative variables. Identify them as discrete or continuous: Number of children in a family Distance a car travels on a tank of gas Number of customers in a store Weight of a textbook Data Collection and Sampling Methods of Collecting Data Sampling Methods of Collecting Data I Observational Study • An observational study observes individuals and measures variables of interest but does not attempt to influence the responses. • The purpose of an observational study is to describe/ compare groups or situations. • Example: Select a sample of men and women and ask whether he/she has taken aspirin regularly over the past 2 years, and whether he/she had suffered a heart attack over the same period. Methods of Collecting Data II Experiment • An experiment deliberately imposes some treatment on individuals in order to observe their responses. • The purpose of an experiment is to study whether the treatment causes a change in the response. • Example: Randomly select men and women, divide the sample into two groups. You assign one group to take aspirin daily and the other group a placebo. After 2 years, determine for each group the percent of people who had suffered a heart attack. Methods of Collecting Data III Observational Study/Experiment • Observational Studies are passive data collection • We observe, record, or measure, but don’t interfere • Experiments are active data production • Experiments actively intervene by imposing some treatment in order to see what happens • Experiments are preferable if they are possible Simple Random Sample • Each possible sample has the same probability of being selected. • The sample size is usually denoted by n. SRS Example • Population of 4 students: Adam, Bob, Christina, Dana • Select a simple random sample (SRS) of size n=2 to ask them about their smoking habits • 6 possible samples of size n=2: (1) A+B, (2) A+C, (3) A+D (4) B+C, (5) B+D, (6) C+D How to choose a SRS? • Old way: use a random number table. • A little more modern: http://www.randomizer.org How to Choose a Simple Random Sample (SRS) • Each possible sample has the same probability of being selected. • The sample size is denoted by n. • Enumerate all possible samples, and then randomly choose one of them • Or, let the computer choose a random sample, for example using this tool: http://www.randomizer.org How not to choose a SRS? • Ask Adam and Dana because they are in your office anyway – “convenience sample” • Ask who wants to take part in the survey and take the first two who volunteer – “volunteer sampling” Problems with Volunteer Samples • The sample will poorly represent the population • Misleading conclusions • BIAS • Examples: Mall interview, call-in poll, internet poll, street corner interview Why are call-in polls usually biased? People are much more likely to call in if they feel strongly about an issue: (Israel-Palestine, Iraq, water company, mountaintop removal, pedestrian safety, name of the UK mascot) The UK Mascot • Wildcat named “Blue” is the official UK mascot • The name was selected in 2002 in an online poll where multiple voting was possible • The choices were “Champ”, “Blue”, or “Tucky” • Somebody felt strongly about it and voted often Sampling: Famous Example • 1936 presidential election • Alfred Landon vs. Franklin Roosevelt • Literary Digest sent over 10 million questionnaires in the mail to predict the election outcome • More than 2 million questionnaires returned • Literary Digest predicted a landslide victory by Alfred Landon Sampling: Famous Example (cont’d) • George Gallup used a much smaller random sample and predicted a clear victory by Franklin Roosevelt • Roosevelt won with 62% of the vote • Why was the Literary Digest prediction so far off? Other Example • TV, radio call-in polls • “should the UN headquarters continue to be located in the US?” • ABC poll with 186,000 callers: 67% no • Scientific random sample with 500 respondents: 28% no • Explain to someone who knows no statistics why the opinions of only 500 randomly chosen respondents are a better guide to what all Americans think than the opinions of 186,000 callers. Homework Please check your online homework. Listen for any announcements made in class today about the first homework assignment!!! Attendance Survey Question 2 • On a 4”x6” index card (or little piece of paper) – Please write down your name and section number – Today’s Question (please answer with a complete sentence): What are the 2 main ways to collect data?
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