Math 161 Spring 2008 Lecture 2 Chapter 2 Samples, Good and Bad Agenda: Chapter 2 Samples, Good and Bad Chapter 2 Chapter 2 Friday, Dec. 11, 2008

Math 161 Spring 2008 Lecture 2 Thought Question 1 Popular magazines often contain surveys that ask their readers to answer questions about hot topics in the news. Do you think the responses the magazines receive are representative of public opinion? Explain why or why not. Chapter 2 Chapter 2 Friday, Dec. 11, 2008

Math 161 Spring 2008 Lecture 2 Thought Question 2 Cable News Network (CNN) often asks its viewers to call the network with their opinions on certain political issues, like whether or not they favor current foreign policy. Do you think the results of these polls represent the feelings of the general population? Do you think they represent the feelings of all those watching CNN at the time? Explain. Chapter 2 Chapter 2 Friday, Dec. 11, 2008

Math 161 Spring 2008 Lecture 2 Thought Question 3 Researchers in health and nutrition often study the effectiveness of new supplements by providing subjects with both the new supplement and a “fake” supplement made to look like the real thing. Do you think the results would be biased if the person providing the products to the participants knew which was which? Chapter 2 Chapter 2 Friday, Dec. 11, 2008

Math 161 Spring 2008 Lecture 2 Thought Question 4 A survey on poverty and welfare included the following question: “Do you agree with the popular notion that government policy should attempt to assist those individuals who have had the misfortune to end up living in poverty by providing them with much needed financial assistance until they can get back on their feet?” Based on the wording, do you think the author of this question was looking for support or opposition to welfare programs? Explain. Chapter 2 Chapter 2 Friday, Dec. 11, 2008

Math 161 Spring 2008 Lecture 2 Thought Question 5 Suppose you access an online listing of all courses at your institution, alphabetized by department, to determine what proportion of all courses have a statistics course as a prerequisite. If you decide to sample 50 courses in order to get a representative sample of courses, how would you select them? Would it be appropriate to simply select the first 50 courses listed? Chapter 2 Chapter 2 Friday, Dec. 11, 2008

Bad Sampling Plans Convenience sampling selecting individuals who are easiest to reach Problem: Sample might not be representative of the target population. Chapter 2

Convenience Sampling Sampling mice from a large cage to study how a drug affects physical activity lab assistant reaches into the cage to select the mice one at a time until 10 are chosen Which mice will likely be chosen? could this sample yield biased results? Chapter 2

Bad Sampling Plans Voluntary response sampling allowing individuals to choose to be in the sample Problem: People with strong opinions / feelings about the issue tend to respond. Example: RateMyProfessor.com Chapter 2

Voluntary Response To prepare for her book Women and Love, Shere Hite sent questionnaires to 100,000 women asking about love, sex, and relationships. 4.5% responded Hite used those responses to write her book Moore (Statistics: Concepts and Controversies, 1997) noted: respondents “were fed up with men and eager to fight them…” “the anger became the theme of the book…” “but angry women are more likely” to respond Chapter 2

Bias The design of a statistical study is biased if it systematically favours certain outcomes. Convenience Sampling and Voluntary Response Sampling often produce biased samples. Chapter 2

Avoiding Bias We select a sample in order to get information about some population. How can we choose a sample that fairly represents the population? Chapter 2

Polls and Surveys Data carelessly collected (even if the sample size is large), is subject to a high degree of bias. To avoid biases, samples must be randomly chosen. Chapter 2

Simple Random Sampling Each individual in the population has the same chance of being chosen for the sample Each group of individuals in the population of the required size (n) has the same chance of being the sample actually selected Chapter 2

Simple Random Sample (SRS) A simple random sample (SRS) of size n consists of n individuals from the population chosen in such a way that every set of n individuals has an equal chance of being selected. Chapter 2

How to choose an SRS Label each individual in the population with a unique number “drawing names (numbers) out of a hat” random number table (see Table A on pg. 550 of text) computer software (www.randomizer.org) or see textbook website (http://bcs.whfreeman.com/scc6e) Statistical Applets – Simple Random Sample Chapter 2

Simple Random Sampling Example: Courses with Statistics Prerequisite Suppose there are 800 courses at an institution, alphabetized by department (and numbered 001-800), and you decide to randomly select 50 of them to determine what proportion of all the courses have a statistics course as a prerequisite. Use a random number table to select which 50 courses to sample. Page 550 of textbook: Pick a line and column at random: suppose we get line 111, column 3 Random numbers: 605 130 929 700 412 712 … TRY: Use line 126, column 6: Random numbers: ___ ___ ___ ___ ___ ___ … Chapter 2

_________________ Sampling - use results that are readily available Math 161 Spring 2008 Lecture 2 _________________ Sampling - use results that are readily available Hey! Do you believe in the death penalty? Chapter 2 Chapter 2 Friday, Dec. 11, 2008

Math 161 Spring 2008 Lecture 2 ____________________Sampling- selection so that each individual has an equal chance of being selected page 19 of text Chapter 2 Chapter 2 Friday, Dec. 11, 2008

Key Concepts Bias Convenience Sampling Voluntary Response Sampling Simple Random Sampling Chapter 2