4.2 Statistics Notes What are Good Ways and Bad Ways to Sample?

Sampling Frame and Design  Sampling Frame – list of all subjects in the population from which to sample  Sampling design – method of selecting subjects for the sample  It is important that the subjects in the sample are representative of the subjects in the population

Simple Random Sampling (SRS)  Simple Random Sampling (SRS) each subject in the population has the same chance of being selected for the sample  A SRS will usually give you a sample that is representative of the population

Random Number Tables  An easy way to conduct a simple random sample is to use a table of random numbers or random numbers generated from a computer.  To use a random number table, use the following steps:  1. Number all subjects in the sampling frame, using numbers of the same length (ex: 1 could be 01)  2. Select numbers of that length from the random number table  3. Include in the sample those subjects whose numbers match the numbers selected from the random number table  Turn to p.157 in the textbook

Methods of Collecting Data in Sample Surveys MethodAdvantagesDisadvantages Personal Interview Subjects are more likely to participate High Cost Subjects are less likely to answer sensitive questions Telephone Interview Low cost Shorter interview Subjects are less likely to participate Self- Administered Questionnaire Low cost Subjects are less likely to participate

Margin of Error  The accuracy of the results of the sample depends on the sample size  The larger the sample, the more accurate your results, the smaller your margin of error  We will learn detailed calculations for specific situations in later chapters, but for now we will estimate the margin of error for a simple random sample to be: 1/√n 1/√n

Bias  Bias – results from the sample are not representative of the population  Types of Bias  Sampling Bias – bias resulting from the sampling method  Nonresponse bias – subjects willing to participate may be different than subjects not willing to participate  Response bias – subject gives an incorrect response (lying, misleading questions)

Convenience Sample  Convenience Sample – when one samples those that are convenient (not random)  A convenience sample is usually not representative of the population and should be avoided if possible

1936 Literary Digest Poll  In 1936, the Literary Digest conducted a poll to see who would win the presidential election between FDR and Alf Landon.  They sent out 10 million surveys to addresses they got from telephone directories, car registrations, and country club memberships.  They got back 2.7 million surveys that predicted Alf Landon would win with 57% of the vote.  In actuality he only received 37% of the vote and FDR won by a landslide. The Literary Digest went out of business shortly thereafter.  What was wrong with the way they sampled?