4.2 statistics notes what are good ways and bad ways to sample?

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

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Page 1: 4.2 Statistics Notes What are Good Ways and Bad Ways to Sample?

4.2 Statistics Notes4.2 Statistics Notes

What are Good Ways and Bad What are Good Ways and Bad Ways to Sample?Ways to Sample?

Page 2: 4.2 Statistics Notes What are Good Ways and Bad Ways to Sample?

Sampling Frame and DesignSampling Frame and Design

Sampling FrameSampling Frame – list of all subjects in – list of all subjects in the population from which to samplethe population from which to sample

Sampling designSampling design – method of selecting – method of selecting subjects for the samplesubjects for the sample

It is important that the subjects in the It is important that the subjects in the sample are representative of the subjects sample are representative of the subjects in the populationin the population

Page 3: 4.2 Statistics Notes What are Good Ways and Bad Ways to Sample?

Simple Random Sampling (SRS)Simple Random Sampling (SRS)

Simple Random Sampling (SRS)Simple Random Sampling (SRS)

each subject in the population has the each subject in the population has the same chance of being selected for the same chance of being selected for the samplesample

A SRS will usually give you a sample that A SRS will usually give you a sample that is representative of the population is representative of the population

Page 4: 4.2 Statistics Notes What are Good Ways and Bad Ways to Sample?

Random Number TablesRandom Number Tables

An easy way to conduct a simple random sample is to An easy way to conduct a simple random sample is to use a table of random numbers or random numbers use a table of random numbers or random numbers generated from a computer.generated from a computer.

To use a random number table, use the following steps:To use a random number table, use the following steps: 1. Number all subjects in the sampling frame, using numbers 1. Number all subjects in the sampling frame, using numbers

of the same length (ex: 1 could be 01)of the same length (ex: 1 could be 01) 2. Select numbers of that length from the random number 2. Select numbers of that length from the random number

tabletable 3. Include in the sample those subjects whose numbers match 3. Include in the sample those subjects whose numbers match

the numbers selected from the random number tablethe numbers selected from the random number table

Turn to p.157 in the textbookTurn to p.157 in the textbook

Page 5: 4.2 Statistics Notes What are Good Ways and Bad Ways to Sample?

Methods of Collecting Data in Methods of Collecting Data in Sample SurveysSample Surveys

MethodMethod AdvantagesAdvantages DisadvantagesDisadvantages

Personal Personal InterviewInterview Subjects are more likely Subjects are more likely

to participateto participate

High CostHigh Cost

Subjects are less likely to Subjects are less likely to answer sensitive answer sensitive

questionsquestions

Telephone Telephone InterviewInterview Low costLow cost

Shorter interviewShorter interview

Subjects are less Subjects are less likely to participatelikely to participate

Self-Self-Administered Administered QuestionnaireQuestionnaire

Low costLow cost Subjects are less Subjects are less likely to participatelikely to participate

Page 6: 4.2 Statistics Notes What are Good Ways and Bad Ways to Sample?

Margin of ErrorMargin of Error

The accuracy of the results of the sample The accuracy of the results of the sample depends on the sample sizedepends on the sample size The larger the sample, the more accurate The larger the sample, the more accurate

your results, the smaller your margin of erroryour results, the smaller your margin of error We will learn detailed calculations for We will learn detailed calculations for

specific situations in later chapters, but for specific situations in later chapters, but for now we will estimate the margin of error now we will estimate the margin of error for a simple random sample to be:for a simple random sample to be:

1/√n1/√n

Page 7: 4.2 Statistics Notes What are Good Ways and Bad Ways to Sample?

BiasBias

BiasBias – results from the sample are not – results from the sample are not representative of the populationrepresentative of the population

Types of BiasTypes of Bias Sampling BiasSampling Bias – bias resulting from the – bias resulting from the

sampling methodsampling method Nonresponse biasNonresponse bias – subjects willing to – subjects willing to

participate may be different than subjects not participate may be different than subjects not willing to participatewilling to participate

Response biasResponse bias – subject gives an incorrect – subject gives an incorrect response (lying, misleading questions)response (lying, misleading questions)

Page 8: 4.2 Statistics Notes What are Good Ways and Bad Ways to Sample?

Convenience SampleConvenience Sample

Convenience Sample – when one samples Convenience Sample – when one samples those that are convenient (not random)those that are convenient (not random)

A convenience sample is usually not A convenience sample is usually not representative of the population and representative of the population and should be avoided if possibleshould be avoided if possible

Page 9: 4.2 Statistics Notes What are Good Ways and Bad Ways to Sample?

1936 Literary Digest Poll1936 Literary Digest Poll

In 1936, the Literary Digest conducted a poll to see who In 1936, the Literary Digest conducted a poll to see who would win the presidential election between FDR and Alf would win the presidential election between FDR and Alf Landon.Landon.

They sent out 10 million surveys to addresses they got They sent out 10 million surveys to addresses they got from telephone directories, car registrations, and country from telephone directories, car registrations, and country club memberships.club memberships.

They got back 2.7 million surveys that predicted Alf They got back 2.7 million surveys that predicted Alf Landon would win with 57% of the vote.Landon would win with 57% of the vote.

In actuality he only received 37% of the vote and FDR In actuality he only received 37% of the vote and FDR won by a landslide. The Literary Digest went out of won by a landslide. The Literary Digest went out of business shortly thereafter.business shortly thereafter.

What was wrong with the way they sampled?What was wrong with the way they sampled?