Chapter 2Chapter 2Sampling Design

How do we gather How do we gather data?data?• Surveys • Opinion polls• Interviews• Studies

– Observational– Retrospective (past)– Prospective (future)

• Experiments

PopulationPopulation• the entire group of individuals that we want information about

CensusCensus•a complete count of the population

How good is a How good is a census?census?

Do frog fairy tale . . .

The answer is 83!

Why would we not Why would we not use a census all use a census all

the time?the time?1) Not accurate

2) Very expensive

3) Perhaps impossible

4) If using destructive sampling, you would destroy population

• Breaking strength of soda bottles

• Lifetime of flashlight batteries

• Safety ratings for cars

Look at the U.S. census – it has a huge amount of

error in it; plus it takes a long to compile the data making the data obsolete

by the time we get it!

Suppose you wanted to know the average weight

of the white-tail deer population in Texas –

would it be feasible to do a census?

Since taking a census of any population takes

time, censuses are VERY costly to do!

SampleSample• A part of the population that

we actually examine in order to gather information

• Use sample to generalize to population

Sampling Sampling designdesign

•refers to the method used to choose the sample from the population

Sampling Sampling frameframe

•a list of every individual in the population

• consist of n individuals from the population chosen in such a way that–every individual has an equal

chance of being selected–every set of n individuals has an

equal chance of being selected

Simple Random Simple Random Sample (SRS)Sample (SRS)Suppose we were to take an

SRS of 100 AHS students – put each students’ name in a hat.

Then randomly select 100 names from the hat. Each

student has the same chance to be selected!

Not only does each student has the same chance to be selected – but every possible group of 100 students has the same chance to be selected! Therefore, it has to be possible for all 100 students

to be seniors in order for it to be an SRS!

Stratified Stratified random random samplesample

• population is divided into homogeneous groups called strata

• SRS’s are pulled from each strata

Homogeneous groups are groups that are alike based upon some

characteristic of the group members.

Suppose we were to take a stratified random sample of 100

AHS students. Since students are already divided by grade level, grade level can be our strata.

Then randomly select 50 seniors and randomly select 50 juniors.

Systematic Systematic random random samplesample• select sample by

following a systematic approach

• randomly select where to begin

Suppose we want to do a systematic random sample of AHS students -

number a list of students(There are approximately 2000 students – if we want a sample of 100, 2000/100 =

20)Select a number between 1 and 20 at

random. That student will be the first student chosen, then choose

every 20th student from there.

Cluster Cluster SampleSample

•based upon location

•randomly pick a location & sample all there

Suppose we want to do a cluster sample of AHS students. One way to do this would be to randomly select 10 classrooms during 2nd period. Sample all students in

those rooms!

Multistage Multistage samplesample

•select successively smaller groups within the population in stages

•SRS used at each stage

To use a multistage approach to sampling AHS students, we could first divide 2nd period classes by

level (AP, Honors, Regular, etc.) and randomly select 4 second period

classes from each group. Then we could randomly select 5 students from each of those classes. The

selection process is done in stages!

SRSSRS•Advantages–Unbiased–Easy

•Disadvantages–Large variance–May not be representative

–Must have sampling frame (list of population)

StratifiedStratified•Advantages

– More precise unbiased estimator than SRS

– Less variability– Cost reduced

if strata already exists

•Disadvantages– Difficult to do if

you must divide stratum

– Formulas for SD & confidence intervals are more complicated

– Need sampling frame

Systematic Random Systematic Random SampleSample

•Advantages– Unbiased– Ensure that the

sample is distributed across population

– More efficient, cheaper, etc.

•Disadvantages–Large variance–Can be confounded by trend or cycle

–Formulas are complicated

Cluster Cluster SamplesSamples

•Advantages–Unbiased –Cost is reduced

–Sampling frame may not be available (not needed)

•Disadvantages–Clusters may not be representative of population

–Formulas are complicated

Identify the sampling Identify the sampling designdesign

1)The Educational Testing Service (ETS) needed a sample of colleges. ETS first divided all colleges into groups of similar types (small public, small private, etc.) Then they randomly selected 3 colleges from each group.

Stratified random sample

2) A county commissioner wants to survey people in her district to determine their opinions on a particular law up for adoption. She decides to randomly select blocks in her district and then survey all who live on those blocks.

Identify the sampling Identify the sampling designdesign

Cluster sampling

3) A local restaurant manager wants to survey customers about the service they receive. Each night the manager randomly chooses a number between 1 & 10. He then gives a survey to that customer, and to every 10th customer after them, to fill it out before they leave.

Identify the sampling Identify the sampling designdesign

Systematic random sampling

Random Random digit tabledigit table

•each entry is equally likely to be any of the 10 digits

•digits are independent of each other

The following is part of the random digit table found on page 847 of your textbook:

Row

1 4 5 1 8 5 0 3 3 7 1

2 4 2 5 5 8 0 4 5 7 0

3 8 9 9 3 4 3 5 0 6 3

Numbers can be read across.

Numbers can be read vertically.

Numbers can be read diagonally.

Suppose your population consisted of these 20 Suppose your population consisted of these 20 people:people:

1) Aidan6) Fred 11) Kathy 16) Paul2) Bob 7) Gloria 12) Lori 17) Shawnie3) Chico 8) Hannah 13) Matthew 18) Tracy4) Doug 9) Israel 14) Nan 19) Uncle Sam5) Edward 10) Jung 15) Opus 20) Vernon

Use the following random digits to select a sample of five from these people.

We will need to use double digit random

numbers, ignoring any number greater than 20. Start with Row 1

and read across.

Row1 4 5 1 8 0 5 1 3 7 12 0 1 5 5 8 0 1 5 7 03 8 9 9 3 4 3 5 0 6 3

Ignore.

18) Tracy

5) Edward

13) Matthew

1) Aidan

15) Opus

Ignore.Ignore.Ignore.

Stop when five people are selected. So my sample would

consist of :

Aidan, Edward, Matthew, Opus, and Tracy

BiasBias•ERROR

•favors certain outcomes

Anything that causes the data to be wrong!

It might be attributed to the researchers, the

respondent, or to the sampling method!

Sources of Sources of BiasBias

• things that can cause bias in your sample

•cannot do anything with bad data

Voluntary Voluntary responseresponse

•People chose to respond

•Usually only people with very strong opinions respond

An example would be the surveys in magazines that ask readers to mail in the survey.

Other examples are call-in shows, American Idol, etc.

Remember, the respondent selects themselves to

participate in the survey!

Remember – the way to determine

voluntary response is:

Self-selection!!

Convenience Convenience samplingsampling

•Ask people who are easy to ask

•Produces bias results

An example would be stopping friendly-looking people in the

mall to survey. Another example is the surveys left on

tables at restaurants - a convenient method!

The data obtained by a convenience sample will be

biased – however this method is often used for surveys &

results reported in newspapers and magazines!

UndercoveraUndercoveragege

•some groups of population are left out of the sampling process

Suppose you take a sample by

randomly selecting names from the phone

book – some groups will not

have the opportunity of being selected!

People with unlisted phone numbers – usually high-income families

People without phone numbers –usually low-income families

People with ONLY cell phones – usually young adults

NonresponseNonresponse•occurs when an individual chosen for the sample can’t be contacted or refuses to cooperate

•telephone surveys 70% nonresponse

People are chosen by the researchers, BUT refuse to

participate.

NOTNOT self-selected!

This is often confused with voluntary response!

Because of huge telemarketing efforts in the past few years,

telephone surveys have a MAJOR problem with

nonresponse! One way to help with the

problem of nonresponse is to make follow contact with

the people who are not home when you first contact

them.

Response biasResponse bias•occurs when the behavior of respondent or interviewer causes bias in the sample

•wrong answers

Suppose we wanted to survey high school students on drug

abuse and we used a uniformed police officer to

interview each student in our sample – would we get honest

answers?

Response bias occurs when for some reason (interviewer’s or

respondent’s fault) you get incorrect answers.

Wording of the Wording of the QuestionsQuestions

•wording can influence the answers that are given

•connotation of words•use of “big” words or technical words

Questions must be worded as neutral as possible to

avoid influencing the response.

The level of vocabulary should be appropriate for

the population you are surveying

– if surveying Podunk, TX, then you should

avoid complex vocabulary.

– if surveying doctors, then use more

complex, technical wording.

Source of Bias?Source of Bias?1) Before the presidential election of 1936, FDR against Republican ALF Landon, the magazine Literary Digest predicting Landon winning the election in a 3-to-2 victory. A survey of 10 million people. George Gallup surveyed only 50,000 people and predicted that Roosevelt would win. The Digest’s survey came from magazine subscribers, car owners, telephone directories, etc.

Undercoverage – since the Digest’s survey comes from car owners, etc., the people selected were mostly from high-income families and thus mostly Republican! (other answers are possible)

2) Suppose that you want to estimate the total amount of money spent by students on textbooks each semester at SMU. You collect register receipts for students as they leave the bookstore during lunch one day.

Convenience sampling – easy way to collect data

orUndercoverage – students who

buy books from on-line bookstores are included.

3) To find the average value of a home in Austin, one averages the price of homes that are listed for sale with a realtor.

Undercoverage – leaves out homes that are not for sale or

homes that are listed with different realtors.

(other answers are possible)