5.1 Power Point

8/7/2019 5.1 Power Point

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Designing SamplesSection 5.1


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Trick orTreatment?


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Big orSmall?


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Two Collection Methods


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Bad Sample, Bad!


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Bias:

In everyday language, we say an

opinion is biased if it unreasonably

favors one point of view overothers. A

biased opinion is not balanced, notobjective.

In statistics, a sampling method isbiased if it systematically favors certainoutcomes.


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By Chance orby Design?

Choosing yoursample by chance is the

only method guaranteed to be unbiased.

Youve seen how common sampling

methods are biased: Those who care enough to respond voluntarily may

not be typical of others

The members of yourclass, although convenient to

survey, dont represent some groups well at all Even yourown personal judgment doesnt workwell.

Overthe long run, chance beats all of

these methods.


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A Simple Random

Sample (SRS)


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In Theory

The simplest waywould be to putall the individuals from apopulation into a gigantic hat,

mix them thoroughly, and drawthe individuals out one at a timeuntil you have enough foryour

sample.


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SRS in Practice

We can use computersoftware or

a calculatorto choose an SRS from

a list of the individuals in apopulation.

We can also select oursampleusing a table of random digits.


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Can I Have YourNumber?


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Choosing an SRS

Label, Table, Stop, ID:


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SRS orNot?

From a class of 30 students

1. Select the first 6 on the roster.

2. Pick a digit at random and select those studentswhose phone numberends with that digit.

3. If the classroom has 6 rows of desks with 5 desks ineach row, choose a row at random and select all

students in that row.

4. If the class consists of 15 males and 15 females,assign the males numbers 1-15 and the females #16-30. Then use a random digit table to select sixnumbers from 1-30. The students who were assignedthose numbers are in yoursample.


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4. If the class consists of 15 males and 15females, assign the males numbers 1-15 andthe females #16-30. Then use a random digittable to select three numbers from 1-15 and

3 numbers from 16-30. The students whowere assigned those numbers are in yoursample.

5. Randomly choose a letterof the alphabetand select those students fro the samplewhose last name begins with that letter. If nolast name begins with that letter, randomlychoose another letterof the alphabet.


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OtherSampling Methods

Stratified Random Sample:

ClusterSample:


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A Nightmare on SRS Street

To see howwell US third graders do on anarithmetic test, you might choose an SRS ofchildren enrolled in third grade and give

each child a standardized test. In theory thisis reasonable, but it is just not practical. Forone thing, howwould you go about makinga complete list of all the third graders in the

US? Foranother, imagine the workrequiredto track down each selected child and makethem take the test.


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ClusterSampling Saves the Day

Instead of an SRS of all third graders, itwould be much betterto take an SRS of allthe elementary schools in the US and thengive the test to all the third graders in those

schools. Its a lot easierto get a list of allthe elementary schools in the US.Moreover, once youve chosen yoursample of schools, its relatively easy togive the test to all the third graders in thoseschools. This is an example of clustersampling, in which each elementary

school is a clusterof third grade students.


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Systematic Sampling

Make and numbera list of all the units in yourpopulation.

Choose a random starting point between 1and k then sample everykth unit thereafter.


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Multi-Stage Samples

You can do multi-layered sampling if

you want.

Forexample, stratify first and thenclusterwithin each strata.

Orclusterthen SRS within each cluster.


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Cautions About Sample Surveys

Undercoverage: occurs when some groups inthe population are left out of the process ofchoosing the sample

Nonresponse: occurs when an individualchosen forthe sample cant be contacted ordoes not cooperate

Response Bias: occurs when an individual lies,

mis-remembers, orwhen theirresponses areinfluenced by the interviewer

Question Wording: is important so as to not biasthe results of a survey


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Inference About the Population

Always rememberthat sample results are onlyestimates of the truth about the population.

If we select two random samples from the

same population, we will draw differentindividuals, so the results will differsomewhat.

We can improve ourresults by knowing thatlargerrandom samples give you moreaccurate results than smallersamples.

By taking a very large sample, you can beconfident that the sample result is very close

to the truth about the population.

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5.1 Power Point