Section 4.1 - Why Take Samples and

How Not toObjectives:

• Learn basic terminology of sampling and sample surveys• Learn reasons for using samples• Learn to recognize common instance of sample selection bias

and response bias

Why to Sample

• Testing sometimes destroys the items/units• Sampling can save money and/or time• Allow collecting more or better info from each unit due to

time/money/item limitations

Homework

• PG 229# E1-E9 ODD

Census Versus Sample

Population – set of people or thingsUnits – individual elements of a populationPopulation size – number of unitsCensus – study where data is collected for the entire populationParameter – proportion of a censusStatistic – proportion of a sample

Pg 228 P1 – 2 min

You want to estimate the average number of TV sets per household in your community.a) What is your population? What are the unitsPopulation = all households in community; unit = tvs per individual householdb) Explain the advantages of the sampling over conducting a census.Quicker, cheaper, & easier to carry out a samplec) What problems do you see in carrying out this sample survey?Some households may not respond

Sample – representative piece of population• Sample size – number of units selected as a representation• Sampling frame – list of all population units from which sample is

chosen• Sampling units

Bias – produces samples such that estimates from the sample are smaller or larger on average than the populating parameter being estimated…aka unreasonably favors one point of view over another.

Pg 228 P2 – 2 min

• A) biased, low variabilityAl – off center, closely spaced

• B) biased, high variabilityCal – off center, widely spaced

• C) unbiased, low variabilityBal – around center, closely spaced

• D) unbiased, high variabilityDal – around center, widely spaced

• E) Who the easiest fix?Al – consistency is harder to teach then direction adjustment

Activity 4.1a Time in the Hospital

• Pg 220-222 – 15 minutes• Pair up and grab a deck of cards. Remove the face cards.• Follow the steps using the cards to simulate the hospital stay of each

patient for each of the five beds.• Once you have completed step FIVE, share your information on the

white board for the class.• Continue answering questions while other students finish

Bias vs Nonrepresentative

• Bias refers to the method – not the sample created• Nonrepresentative samples do NOT accurately display the trends of

the entire population

• Biased sample methods tend to create nonrepresentative samples

Pg 223 D3 (2 min)• Which statements describe an event that is possible? Which describe an event

that is impossible?a) A representative sample results from a biased sample-selection methodb) A nonrepresentative sample results from a biased sample-selection methodc) A representative sample results from an unbiased sample-selection methodd) A nonrepresentative sample results from an unbiased sample-selection

methodAll are possible. Unbiased results in representative, but even biased selection methods can produce some correct estimates because they will be too large or small ON AVERAGE.

Sample Selection Bias or Sampling Bias:Bias in choosing your sample• Size bias – the size of the unit makes it more likely to be selected• Voluntary response bias – units with more interest will be over

represented• Convenience sampling – units are chosen for the ease to include• Judgement samples – use of an expert to select the units of a sample

Pg 225 D4 – 30 sec each

Identify the type of sampling method used in each of these surveys. Would you expect the estimate of the parameter to be too high or too low?• A) You use your stat class to estimate the percentage of students in your school who study

at least 2 hours a night. Convenience sample

• B) you send a survey to all people who have graduated from GW in the past 10 years. You use the mean annual income of those who reply to estimate the mean annual income of all graduates of GW in the past 10 years.

Volunteer sample• C) A study designed to estimate how long people have been diagnosed with dementia.

Researchers took a random sample of people with dementia alive on a given day. The date the person was diagnosed was recorded and after the person died the date of death was recorded.

Size bias

Pg 225 D5 – 3 min

• You want to know the percentage of voters who favor state funding for bilingual education. Your population of interest is the set of people likely to vote in the next election. You use as your frame the phone book listing of the residential telephone numbers. How well do you think the frame represents the population? Are there important groups of individuals who belong to the population but not to the frame? To the frame but not to the population? If you think bias is likely, identify what kind of bias and how it might arise.

Pg 225 D5 – Answer

• Two groups that belong to population will not be in the frame:Those who will likely vote but are unlisted numbers and those who do not have residential telephones.

• The Frame includes people not in the population:Those too young to vote or those nonregistered can still be in the frame (phonebook)

• Frame is a poor fit of population cannot determine bias since frame is so poor

Pg 228 P3 – 2 min

a) Size bias – larger farms more likely to be chosenb) Judgment bias – professor maybe have chosen too few “typical”

high schools in his quest for diversityc) Voluntary bias – students who do well are more likely to reportd) Size bias – longer stringers are more likely chosene) Voluntary bias – responders tend to have stronger opinions than

nonresponders regardless of sample size

Response bias -

• Nonresponse bias – bias derived from a lack of data or response• Questionnaire bias – bias created by how the questions are delivered:

diction, voice, tone, or appearance of the interview, order of questions.• Incorrect responses – intentional lying, inaccurate memories of

people , or inaccurate measuring devices

Pg 227 D6

People generally want to appear knowledgeable and agreeable, and they want to present a favorable face to the world. How might that affect the results of a survey conducted by a school on the satisfaction of its graduates with their education?

Graduates who have been successful are more likely to respond to such survey and will probably be happier with their education than those who do not respond. Nonresponse bias

Pg 229 P4 & P5

P4 Estimate will be too high. Sample will catch almost all those who came to Boston to come to the museum and very few people who actually in the museum but did not plan on going to the museum

P5 Question I is more likely to draw “yes” responses and indicate more gun control, while questions II is more likely to draw “no” responses and indicate less control.

Homework

• PG 229# E1-E9 ODD

• 4.2 RG