Sampling

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Sampling
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Polls predicting 1992 U.S. presidential election
outcomes
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Polls predicting 1996 U.S. presidential election
outcomes
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How many interviews it took to estimate the
behaviors of 90 million voters?

• Less than 2,000

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The History of Sampling

• In 1920, Literary Digest mailed postcards to
  people in 6 states, asking whom they were
  planning to vote for in the presidential
  campaign.
• The Digest correctly predicted that Harding would
  be elected.
• In the elections that followed, the Literary
  Digest expanded the size of its poll and made
  correct predictions in 1924, 1928, 1932.

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The History of Sampling

• In 1936, Literary Digest conducted its most
  ambitious poll 10 million ballots were sent to
  people listed in the telephone directories and on
  lists of automobile owners.
• Over 2 million responded, given the Republican
  contender Alf London, a 57 to 43 percent
  landslide over the incumbent, president
  Roosevelt.
• Election results Roosevelt won 61 of the votes.

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The History of Sampling

• Problem 22 return rate.
• A part of the answer to these questions lay in
  the sampling frame used by the Digest telephone
  subscribers and automobile owners.
• Such a design selected a disproportionately
  wealthy sample.
• The sample effectively excluded poor people, and
  the poor people predominantly voted for
  Roosevelts New Deal recovery program during the
  depression period.

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The History of Sampling

• In the same year (1936), George Gallup correctly
  predicted that Roosevelt would beat London.
• Gallups success in 1936 hinged on his use of
  quota sampling, which is based on a knowledge of
  the characteristics of the population being
  sampled. People are selected to match the
  population characteristics.
• Using quota sampling, Gallup successfully
  predicting the presidential winner in 1940 and
  1944.

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The History of Sampling

• In 1948, Gallup mistakenly picked Thomas Dewey
  over incumbent president Harry Truman.
• Factors accounted for 1948s failure
• 1). Most of the pollsters stopped polling in
  early Oct despite a steady trend toward Truman
  during the campaign.
• 2). Undecided voters went disproportionately
  for Truman.
• 3). Unrepresentativeness of the sample (resulting
  from quota sampling).

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The History of Sampling

• Quota sampling technique requires that the
  researcher know something about the total
  population.
• For national political polls, such information
  came primarily from census data.
• By 1948, however, WWII had produced a massive
  movement from country to city, radically changing
  the character of the U.S. population, and Gallup
  relied on 1940 census data (City dwellers tended
  to vote Democratic hence the over-representation
  of rural voters also underestimated the number of
  Democratic votes).

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Population and Sample element

• Element An element is that unit about which
  information is collected and that provides the
  basis of analysis.
• People, families, corporations
• usually the same as unit of analysis
• Population The entire group of individuals that
  we want information about is called the
  population. A population is the theoretically
  specified aggregation of study elements.
• A sample is a part of the population that we
  actually examine in order to gather information.

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Defining the target population????

• It is vitally important to carefully define the
  target population so the proper source from which
  the data are to be collected can be identified.
• Question "To whom do we want to talk?" What or
  who will be observed?---answer the questions
  about the tangible characteristics of the
  population (1) definition of the element (2) time
  referent for the study.
• EXgt ???????? Or female between age 12-50?.
• EXgt????????
• EXgt ?????????????????????

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Defining the study population????

• Study Population A study population is that
  aggregation of elements from which the sample is
  actually selected.
• Lists of elements are usually somewhat incomplete
• ?????????????????
• ??????? ?????????

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Sampling units????

• A sampling unit is that element or set of
  elements considered for selection in some stage
  of sampling.
• In a simple single-stage sample, the sampling
  units are the same as the elements and are
  probably the units of analysis.
• EXgt passengers on a passengers list ? sampling
  unit elements
• In a multi-stage sample
• EXgt the airlines could first select flights as
  the sampling unit, then select certain passengers
  on the previously select flights.
• PSU (primary sampling units) flights
• Secondary sampling units passengers

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Observation unit

• An observation unit, or unit of data collection,
  is an element or aggregation of elements from
  which information is collected.
• EX) Researcher may interview heads of households
  (the observation units) to collect information
  about all members of the households (the units of
  analysis).

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Sampling Design
Sample designs

• Nonprobability samples
• Voluntary Response Sample
• Convenience
• Judgment
• Quota
• Snowball

• Probability samples
• Simple random
• Systematic
• Stratified
• Proportionate
• Disproportionate
• Cluster
• Multistage

There are no appropriate statistical techniques
for measuring random sampling error from a
non-probability sample. Thus projecting the data
beyond the sample is statistical inappropriate.
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Nonprobability Sampling

• Social research is often conducted in situations
  where you can't select the kinds of probability
  samples used in large-scale social surveys.
• Lack of population list Suppose you wanted to
  study homelessness There is no list of all
  homeless individuals, nor are you likely to
  create such a list.

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Voluntary Response Sample

• A voluntary response sample consists of people
  who choose themselves by responding to a general
  appeal. Voluntary response samples are biased
  because people with strong opinions, especially
  negative opinions, are most likely to respond.
• radio station call in to reflect public opinions.

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Convenience Sampling

• ???? (haphazard or accidental sampling), relying
  on available subjects
• EXgt man-on-the-street interviews, talk to friend
  about their political sentiment
• EXgt professor uses students as sample
• EXgt every tenth student entering the university
  library.
• EXgt Survey over sea Chinese for international
  marketing?

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Convenience Sampling

• Advantages Very low cost, extensively used, No
  need for list of population.
• It is justified only if the researcher wants to
  study the characteristics of people passing the
  sampling point at specified times or if less
  risky sampling methods are not feasible.

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Convenience Sampling

• Problems
• (1) no way of knowing if those included are
  representative.
• (2) Variability and bias of estimates cannot be
  measured or controlled.
• (3) Projecting the results beyond the specific
  sample is inappropriate.
• Should be use only for exploratory design to
  generate ideas and insights.
• you should alert readers to the risks associated
  with this method.

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Judgment Samples (Purposive Samples)????

• hand-picked sample elements, believed to be
  representative of the population of interest
• EXgt a fashion manufacturer regularly selects a
  sample of key accounts that it believes are
  capable of providing the information to predict
  what will sell in the fall.
• EXgt Dow Jones industrial average select 30
  blue-chip stocks out of 1,800 stocks. Highly
  correlated with other NYSE indicators on the
  daily percentages of price changes
• EXgtRepresentative communities in U.S.
  presidential election.
• EXgt CPI????????

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Snowball sample????

• Locate an initial set of respondents. These
  individual are then used as informants to
  identify others with the desired characteristics.
  
• Appropriate when the members of a special
  population are difficult to locate.
  ????????????????

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Snowball sample????

• EXgt survey users of an unusual product a study
  among deaf for product that would allow deaf
  people to communicate over telephone.
• EXgt ??????(????),homeless, gangsters, migrant
  workers, undocumented immigrants.
• EXgt network study,????(HIV)
• Bias a person who is known to someone has a
  higher probability of being similar to the first
  person.

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Quota samples????

• by selecting sample elements in such a way that
  the proportion of the sample elements possessing
  a certain characteristics is approximately the
  same as the proportion with the characteristics
  in the population.
• Establishing a characteristics matrix What
  proportion of the target population is male and
  female? what proportions of each gender fall
  various age categories, educational level, ethnic
  groups,etc.
• Once such a matrix has been created and a
  relative proportion assigned to each cell in the
  matrix, you collect data from people having all
  the characteristics of a given cell.
• All the persons in a given cell are then assigned
  a weight appropriate to their portion of the
  total population.

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Quota samples????

• Problems
• The sample could be far off with respect to other
  important characteristics.
• The quota frame must be accurate, and it is often
  difficult to get up-to-date information for this
  purpose.

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Quota samples????

• Biases may exist in the selection of sample
  elements within a given cell. The interviewer has
  a quota to achieve. The actual choice of elements
  left to the discretion of the individual field
  worker. Interviewers are prone to follow certain
  practices

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Quota samples????

• those who are similar to the interviewers are
  more likely to be interviewed,
• toward the accessible (first floor, airline
  terminals, business district, college campus),
• toward household with children, exclude working
  people,
• against workers in manufacturing (service and
  administrative),
• against extreme of income (EXgt "mansions" were
  skipped because the interviewer did not feel
  comfortable knocking on doors that were answered
  by servants. ),
• against the less educated, against low-status
  individuals

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Probability sample

• A probability sample is a sample chosen by
  chance. We must know what samples are possible
  and what chance or probability, each possible
  sample has.

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Probability sampling offers two advantages

• First, probability samples, although never
  perfectly representative, are typically more
  representative than other types of samples
  because the biases previously discussed are
  avoided.
• Second, and more important, probability theory
  permits us to estimate the accuracy or
  representativeness of the sample.

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Types of Sampling Designs

• Simple Random Sampling
• Systematic Sampling
• Stratified Sampling
• Cluster Sampling

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Simple random sample

• A simple random sample (SRS) of size n consists
  of n individuals from the population chosen in
  such a way that every set of n individuals has an
  equal chance to be the sample actually selected.

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Simple Random Sampling??????

• Simple random sampling is the basic sampling
  method assumed in the statistical computations of
  social research.
• Establish a sampling frame
• Assigns a single number to each element in the
  list, not skipping any number in the process.
• generates series of random numbers to select the
  elements
• Simple random sampling is seldom used in practice

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Systematic Sampling????

• A systematic sample with a random start--a
  procedure in which an initial starting point is
  selected by a random process, and then every kth
  number on the list is selected.
• Sampling interval the number of population
  elements between the units selected for the
  sample.
• Sampling interval population size / sample
  size
• Sampling ratio sample size / population size
• Systematic sampling is virtually identical to
  simple random sample. If the list of elements is
  indeed randomized before sampling, one might
  argue that a systematic sample drawn from that
  list is in fact a simple random sample.
• Systematic sampling is much easier to conduct.

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Problem of periodicity

• The arrangement of elements in the list can make
  systematic sampling unwise.
• EXgt collecting retail sales information every
  seventh day (Monday)
• EXgt apartment number

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Stratified Random Sampling????

• The parent population is divided into mutually
  exclusive and exhaustive subsets.
• A simple random sample of elements is chosen
  independently from each group or subset.
• To organize the population into homogeneous
  subsets and to select the appropriate number of
  elements from each.?????????(strata),?????????????
  ?????????

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Stratified Random Sampling????

• Sampling error can be reduced by
• (1) increase sampling size
• (2) a homogeneous population produces samples
  with smaller sampling errors than does a
  heterogeneous population.
• The logic of stratified sampling rather than
  selecting your sample from the total population
  at large, you ensure that appropriate numbers of
  elements are drawn from homogeneous subsets of
  that population.

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Stratified Random Sampling????

• EXgt urban and rural groups differ widely on
  attitudes toward energy conservation, members
  within each group hold very similar attitudes.
• EXgt divide the university by college class
  (freshmen, sophomores, juniors, seniors)
• In selecting stratification variables, you should
  be concerned primarily with those that are
  presumably related to variables that you want to
  represent accurately. Such as sex, education,
  geographic location,etc.
• EXgt estimate income stratified by educational
  level.

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Example 3.17

• ?????????(ASCAP) ?????????????????????ASCAP???????
  ?,?????????4????????????????????????
• ????60,000????????????????????
• Radio stations are stratified by type of
  community (metropolitan, rural), geographic
  location, and the size of the license fee paid to
  ASCAP, which reflect the size of the audience.

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Stratified Random Sampling????

• ??????????????????(homogeneous within
  strata),??????????(sampling error is smaller)?
• The investigator should divide the population
  into strata so that the elements within any given
  stratum are as similar in value as possible and
  the values between any two strata are as
  disparate as possible.
• In the limit, if the investigator is successful
  in partitioning the population so that the
  elements in each stratum are exactly equal, there
  will be no error associated with the estimate of
  the population parameters.

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Increased precision of stratified samples

• EXgt N1,000
• Mean 5 (.2) 10 (.3) 20 (.5) 14, variance
  39
• Suppose that a researcher was able to
  partitioning the total population so that all the
  elements with a value of 5 in one stratum, those
  with value of 10 were in the second, and those
  with the value of 20 were in the third.
• Take a proportionate stratified sample of n10.
• Or select a sample of n3, and calculate the
  weighted average.

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Proportional stratified sample

• Proportional stratified sample the number of
  sampling units drawn from each stratum is in
  proportion to the relative population size of
  that stratum.
• (1) Sort the population into discrete groups (2)
  On the basis of relative proportion of the
  population represented by a given group, select
  several elements from tat group constituting the
  same proportion of your desired sample size.
• (1) Group elements and then put groups together
  in a continuous list (an ordered list, if no
  periodicity, is sometime better than randomized
  list--implicit stratification in systematic
  sampling). (2) Select a systematic from the
  entire list.

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Disproportionate stratified sampling

• Balancing the two criteria of strata size and
  strata variability. Strata exhibiting more
  variability are sampled more than proportionately
  to their relative size those strata that are
  very homogeneous are sampled less than
  proportionately.

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Multistage cluster sampling????

• Used when it is either impossible or impractical
  to compile an exhaustive list of the elements
  composing the target population.
• ??????(cluster),??(cluster)??????????????
• EX) ????????????,??????????????????????,??????????
  ??????????????,??????
• EX) census blocks---sampled blocked? sample
  household? sample individual
• EXgt sampling high school students in Taiwan
  requires the entire student list. Cluster
  sampling no initial listing is required.

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Multistage cluster sampling????

• ????
• ???,???????
• ????????????????
• ????????????????
• ????
• ???,???????
• ????????????
• ?????????????????????????

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Multistage cluster sampling????

• Price of the efficiency? less accurate sample A
  simple random sample drawn from a population list
  is subject to a single sampling error, but a
  two-stage cluster sample is subject to two
  sampling errors. (exgt selecting a sample of
  disproportionately wealthy city blocks, plus a
  sample of disproportionately wealthy households
  within those blocks.)

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Comparisons of sampling techniques
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Comparisons of sampling techniques
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Comparisons of sampling techniques
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Comparisons of sampling techniques
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Sampling Bias

• A sample is biased if it is obtained by a method
  that favors the selection of elementary units
  having particular characteristics.

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Sampling Error or Error of Estimation
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Error in survey research
Systematic (nonsampling) error
Random sampling error
Respondent error
Administrative error
Data processing error
Response bias
Nonresponse error
Sample selection error
Deliberate falsification Unconscious
misrepresentation
Self-selection bias
Interviewer cheating
Interviewer error
Acquiescence bias
Extremity bias
Interviewer bias
Auspices bias
Social desirability bias
Contamination by others
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Random Sampling Error

• A statistical fluctuation that occurs because of
  chance variation in the elements selected for a
  sample.
• Can be estimated.
• Can be reduce through increasing sample size.

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Systematic Error???? nonsampling errors

• ???????imperfect aspect of the research design
• ????????mistake in the execution of the research
• A sample bias exists when the results of a sample
  show a consistent tendency to deviate in one
  direction from the true value of the population
  parameter.
• Two general categories
• ) Respondent error Nonresponse error Response
  bias
• ) Administrative error

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Non-response error

• The statistical difference between a survey that
  includes only those who responded and a survey
  that also includes those who failed to respond.
• Non-respondenta person who is not contacted or
  who refuses to cooperate
• 1. not-at-homemarried women
• 2. refusal a person who is unwilling to
  participate.

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Non-response error

• To identify the extent of nonresponse error,
  business researcher often select a sample of
  nonrespondents who are then recontacted.
  ??????????????(call back or follow-up),???????????
  ???
• Comparing the demographics of the sample with the
  demographics of the target population is one mean
  of inspecting for possible bias. ????????
• EX) 500???????????????????
• EXgt sample from the educational or personnel
  records

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Self-selection bias

• (EX) who are more likely to respond to customer
  satisfaction survey on the dining table?
• (EX) PC software--expert views on degree of "user
  friendly", might be more critical.
• Self-selection biases the survey because it
  allows extreme positions to be over-represented
  while those who are indifferent are
  under-represented????.

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Deliberate falsification

• Appear to be intelligentEXgt price of a good,
  reluctant to say "can't remember".
• Conceal personal informationEXgtincome, political
  attitude
• To avoid embarrassmentEXgtsexual behaviors,
  smoking/drinking
• Become boredto get rid of the interviewer
• Reluctant to give negative feelingEXgt in
  employee survey to safeguard their job
• To please interviewer.
• Average man" hypothesisto conform to their
  perception of the average person. EXgt number of
  hour worked.

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Unconscious Misrepresentation

• in the absence of strong preference, respondents
  will choose answers to justify their behavior
• (EX) which PC is better? In-flights survey
  concerning aircraft preference
• Misunderstand the question
• EXgt ????????
• Never thought about the question
• EXgtbuying intention, quitting intention
• Forgot the exact details
• EXgtwhen was last time you? How many times did
  you?

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Acquiescence bias????

• A tendency to agree with all questions or to
  indicate a positive connotation. yea (no)
  sayers
• EXgt Japanese do not wish to contradict others
• particularly prominent in ideas previously
  unfamiliar to the respondents

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Extremity bias (or avoid extreme position)

• Consistently low or high scores were given to
  every question.
• EX) student evaluation of the class.

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Interviewer bias

• Bias due to the influence of the interviewer
  (mere presence)
• Provide the right answer to please interviewer
  
• Appear intelligent and wealthy to save face.
• Interviewers age, sex, tone of voice, facial
  expressions, or other noverbal characteristics.
• Will interviewers gender make a difference when
  asking the following questions?
• EX)???????????,???????????
• EX)???????????????????
• Interviewer shorten or rephrase question

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Auspices bias??????

• bias in the responses of subjects caused by the
  respondents being influenced by the organization
  conducting the study.
• EX) ????????????
• EX) ?????????????????????

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Social desirability bias

• bias in the responses of subjects caused by
  respondent's desire, either consciously or
  unconsciously, to gain prestige or to appear in a
  different social role.
• inflated income
• have you ever been fired from a job?
• Do you have roaches in your home?
• how many times you brash your teeth per day
• Likelihood for social desirability bias
• face-to-face gt telephone gt mail

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Contamination by others

• EXgt complete a question on the satisfaction with
  family (marital) relationship (Under the presence
  of a spouse).

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Administrative error

• Data processing error
• Sample selection errorunlisted telephone
  respondent, stopping respondents during daytime
  hours in shopping center exclude working women,
  wrong household member answer the phoneetc.
• Interviewer errorcheck the wrong response, can't
  write fast enough to record answers, selective
  perception (take liberty in interpreting
  questions, specific words may unconsciously be
  emphasized).
• Interviewer cheating (deliberate subversion)
• fills in the answers to certain questions, skip
  questions, in order to finish the question as
  soon as possible.
• remedymini-re-interviews a percentage of
  respondent will be call upon to verify the data.

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What can be done to reduce error

• Questionnaire designto reduce response bias
• Samplingto control random sampling error
• Interviewer training
• Use rule-of-thumb estimates for systematic error
• based on the result of other studies (areas),
  create benchmark figures or standards of
  comparison
• EXgt½ of those who say they will definitely buy
  within the next three months actually do make a
  purchase. For durable1/3. "will probably buy"
  durable no actual buy