Ch 4 - Designing Studies

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Ch 4 - Designing Studies
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I can identify the population and sample in a
survey.

• Population - the entire group of individuals
  about which we want information.
• Sample - the part of the population from which we
  actually collect information.

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Sample Survey

• 1st - determine what population we want to
  describe
• 2nd - determine exactly what we want to measure
  (define our variables)

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• The student government at a high school surveys
  100 of the students at a the school to get their
  opinions about a change to the bell schedule.
• Whats the population? Sample?
• What was being studied?

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• An archaeological dig turns up large numbers of
  pottery shards, broken stone tools, and other
  artifacts. Students working on the project
  classify each artifact and assign it a number.
  The counts in different categories are important
  for understanding the site, so the project
  director chooses 2 of the artifacts at random
  and checks the students work. Identify the
  population and sample.

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I can understand two types of bias in sampling.

• Bias - when the design on a study will favor
  certain outcomes
• Convenience Sample - choosing individuals who are
  easiest to reach
• Voluntary Response - when the sample chooses
  themselves by responding to a general appeal.

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Why do each lead to bias?

• unrepresentative of the entire population because
  answer will be influence by where you are.
• i.e. if you are surveying how people feel about
  the library tax and only ask people who are at
  the library
• only people with strongly opinions (in either
  direction) will respond.
• people can respond more than once
• i.e. call-ins, write-ints, internet voting

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• You are on the staff of a member of Congress who
  is considering a bill that would provide
  government-sponsored insurance for nursing-home
  care. You report that 1128 letters have been
  received on the issue, of which 871 oppose the
  legislation. Im surprised that most of my
  constituents oppose the bill. I thought it would
  be quite popular, says the congresswoman. Are
  you convinced that a majority of the voters
  oppose the bill? How would you explain the
  statistical issue to the congresswoman?

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• In June 2008, Parade magazine posed the following
  question Should drivers be banned from using
  all cell phones? Readers were encouraged to vote
  online at parade.com. The July 13, 2008 issue
  reported 2407 (85) said Yes and 410 (15) said
  No.
• a) What type of sample did Parade survey obtain?
• b) Explain why this is biased and is 85 too high
  or too low? Why?

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HW Day 1 on the outline
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So, whats a good method?

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

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Random Rectangle ActivityHW day 2 on outline
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• How can I select a SRS of 4 students from this
  class?
• Ideas put all names in a hat, on equally sized
  slips of paper and select 4 of them
• Assign everyone a number and use a Random Digit
  Table (Table D) to select the four people

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How to use Table D

1. assign every individual in the population a
   digit.
2. the number of digits have to equal the number of
   digits in the population
3. start with 0 (or 00 or 000...)
4. decide what to do if you get a repeated digit or
   a digit not in the range you need
5. pick a line to start at and read consecutive
   groups of digits to select your sample

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Day 3
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Other Sampling Methods

• Stratified Random Sample when the population is
  grouped based on a similarity.
• Cluster Sample when the population is divided
  into smaller groups that mirror the
  characteristics of the population.

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Other Sampling Methods

• first, divide the population into smaller groups
  (mirror the population)
• next, choose an SRS of the clusters
• all individuals in each cluster are included in
  the sample
• groups are heterogenous - like CLC groups

• first, classify population into similar groups
  (strata)
• next, choose a separate SRS from each stratum
• combine all SRSs to form the full sample
• groups are homogeneous - like the math class
  youre in

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• A manager of a beach-front hotel wants to survey
  guests in the hotel to estimate overall customer
  satisfaction. The hotel has two towers, an older
  one to the south and a newer one to the north.
  Each tower has 10 floors of standard rooms (40
  rooms per floor) and 2 floors of suites (20
  suites per floor). Half of the rooms in each
  tower face the beach, while the other half of the
  rooms face the street. There are a total of 880
  rooms.
• a) Explain how to select a simple random sample
  of 88 rooms.
• b) Explain how to select a stratified random
  sample of rooms.
• c) Explain how to select a cluster of rooms.
• d) Explain why selecting 2 of the 24 different
  floors would not be a good way to obtain a
  cluster sample.

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Advantages Disadvantages
Advantage Disadvantage
SRS simple to carry out each individual in the population has the same chance to be selected chance of over- or under- representing in the sample
Stratified no chance of over- or under-representing each individual in the population still has the same chance of being selected a little more complicated to execute
Clustering can be convenient when groups are already created each individual in the population still has the same chance of being selected chance of over- or under- representing in the sample
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A Sample Free Response

• In response to nutrition concerns raised last
  year about food served in school cafeterias, the
  Smallville School District entered into a
  one-year contract with the Healthy Alternative
  Meals (HAM) company. Under this contract, the
  company plans and prepares meals for 2,500
  elementary, middle, and high school students,
  with a focus on good nutrition. The school
  administration would like to survey the students
  in the district to estimate the proportion of
  students who are satisfied with the food under
  this contract.
• Two sampling plans for selecting the students to
  be surveyed are under consideration by the
  administration. One plan is to take a simple
  random sample of students in the district and
  then survey those students. The other plan is to
  take a stratified random sample of students in
  the district and then survey those students.
• (a) Describe a simple random sampling procedure
  that the administrators could use to select 200
  students from the 2,500 students in the district.
• (b) If a stratified random sampling procedure is
  used, give one example of an effective variable
  on which to stratify in this survey. Explain your
  reasoning.
• (c) Describe one statistical advantage of using a
  stratified random sample over a simple random
  sample in the context of this study.

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Answers to part A
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Answers to part B
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Answers to part C
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What type of sampling is this?

• At a party there are 30 students over age 21 and
  20 students under age 21. You choose at random 3
  of those over 21 and separately at random 2 of
  those under 21 to interview about attitudes
  towards alcohol. You have given every student at
  the party the same chance to be interviewed.
• What is that chance?
• What type of sampling procedure was this?

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HINT an SRS will allow for a sample to have all
of a certain group or none of a groups
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• One the west side of Rocky Mountain National
  Park, many mature pine trees are dying due to
  infestation by pine beetles. Scientists would
  like to use sampling to estimate the proportion
  of all pine trees in the area that have been
  infested.
• Why would an SRS not be practical?
• Could they just sample the pines along the road?
• Suppose the sampling was carried out randomly and
  accurately and 35 of the pine trees sampled were
  infested. Can they conclude 35 of all pine trees
  are infested?

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Day 4

• Inference and what can go wrong?

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Why do we sample?

• to infer about a population
• surveying a population takes too much time and
  money!

Can we trust it?

• YES - the law of probability allows for random
  sampling to work!
• there are margins of error to account for the
  variability between the sample and the
  population. Nothing was wrong with the procedure!

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What can go wrong?

• There are different types of bias to cause
  sampling to go wrong
• Sampling Errors
• Nonsampling Errors

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Sampling Nonsampling

• Voluntary Response
• Convenience Sample
• Undercoverage
• (we already know about voluntary and convenience)
• Nonresponse
• Response Bias
• Wording of Question

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Undercoverage

• when some groups in the population are left out
  of the process when choosing the sample
• Example if you were to go to peoples houses and
  survey about the unemployment rate - you are
  leaving out all the homeless people and those who
  have jobs and are not home.

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Nonresponse

• when an individual chosen for the sample cant
  be contacted or refuses to participate
• WARNING the is not voluntary response bias,
  these individuals were chosen to be in the sample
  and do not want to be
• Example when you make a call at SIRS and they
  hang up on you or tell you something rude of why
  they dont want to participate!

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Response Bias

• when the individual gives the wrong answer
• Many factors contribute to this
• people know what the answer should be and give
  that
• what the interviewer looks like
• recalling past events

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Wording of Questions

• confusing/leading questions that lead to a
  certain response
• MOST IMPORTANT INFLUENCE ON ANSWERS! Never trust
  a survey unless you have seen the questions!
• Examples Order of the questions, any
  prompts/cues given before the question

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Ch 4 Project

• by yourself or with a partner
• You will design and conduct an experiment to
  investigate the effects of response bias in
  surveys
• You can choose the topic, but you must design
  your experiment to answer one of the following
  questions
• Can the wording of a questions create response
  bias?
• Do the characteristics of the interviewer create
  response bias?
• Does anonymity change the responses to sensitive
  questions?
• Does manipulating the answer choices change the
  response?

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Ch 4 Project

• see page 267 for what is required
• I will hand out a rubric - USE IT!
• Not only are you going to analyze the survey
  results, you will analyze if the way the survey
  was conducted biased the results
• due October 31, 2013
• (approved by Friday, October 24)

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start on HW day 4