4.1 Sampling and Surveys

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Chapter 4

• 4.1 Sampling and Surveys

2
Sampling

• When we want to know more information about an
  entire group of individuals called a population,
  we collect information from a smaller group
  called the sample.
• We can draw conclusions from the sample about the
  entire population.

3
Which is which?

• The student government at a high school surveys
  100 students at the school to get their opinions
  about a change to the bell schedule.
• Population ALL students at the school
• Sample 100 students

4
Sample Survey

• Ice Cream Sampling a tiny bit lets you know if
  you want a whole cone because the sample
  represents the whole very well!
• Exactly what population do you want to find out
  about?
• Exactly what do you want to measure?

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Sample Survey

• Only call it a sample survey if its an
  organized plan to choose a sample that is
  representative of the entire population.
• Population can consist of people, animals, or
  things.

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BAD sampling

• A convenience sample is a bad way to sample.
• Involves asking people who are close by.
• Provides unrepresentative data.
• Creates BIAS- using a method that will usually
  overestimate or underestimate the value we are
  wanting to know.

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BAD sampling

• Voluntary response sample is another bad method.
• People with STRONG opinions are more likely to
  respond on a voluntary basis.
• Calling/writing in to a talk show, etc.
• CYU on page 211- 1. Convenience 2. VRS

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GOOD sampling

• Simple Random Sample
• Everyone has an equal chance of being chosen.
• Ex put everyones name on a slip of paper and
  draw names.
• Table of Random Digits (Table D in the back of
  the book) is a good way to sample this way. Read
  p.212 to find out how to use it.

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Stratified Random Sample

1. Break the population into smaller groups of
   similar make-up. The groups are called strata.
2. Choose a separate SRS in each stratum and combine
   them to form the full sample.

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Cluster Sample

• 1. Divide the population in to smaller groups
  which mirror the population.
• 2. Randomly choose an entire cluster to
  participate in the sample.
• Dont get stratified and cluster confused!
• CYU on page 219- answers on next slide.

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CYU p.219

1. We would have to choose 200 different seats and
   go to each one. This would take a long time.
   Also, people sometimes get up and get
   concessions, etc. and might not be there.
2. Use lettered rows as the strata. Each row is the
   same distance from the court and should be the
   same ticket price.
3. Use numbered sections as clusters. Each section
   contains seats with many different ticket prices
   so those people should mirror the entire
   population.

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Inference for Sampling

• We infer info about the population from what we
  know about the sample.
• Rely on random sampling by eliminating bias.
• It is unlikely the results are exactly the same
  as for the entire population.
• However, the laws of probability allow
  trustworthy inference about the population.
• Results come with a margin of error.
• Larger random samples give better info about the
  population than smaller ones!

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What can go wrong?

• Sampling Errors
• Undercoverage (some group gets left out)
• Nonsampling Errors
• Nonresponse (an individual chosen cant be
  contacted or refuses to participate)
• Response Bias (a systematic pattern of incorrect
  responses, sometimes people lie)
• Wording of questions (confusing or leading
  questions)
• Order the questions are asked in (see page 224)

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CYU answers page 224

1. (a) sampling error (b) Nonsampling error (c)
   sampling error
2. The question makes it sound like diapers are NOT
   a problem in the landfill. Fewer people will
   probably suggest that we should ban them.

15
Chapter 4

• 4.2 Experiments

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Observational Studies

• Observes individuals
• Does not attempt to influence the responses
• No interference with participants
• GOAL to describe a group/situation, compare
  groups, examine relationship between variables.

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Experiments

• Deliberately interferes with/imposes some
  treatment on individuals
• Measures the responses to such treatments
• GOAL determine whether a specific treatment
  causes a change in the response (think about
  medical studies)
• When we need to understand cause and effect,
  experiments are the way to go

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Potential Problems

• Lurking Variable influences the response
  variable and makes it hard to see the
  relationship between the explanatory and response
  variables.
• Confounding 2 variables are associated in a way
  that makes their effects hard to distinguish from
  one another.

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CYU answers page 233

1. experiment- treatment (brightness of screen) was
   imposed on the laptops.
2. Observational study
3. Explanatory of meals eaten per week with
   family. Response GPA
4. Observational study- might be lurking variables.

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Experiments

• Treatment- a specific condition applied to the
  individuals
• Experimental units- the individuals to which
  treatments are applied
• Subjects- name from experimental units when they
  are humans
• Factors- another name for explanatory variables

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Random Assignment

• Experimental Units/Subjects are assigned to
  different treatments AT RANDOM (using a chance
  process)

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Control Group

• Sometimes a control group is used. They do not
  receive a treatment. They provide a BASELINE for
  comparing effects of the other treatments. In
  other words, what would happen if we did nothing?

23
CYU answers page 240

• 2. Use an alphabetical list of students- assign
  each one a 1-29. Use Table D and choose 15
  numbers between 1 and 29- these students will
  meet in small groups. The others will view the
  videos alone.
• 3. A control group would allow us to have a group
  to compare to the treatment group. We can
  evaluate whether the group work is actually
  better.

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Principles for Designing Experiments

• Control
• Random Assignment
• Replication
• Replication means you should use enough subjects
  so that the effects of a treatment can be
  distinguished from chance or a fluke.

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Placebo Effect

• Medical treatments
• If some subjects take a pill and others dont,
  they KNOW they are not taking anything.
• Usually a placebo will be given instead (a sugar
  pill that does nothing) so they dont know what
  they are taking.
• The placebo effect is the effect of simply taking
  pills, even though they did not contain medicine.

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Double-Blind

• Subjects dont know which treatment they receive.
• People who interact with them and measure results
  dont know, either.
• Sometimes this wont work.

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CYU answers page 244

1. No. Women who thought they were getting an
   ultrasound may have had different reactions to
   pregnancy.
2. No. Mothers knew if they had an ultrasound.
3. All mothers could have been treated as if they
   were receiving an ultrasound, but for some the
   machine wouldnt have been turned on. Women would
   have had to not see the screen for that to work.

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Statistically Significant

• An effect so large there is probably no way it
  could have occurred by chance.

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Blocking

• A group of subjects that are known to be similar
  in a way that would probably affect the response
  to the treatment
• Randomized block design- random assignment to
  treatments is carried out separately within each
  block

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Matched Pairs Design

• Read page 249-251
• Special case of a randomized block design that
  uses blocks of size 2.

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Chapter 4

• 4.3 Using Studies Wisely

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Scope of Inference

• Most experiments dont select subjects at random
  from the population.
• This limits inference about cause and effect.
• Observational studies dont randomly assign
  subjects to groups so they cant use cause and
  effect.
• We can only make inferences about the population.

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Why cant we use an experiment?

• Doctors have noticed that people who frequently
  use tanning beds are at a greater risk for skin
  cancer. Could this be due to some other lurking
  variable like sun exposure?
• An experiment could help settle this but forcing
  people to use tanning beds would be unethical.

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Establishing Causation

• Sometimes we cant do an experiment because its
  unethical, so we must do an observational study.
  This is what we look for
• Strong association
• Consistent association
• Larger values of x (explanatory) are associated
  with stronger responses
• The alleged cause precedes the effect in time
  (see page 264)
• Alleged cause is plausible

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Data Ethics

• Read examples on page 265 and decide whether you
  think each one is ethical.
• It can be tricky to stay ethical when collecting
  data from people, especially when we impose a
  treatment.
• 3 basic standards to keep in mind
• Planned studies must be reviewed by an
  institutional review board (IRB)
• Individuals must give informed consent
• Data must be kept confidential.

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Data Ethics

• Read more about each of the standards for data
  ethics on page 266.
• When I was preparing my thesis for my masters
  degree, I did a research study. I had to
• Get my study approved through the IRB at my
  school
• Have students/parents sign a consent form
• Keep all student information/names confidential
  as I prepared my reports/presentation