AP Statistics

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AP Statistics

• Chapter 5 Notes

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Ways to Collect Data

• Survey
• Select a sample, ask questions, record answers.
• Observational Study
• Observe individuals and measure variables of
  interest, but do not attempt to influence the
  response, (lack of control, often no random
  assignment to experimental groups).
• Experiment
• Study in which we deliberately manipulate and
  control the sample and measure variables.

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Survey Terms

• Population The entire group of individuals that
  we want information about.
• Sample A part of the population that we actually
  examine in order to gather information.
• Sampling The process of choosing and studying a
  part, in order to get information about the
  whole.
• Census Attempts to contact every individual in
  the population.

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Bad Sampling Methods

• Voluntary Response Sample
• Consists of people who choose themselves by
  responding to a general appeal.
• Convenience Sampling
• Choosing individuals who are the easiest to
  contact.
• Bias.the result of poor sampling
• Systematic favoring of certain outcomes

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Proper Sampling Methods

• Probability Sample Sample chosen by chance.
• Simple Random Sample (SRS)
• 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.
• Stratified Random Sample
• Population is first divided into groups called
  strata, that are similar in a way that is
  important to the response. SRS is then taken
  from each stratum to form the sample.
• of individuals taken from the strata should be
  proportional to the number of individuals in the
  strata.

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Other Sampling Methods

• Cluster Sampling
• Divide population into clusters
• Randomly select some clusters.
• All individuals in chosen clusters are included
  in the sample
• Multistage sampling
• Sampling done in steps using a combination of
  methods, (used for very large populations).

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Problems with surveys (even when sampling methods
are good)

• Undercoverage
• Some groups in the population are left out of the
  process of choosing a sample.
• Nonresponse
• Individual chosen for the sample cant be
  contacted or does not cooperate
• These problems may or may not cause bias.
• Bias will result if the people left out are
  different, as a group, than the people included.

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Error/Bias

• Sampling Error
• Occurs because the sample rarely reflects the
  population perfectly.
• Cant be avoidedwe just have to account for it
  in our calculations (example margin of error).
• Response Bias
• Occurs when a respondent does not give an
  accurate response.
• Causes characteristics of the interviewer,
  lying, etc.
• Poor Question Wording
• One-sided, leading

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Parts of an Experiment

• Experimental Units Individuals on which the
  experiment is being performed, (called subjects
  or participants when human)
• Treatment An experimental condition applied to
  the units.
• Factors The explanatory variables in an
  experiment.
• Level A specific value of a factor
• Examples Dosage, temperature
• Combination of levels and factors form the
  treatment.
• Example 200mg given orally, 400mg administered
  intravenously

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Principles of Experimental Design

• 1. Control
• Minimize the effects of lurking variables by
  comparing several treatments in the same
  environment. (utilize placebos and control
  groups)
• Placebo Effect response to a dummy treatment
• 2. Replication
• Use many experimental units to reduce chance
  variation in the results
• 3. Randomization
• Use impersonal chance to assign experimental
  units to treatments.
• Goal Find statistical significancethe observed
  effect is so large that it is unlikely to have
  occurred by chance.

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Types of Experimental Designs

• Completely Randomized Design
• aka a basic comparative experiment
• All experimental units are allocated at random
  among all the treatments

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Comparative Experiment
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Types of Experimental Designs

• Block Design
• An experiment is conducted separately for
  different groups (blocks) of experimental units.
• Use blocks if you expect certain groups of
  units/subjects to systematically affect the
  response to the treatments.
• It is similar to stratified random sampling.

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Block Design
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Types of Experimental Designs

• Matched Pairs Design (type of block design)
• Compares two treatments by comparing the response
  of two matched experimental units.
• Units are matched one of two ways.
• (a) Two different units/subjects matched based on
  similar characteristics (e.g. identical twins)
• (b) One subject/unit receives both treatments
  (i.e. A person is paired with him/herself. Each
  subject serves as his/her own control.)
• Randomization is still used to determine who gets
  which treatment, or which treatment is given
  first.

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Example Fertilizing a Field
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Other Considerations with Experiments

• It is sometimes better if the experiment is
  conducted in a double-blind manner.
• Neither the subjects nor the people administering
  the experiment know which treatment the subjects
  received.
• Sometimes a lack of realism is a problem for
  experiments.
• A laboratory setting is not always the same as
  real life, which makes it difficult to generalize
  your findings.

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Other Considerations Cont

• Dont forget to describe your randomization
  process in detail when writing an open-ended
  response.
• Random sample
• Allows you to generalize your results to the
  population
• Random allocation to treatment groups
• Allows you to state that the difference between
  the responses in the treatment groups was due to
  the effects of the explanatory variable, not the
  personal characteristics of the subjects.