Generating Data

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Chapter 3

• Generating Data

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Introduction to Data Collection/Analysis

• Exploratory Data Analysis Plots and Measures
  that describe a set of measurements with no clear
  research questions posed.
• Statistical Inference Methods used to make
  statements regarding population(s) based on
  sample data
• Statistical Design Strategy to obtain data to
  answer research questions (gameplan)
• Anecdotal Evidence Information obtained from
  individual, high profile, cases (plane crashes,
  storms, etc)

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Data Sources

• Available Data Information previously obtained
  and available in libraries and/or the Internet
• Sampling Selecting a subset from population of
  interest and obtaining relevant information from
  individuals (observational study)
• Census Information collected from all
  individuals in a population
• Experiment Individuals are placed in various
  conditions by researchers and responses are then
  obtained

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Experimental Design

• Experimental Units Individuals participating in
  experiment (Humans often called Subjects or Ss)
• Treatment Specific condition applied to units
• Factor Explanatory variable used in experiment.
  Many experiments have more than 1 factor
• Factor Level Value that a factor takes on.
• Example Unplanned Purchases
• 68 subjects selected, response unplanned items
  purchased
• Factors Store Knowledge and Time Pressure
• Factor Levels Knowledge(Familiar/Unfamiliar)
  Time Pressure(Present/Absent)
• Treatments 4 Cominations of Knowledge and Time
  Pressure

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Unplanned Purchases Experiment
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Comparative Experiments

• Goal Compare two or more conditions (treatments)
• Units assigned at random to receive 1 treatment
  (usually, although some designs have each unit
  receive each treatment)
• Placebo Effect Phenomena where subjects show
  improvement even when given a dummy treatment
• Control Group Subjects that receive a placebo or
  non-active agent or no treatment at all
• Biased Design Favors certain response outcomes
• Randomization Use of chance to assign units to
  treatment conditions

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Principles of Experimental Design

• Control Removing effects of lurking variables by
  comparing two or more treatments
• Randomization Use of chance to allocate subjects
  to treatments. Removes personal biases. Makes use
  of tables/computer programs for random digits
• Replication Apply treatments to as many units as
  possible
• Statistical Significance Observed effect that
  exceeds what could be expected by chance

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Miscellaneous Topics

• Blinding Whenever possible, subject and observor
  should be unaware of which treatment was
  assigned. When neither knows its called
  double-blind
• Realism Do the conditions in the experiment the
  real-world setting of interest to investigators
• Matching Identifying pairs of units based on
  some criteria expected to be related to response,
  then randomly assigning one from each pair to
  each treatment
• Block Design Extension of matching to more than
  2 groups (subjects can be their own blocks and
  receive each treatment in some experiments)

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Sampling Design

• Population Entire set of individuals of interest
  to researcher
• Sample Subset of population obtained for data
  collection/information gathering
• Voluntary Response Sample Individuals who
  self-select themselves as respondents. Internet
  polls are example. Tend to be very biased.
• Simple Random Sample Sample selected so that
  each group of n individuals is equally likely to
  be selected
• Probability Sample Sample chosen by chance
• Stratified Random Sample Simple Random samples
  selected from pre-specified groups (strata)

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Miscellaneous Topics in Sampling

• Multistage Sampling Government surveys tend to
  have multiple levels in the sampling process.
• Primary Sampling Unit Block Clusters
  of units
• Undercoverage Groups in the population are not
  included in sample
• Nonresponse Individuals Selected who do not
  respond
• Biases
• Response Bias Subject gives answer to please
  interviewer
• Recall Bias Tendency for some subjects to
  remember something from past
• Wording Questions can be phrased to elicit
  certain responses

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Introduction to Statistical Inference

• Parameter Number describing a population

• Statistic Number describing a sample

Parameters are fixed (usually Unknown) values.
Statistics vary from one sample to another due
to different individuals
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Sampling Distributions

• Sampling Distribution Distribution of values
  that a statistic can take on across all samples
  from the population.
• Shape For large samples, the sampling
  distributions of sample means and proportions
  tend to be approximately normal
• Center The center of he sampling is equal to the
  parameter value in the population (unbiased)
• Spread The spread of the distribution decreases
  as the sample size increases (variability of
  statistic shrinks as sample size gets larger)
• Margin of error Bounds on the size of likely
  sampling error (difference between sample
  statistic and population parameter)