Statistical Inference

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Statistical Inference

• Statistical thinking will one day be as
  necessary for efficient citizenship as the
  ability to read and write. (H.G. Wells, 1946)
• There are three kinds of lies white lies, which
  are justifiable common lies, which have no
  justification and statistics. (Benjamin
  Disraeli)
• Statistics is no substitute for good judgment.
  (unknown)

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Statistical Inference

• Suppose
• A mechanical engineer is considering the use of a
  new composite material in the design of a vehicle
  suspension system and needs to know how the
  material will react under a variety of conditions
  (heat, cold, vibration, etc.)
• An electrical engineer has designed a radar
  navigation system to be used in high performance
  aircraft and needs to be able to validate
  performance in flight.
• An industrial engineer needs to validate the
  effect of a new roofing product on installation
  speed.
• A motorist must decide whether to drive through a
  long stretch of flooded road after being assured
  that the average depth is only 6 inches.

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Statistical Inference

• What do all of these situations have in common?
• How can we address the uncertainty involved in
  decision making?
• a priori
• a posteriori

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Probability

• A mathematical means of determining how likely an
  event is to occur.
• Classical (a priori) Given N equally likely
  outcomes, the probability of an event A is given
  by,
• where n is the number of different ways A can
  occur.
• Empirical (a posteriori) If an experiment is
  repeated M times and the event A occurs mA times,
  then the probability of event A is defined as,

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The Role of Probability in Statistics

• In statistical inference, we want to make general
  statements about the population based on
  measurements taken from a sample.
• How will all suspension systems produced with the
  new composite behave?
• How will the radar navigation system perform in
  all aircraft?
• What speed improvements will we obtain for all
  roofing applications using the new product?
• To answer these questions, we ___________ from
  the population and hope to generalize the results.

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Observations Statistical Inference

• Example,
• An experiment is designed to determine how long
  it takes to install a roof using a new product.
• Experiment
• Design
• Result t 2.32 sec/ft2, P 0.023
• p value

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Descriptive Statistics

• Numerical values that help to characterize the
  nature of data for the experimenter.
• Example The absolute error in the readings from
  a radar navigation system was measured with the
  following results
• the sample mean, x _________________________
• the sample median, x _____________

17 22 39 31 28 52 147