Probability

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Chapter 6 Probability
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Outline

• Hypothesis Testing Review/experience
• Probability defined
• Probability and frequency tables
• Probability and the Normal Distribution
• Using the tables in the back

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Hypothesis Testing
Type I/alpha, Type II/beta, Power/1-beta,
1-alpha, sigma, 1-sigma
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Distraction and Perception

• What is the impact of distract when performing a
  perceptual task?
• Flip your quiz over
• Label with your PID, gender (M/F), group
  (D/N)distraction vs. nondistraction
• Task will be assigned
• You will be asked to perform the task for 3
  minutes

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Probability defined

• Fraction or proportion of observing a particular
  phenomenon
• Probability of A
• number of outcomes classified as A
• Total number of possible outcomes
• Examples
• With and without replacement

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Probability and Frequency Tables

• Actually already did this for exam 1
• If have the following scores 6, 6, 6, 7, 8, 8,
  9, 12, 12, 14
• What is the p(Xlt9)?, p(Xgt12)?
• 40 Kindergartners, 18 are boys with 10 being
  blue-eyed and 8 being brown-eyed 22 are girls
  with 11 being blue-eyed and 11 being brown-eyed
• Pick one what is the p(girl)? P(boy)?
  p(blue-eyed)?
• What is the p(boy with brown eyes)?

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Probability and the Normal Distribution

• z-score and the normal distribution
• Area under curve is the probability
• Proportion under graph for
• z lt 1.2, z gt -2.00, z lt -0.50
• Z-score for
• Highest 25, lowest 40
• Between scores (hardest)

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Major Points--cont.

• An example
• Review questions

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Probability Defined

• Analytic view
• Relative frequency view
• Subjective probability view

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Basic Terminology

• Sample with replacement
• Sample without replacement
• Events
• Independent events
• Mutually exclusive events
• Exhaustive outcomes

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More Terminology

• Joint probability
• The probability of the co-occurrence of two or
  more events
• Conditional probability
• The probability of the occurrence of one event
  given that some other event has occurred

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Laws of Probability

• The additive law
• Given a set of mutually exclusive events, the
  probability of the occurrence of one event or
  another is equal to the sum of their separate
  probabilities.
• The multiplicative law
• The probability of the joint occurrence of two or
  more independent events is the product of their
  individual probabilities.

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Discrete Variables

• A discrete variable is one that can take on only
  a limited number of possible values.
• Events are clearly classed as falling into one or
  another category or value.
• We can talk about the probability of a specific
  outcome

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Continuous Variables

• There are a limitless number of possible values
  for this variable
• The probability distribution is continuous, and
  we speak about the probability of falling in an
  interval, but not the probability of a specific
  outcome
• The ordinate of the distribution is labeled
  density

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An Example

• The Associated Press reported on a study linking
  radioactivity to cancer deaths among nuclear
  workers.
• 29 of all deaths among former workers at a
  nuclear site were due to cancer.
• But...
• 35 of deaths in general population aged 44-65
  are attributable to cancer
• http//www.stats.org/awards/dubious97.htm

Cont.
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Example--cont.

• Apply as many of the terms and concepts that have
  been defined above as possible to this example.
• Should nuclear workers be worried?
• Should non-nuclear workers be worried?

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Review Questions

• What are the three different views of
  probability?
• What is the difference between mutually
  exclusive and exhaustive?
• When would you use the additive law, and when the
  multiplicative law?
• Give an example of a joint probability.

Cont.
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Review Questions--cont.

• Give an example of a conditional probability.
• Why do we use density rather than probability
  on the ordinate with a continuous variable?
• How might we tell if two events are independent?