Chapter 6 Probability. Outline. Hypothesis Testing Review/experience Probability defined Probability and frequency tables Probability and the Normal Distribution Using the tables in the back. Hypothesis Testing. Type I/alpha, Type II/beta, Power/1-beta, 1-alpha, sigma, 1-sigma.
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Chapter 6 Probability
Outline • Hypothesis Testing Review/experience • Probability defined • Probability and frequency tables • Probability and the Normal Distribution • Using the tables in the back
Hypothesis Testing Type I/alpha, Type II/beta, Power/1-beta, 1-alpha, sigma, 1-sigma
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
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
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(X<9)?, p(X>=12)? • 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)?
Probability and the Normal Distribution • z-score and the normal distribution • Area under curve is the probability • Proportion under graph for • z < 1.2, z > -2.00, z < -0.50 • Z-score for • Highest 25%, lowest 40% • Between scores (hardest)
Major Points--cont. • An example • Review questions
Probability Defined • Analytic view • Relative frequency view • Subjective probability view
Basic Terminology • Sample with replacement • Sample without replacement • Events • Independent events • Mutually exclusive events • Exhaustive outcomes
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
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.
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
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
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.
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?
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.
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?