Fundamental Statistics for the Behavioral Sciences, 5th edition David C. Howell

1. Chapter 7 Probability Fundamental Statistics for the Behavioral Sciences, 5th edition David C. Howell ©2003 Brooks/Cole Publishing Company/ITP    

2. Chapter 7 Probability Major Points • Probability defined • Basic terminology • Laws of probability • Discrete variables • Continuous variables Cont.

3. Chapter 7 Probability Major Points--cont. • An example • Review questions

4. Chapter 7 Probability Probability Defined • Analytic view • Relative frequency view • Subjective probability view

5. Chapter 7 Probability Basic Terminology • Sample with replacement • Sample without replacement • Events • Independent events • Mutually exclusive events • Exhaustive outcomes

6. Chapter 7 Probability 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

7. Chapter 7 Probability 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.

8. Chapter 7 Probability 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

9. Chapter 7 Probability 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

10. Chapter 7 Probability 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/ • Search for “radioactivity” and select 1997 dubious awards. Cont.

11. Chapter 7 Probability 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?

12. Chapter 7 Probability 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.

13. Chapter 7 Probability 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?