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Probability and Life Tables
Probability and Life Tables Chapter Outline 4.1 A Definition of Probability 4.2 Rules for Calculating Probabilities 4.3 Definitions from Epidemiology 4.4 Bayes’ Theorem 4.5 Probability in Sampling 4.6 Estimating Probabilities by Simulation 4.7 Probability and the Life Table As was mentioned in Chapter 3, often we want to do more than simply analyze or summarize the data in graphs or statistics. For example, we may want to determine whether two drugs or treatments are equally effective and safe or whether the age-adjusted death rates for two areas are the same. To answer these questions, we require knowledge of probability, the topic of this chapter.
4.1
A Definition of Probability
We have all encountered the use of probability — in the weather forecast, for example. The forecast usually involves an estimate of the probability of rain, as in the statement that “the probability of rain tomorrow is 20 percent.” As its use in the weather forecast demonstrates, probability is a numerical assessment of the likelihood of the occurrence of an outcome of a random variable. In the weather forecast, weather is the random variable and rain is one of its possible outcomes. Before considering the numerical assessment of likelihood, we should consider random variables. There are both discrete and continuous random variables. A discrete (nominal, categorical or ordinal) random variable is a quantity that reflects an attribute or characteristic that takes on different values with specified probabilities. A continuous (interval or ratio) random variable is a quantity that reflects an attribute or characteristic that falls within an interval with specified probabilities. Hypertension status is a discrete random variable when the values or levels of this variable are defined as its presence (can be defi ned as systolic blood pressure greater than 140 mmHg, diastolic blood pressure greater than 90 mmHg, or taking antihypertensive medication) or absence. Other examples of discrete random variables include racial status, the number of children in a family, and type of health insurance. Examples of continuous random variables include height, blood pressure, and the amount of lead emissions as they are usually measured.
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4.1
A Definition of Probability
We have all encountered the use of probability — in the weather forecast, for example. The forecast usually involves an estimate of the probability of rain, as in the statement that “the probability of rain tomorrow is 20 percent.” As its use in the weather forecast demonstrates, probability is a numerical assessment of the likelihood of the occurrence of an outcome of a random variable. In the weather forecast, weather is the random variable and rain is one of its possible outcomes. Before considering the numerical assessment of likelihood, we should consider random variables. There are both discrete and continuous random variables. A discrete (nominal, categorical or ordinal) random variable is a quantity that reflects an attribute or characteristic that takes on different values with specified probabilities. A continuous (interval or ratio) random variable is a quantity that reflects an attribute or characteristic that falls within an interval with specified probabilities. Hypertension status is a discrete random variable when the values or levels of this variable are defined as its presence (can be defi ned as systolic blood pressure greater than 140 mmHg, diastolic blood pressure greater than 90 mmHg, or taking antihypertensive medication) or absence. Other examples of discrete random variables include racial status, the number of children in a family, and type of health insurance. Examples of continuous random variables include height, blood pressure, and the amount of lead emissions as they are usually measured.
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