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KEY CONCEPTS
Probability is an important concept in statistics. Both objective and subjective probabilities are used in the medical field.
Basic definitions include the concept of an event or outcome. A number of essential rules tell us how to combine the probabilities of events.
Bayes’ theorem relates to the concept of conditional probability—the probability of an outcome depending on an earlier outcome. Bayes’ theorem is part of the reasoning process when interpreting diagnostic procedures.
Populations are rarely studied; instead, researchers study samples.
Several methods of sampling are used in medical research; a key issue is that any method should be random.
When researchers select random samples and then make measurements, the result is a random variable. This process makes statistical tests and inferences possible.
The binomial distribution is used to determine the probability of yes/no events—the number of times a given outcome occurs in a given number of attempts.
The Poisson distribution is used to determine the probability of rare events.
The normal distribution is used to find the probability that an outcome occurs when the observations have a bell-shaped distribution. It is used in many statistical procedures.
If many random samples are drawn from a population, a statistic, such as the mean, follows a distribution called a sampling distribution.
The central limit theorem tells us that means of observations, regardless of how they are distributed, begin to follow a normal distribution as the sample size increases. This is one of the reasons the normal distribution is so important in statistics.
It is important to know the difference between the standard deviation, which describes the spread of individual observations, from the standard error of the mean, which describes the spread of the mean observations.
One of the purposes of statistics is to use a sample to estimate something about the population. Estimates form the basis of statistical tests.
Confidence intervals can be formed around an estimate to tell us how much the estimate would vary in repeated samples.
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The World Health Organization (WHO) collects influenza rates worldwide. The CDC collects the statistics for the United States and territories. The data collection is completed weekly through the NREVSS collaborating laboratories. The data for the 2017–2018 flu season is used as a Presenting Problem to demonstrate the concepts of probability and displayed in Table 4–1.
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