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Sequential Analysis: A Revolution in Statistical Theory

Warren Bell

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Published in Sequential Analysis Abraham Wald

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Sequential analysis is a powerful statistical technique that has revolutionized the way we make decisions in the face of uncertainty. It was developed by Abraham Wald, a Hungarian-American mathematician, during World War II. Wald's work on sequential analysis has had a profound impact on a wide range of fields, including quality control, clinical trials, and finance.

The Problem of Hypothesis Testing

Before Wald's work, statisticians relied on hypothesis testing to make decisions about the parameters of a probability distribution. Hypothesis testing involves collecting a fixed sample of data and then using that data to test a hypothesis about the population from which the sample was drawn. However, hypothesis testing has a number of limitations.

Sequential Analysis

by Abraham Wald

4.6 out of 5

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It is inefficient because it requires collecting a fixed sample size, even if the data collected so far is sufficient to make a decision.
It is not adaptive because it does not take into account the results of the data collected so far when making decisions about whether to continue sampling.
It does not allow for risk minimization because it does not take into account the costs of making a wrong decision.

Wald's Solution: Sequential Analysis

Wald's sequential analysis provides a solution to the problems of hypothesis testing. Sequential analysis is a method of statistical inference that allows for the collection of data and the making of decisions on a sequential basis. This means that data is collected one observation at a time, and a decision is made after each observation whether to continue sampling or to stop and make a final decision.

Sequential analysis has a number of advantages over hypothesis testing.

It is efficient because it allows for the collection of data to stop as soon as enough information has been gathered to make a decision.
It is adaptive because it takes into account the results of the data collected so far when making decisions about whether to continue sampling.
It allows for risk minimization because it takes into account the costs of making a wrong decision.

Applications of Sequential Analysis

Sequential analysis has been used in a wide range of applications, including:

Quality control
Clinical trials
Finance
Military operations

In quality control, sequential analysis can be used to determine whether a production process is in control or out of control. In clinical trials, sequential analysis can be used to determine whether a new treatment is effective or not. In finance, sequential analysis can be used to determine the optimal time to buy or sell a stock.

Sequential analysis is a powerful statistical technique that has revolutionized the way we make decisions in the face of uncertainty. It is efficient, adaptive, and allows for risk minimization. As a result, sequential analysis has been used in a wide range of applications, including quality control, clinical trials, and finance.

Sequential Analysis

by Abraham Wald

4.6 out of 5