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Notes
Notes

... Ideally we would like a test with α = β = 0. Like most of life this ideal is impossible. For a fixed sample size increasing α will in general decrease β and vice versa. So the general prescription in designing hypothesis tests is to fix α of a small number and design a test that will give as small a ...
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6.1-6.2 Review

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... Empirically, probability can be defined as the number of favorable outcomes divided by the total number of outcomes, in other words, the chance that an event will occur. Formally, the probability, p of an event can be described as the normalized “area” of some event within an event space, S , that c ...
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Week 3 Lecture Notes 7.1 - NIU Math

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Topic 6: Conditional Probability and

... Let A be the event that an individual test positive for some disease and C be the event that the person actually has the disease. We can perform clinical trials to estimate the probability that a randomly chosen individual tests positive given that they have the disease, P {test positive|has the dis ...
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History of statistics

The History of statistics can be said to start around 1749 although, over time, there have been changes to the interpretation of the word statistics. In early times, the meaning was restricted to information about states. This was later extended to include all collections of information of all types, and later still it was extended to include the analysis and interpretation of such data. In modern terms, ""statistics"" means both sets of collected information, as in national accounts and temperature records, and analytical work which requires statistical inference.Statistical activities are often associated with models expressed using probabilities, and require probability theory for them to be put on a firm theoretical basis: see History of probability.A number of statistical concepts have had an important impact on a wide range of sciences. These include the design of experiments and approaches to statistical inference such as Bayesian inference, each of which can be considered to have their own sequence in the development of the ideas underlying modern statistics.
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