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editStatistics is a mathematical science pertaining to the collection, analysis, interpretation or explanation, and presentation of data. It is applicable to a wide variety of academic disciplines, from the natural and social sciences to the humanities, government and business.
Statistical methods can be used to summarize or describe a collection of data; this is called descriptive statistics. In addition, patterns in the data may be modeled in a way that accounts for randomness and uncertainty in the observations, and then used to draw inferences about the process or population being studied; this is called inferential statistics. Both descriptive and inferential statistics comprise applied statistics. There is also a discipline called mathematical statistics, which is concerned with the theoretical basis of the subject.
The word statistics is also the plural of statistic (singular), which refers to the result of applying a statistical algorithm to a set of data, as in economic statistics, crime statistics, etc.
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Margin of error |
The margin of error is a statistic expressing the amount of random sampling error in a survey's results. The larger the margin of error, the less confidence one should have that the poll's reported results are close to the "true" figures; that is, the figures for the whole population.
The margin of error is usually defined as the radius of a confidence interval for a particular statistic from a survey. One example is the percent of people who prefer product A versus product B. When a single, global margin of error is reported for a survey, it refers to the maximum margin of error for all reported percentages using the full sample from the survey. If the statistic is a percentage, this maximum margin of error can be calculated as the radius of the confidence interval for a reported percentage of 50%.
The margin of error has been described as an "absolute" quantity, equal to a confidence interval radius for the statistic. For example, if the true value is 50 percentage points, and the statistic has a confidence interval radius of 5 percentage points, then we say the margin of error is 5 percentage points. As another example, if the true value is 50 people, and the statistic has a confidence interval radius of 5 people, then we might say the margin of error is 5 people.
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Sir Ronald Aylmer Fisher (1890-1962) |
Sir Ronald Aylmer Fisher, FRS (17 February 1890 – 29 July 1962) was an English statistician, evolutionary biologist, and geneticist. He was described by Anders Hald as "a genius who almost single-handedly created the foundations for modern statistical science" and Richard Dawkins described him as "the greatest of Darwin's successors".
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Simpson's paradox for continuous data: a positive trend appears for two separate groups (blue and red), a negative trend (black, dashed) appears when the data are combined.
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