Portal:Statistics

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When census data cannot be collected, statisticians collect data by developing specific experiment designs and survey samples. Representative sampling assures that inferences and conclusions can reasonably extend from the sample to the population as a whole. An experimental study involves taking measurements of the system under study, manipulating the system, and then taking additional measurements using the same procedure to determine if the manipulation has modified the values of the measurements. In contrast, an observational study does not involve experimental manipulation. Two main statistical methods are used in data analysis: descriptive statistics, which summarize data from a sample using indexes such as the mean or standard deviation, and inferential statistics, which draw conclusions from data that are subject to random variation (e.g., observational errors, sampling variation). Descriptive statistics are most often concerned with two sets of properties of a A standard statistical procedure involves the test of the relationship between two statistical data sets, or a data set and synthetic data drawn from an idealized model. A hypothesis is proposed for the statistical relationship between the two data sets, and this is compared as an alternative to an idealized null hypothesis of no relationship between two data sets. Rejecting or disproving the null hypothesis is done using statistical tests that quantify the sense in which the null can be proven false, given the data that are used in the test. Working from a null hypothesis, two basic forms of error are recognized: Type I errors (null hypothesis is falsely rejected giving a "false positive") and Type II errors (null hypothesis fails to be rejected and an actual difference between populations is missed giving a "false negative"). Multiple problems have come to be associated with this framework: ranging from obtaining a sufficient sample size to specifying an adequate null hypothesis. Measurement processes that generate statistical data are also subject to error. Many of these errors are classified as random (noise) or systematic (bias), but other types of errors (e.g., blunder, such as when an analyst reports incorrect units) can also be important. The presence of missing data or censoring may result in biased estimates and specific techniques have been developed to address these problems. Statistics can be said to have begun in ancient civilization, going back at least to the 5th century BC, but it was not until the 18th century that it started to draw more heavily from calculus and probability theory. In more recent years statistics has relied more on statistical software to produce tests such as descriptive analysis. ## Selected article
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## Did you know?- ... that bivariate analysis is one of simplest forms of quantitative (statistical) analysis?
- ... that, while President of the American Statistical Association, Robert V. Hogg wore the name tag "Boss Hogg" after the character on the television series
*The Dukes of Hazzard*? - ... that the
*Journal of the Royal Statistical Society*, today a prominent academic journal in statistics, had as its first work a simple door-to-door survey of occupations in Manchester? - ... that the reason why occupancy frequency distributions tend to be bimodal is not known?
- ... that Russian-born Israeli mathematician Aryeh Dvoretzky is the first graduate of the Hebrew University of Jerusalem to become a full professor there?
- ... that the hierarchical generalized linear model is a useful statistical model in fields ranging from semiconductor fabrication to marketing research?
- ... that univariate analysis is the simplest form of quantitative (statistical) analysis?
- ... that mathematician Lennart Carleson received his Ph.D. when he was 22 years old and later supervised the thesis of Svante Janson, who received his first Ph.D. on his 22nd birthday?
- ...that though he had a brilliant mathematical career, the statistician Pat Moran had difficulty with simple arithmetic and wrote himself, 'Arithmetic I could not do'?
## Topics in Statistics
## Statistics categoriesClick an arrow symbol to expand any of the sub-categories: ## Associated Wikimedia |

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