# 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
The A well-known statement of the problem was published in Because there is no way for the player to know which of the two remaining unopened doors is the winning door, most people assume that each of these doors has an equal probability and conclude that switching does not matter. In fact, the player should switch - doing so doubles the probability of winning the car from 1/3 to 2/3. When the problem and the solution appeared in
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A polar area diagram by Florence Nightingale. The polar area diagram is similar to a pie chart, except that the sectors are each of an equal angle and differ rather in how far each sector extends from the centre of the circle, enabling multiple comparisons on one diagram. This "DIAGRAM of the CAUSES of MORTALITY in the ARMY in the EAST" was published in Notes on Matters Affecting the Health, Efficiency, and Hospital Administration of the British Army and sent to Queen Victoria in 1858. It shows the number of deaths due to preventable diseases (blue), wounds (red), and other causes (black).
## Did you know?- ...that for the number of shuffles needed to randomize a deck, Persi Diaconis concluded that for good shuffling technique, the deck did not start to become random until five good riffle shuffles, and was truly random after seven, in the precise sense of variation distance described in Markov chain mixing time?
- ...that for many standard probability distributions, there are infinitely many outcomes in the sample space, so that attempting to define probabilities for all possible subsets of such spaces would cause difficulties for 'badly-behaved' sets such as those which are nonmeasurable?
- ... that Jan Piekałkiewicz, a leading Polish statistician, became the Polish Underground State's Government Delegate, and died at the hands of Nazi Germany?
- ... that Alec Gallup, co-chairman of The Gallup Organization and the son of founder George Gallup, was described as someone who could "smell out a bad question or an unreasonable interpretation of data"?
- ... that the convergence of the iterative proportional fitting method for estimating the cell values of a contingency table was re-proved using differential geometry?
- ... that statistical properties dictated by Benford's Law are used in auditing of financial accounts as one means of detecting fraud?
- ... that Henry Mann's 1949 book,
*Analysis and design of experiments*, filled mathematical gaps in the statistical writings of Ronald A. Fisher? - ... that Gustav Elfving invented the optimal design of experiments, and so minimized the cost of a cartographic survey, while trapped in his tent in storm-ridden Greenland?
- ... that in 2009, Revolution Analytics named Norman H. Nie, one of the original SPSS developers, as their new CEO?
## Topics in Statistics
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