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Second Place
A ranking is a relationship between a set of items such that, for any two items, the first is either "ranked higher than", "ranked lower than" or "ranked equal to" the second. In mathematics, this is known as a weak order or total preorder of objects. It is not necessarily a total order of objects because two different objects can have the same ranking. The rankings themselves are totally ordered. For example, materials are totally preordered by hardness, while degrees of hardness are totally ordered. If two items are the same in rank it is considered a tie. By reducing detailed measures to a sequence of ordinal numbers, rankings make it possible to evaluate complex information according to certain criteria. Thus, for example, an Internet search engine may rank the pages it finds according to an estimation of their relevance, making it possible for the user quickly to select the pages they are likely to want to see. Analysis of data obtained by ranking commonly requires non-pa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Order Theory
Order theory is a branch of mathematics that investigates the intuitive notion of order using binary relations. It provides a formal framework for describing statements such as "this is less than that" or "this precedes that". This article introduces the field and provides basic definitions. A list of order-theoretic terms can be found in the order theory glossary. Background and motivation Orders are everywhere in mathematics and related fields like computer science. The first order often discussed in primary school is the standard order on the natural numbers e.g. "2 is less than 3", "10 is greater than 5", or "Does Tom have fewer cookies than Sally?". This intuitive concept can be extended to orders on other sets of numbers, such as the integers and the reals. The idea of being greater than or less than another number is one of the basic intuitions of number systems (compare with numeral systems) in general (although one usually is also interested in the actual difference ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kruskal–Wallis One-way Analysis Of Variance
The Kruskal–Wallis test by ranks, Kruskal–Wallis ''H'' testKruskal–Wallis H Test using SPSS Statistics Laerd Statistics (named after and ), or one-way ANOVA on ranks is a method for testing whether samples originate from the same distribution. It is used for comparing two or more independent sample ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Disjoint Sets
In mathematics, two sets are said to be disjoint sets if they have no element in common. Equivalently, two disjoint sets are sets whose intersection is the empty set.. For example, and are ''disjoint sets,'' while and are not disjoint. A collection of two or more sets is called disjoint if any two distinct sets of the collection are disjoint. Generalizations This definition of disjoint sets can be extended to a family of sets \left(A_i\right)_: the family is pairwise disjoint, or mutually disjoint if A_i \cap A_j = \varnothing whenever i \neq j. Alternatively, some authors use the term disjoint to refer to this notion as well. For families the notion of pairwise disjoint or mutually disjoint is sometimes defined in a subtly different manner, in that repeated identical members are allowed: the family is pairwise disjoint if A_i \cap A_j = \varnothing whenever A_i \neq A_j (every two ''distinct'' sets in the family are disjoint).. For example, the collection of sets is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kendall Rank Correlation Coefficient
In statistics, the Kendall rank correlation coefficient, commonly referred to as Kendall's τ coefficient (after the Greek letter τ, tau), is a statistic used to measure the ordinal association between two measured quantities. A τ test is a non-parametric hypothesis test for statistical dependence based on the τ coefficient. It is a measure of rank correlation: the similarity of the orderings of the data when ranked by each of the quantities. It is named after Maurice Kendall, who developed it in 1938, though Gustav Fechner had proposed a similar measure in the context of time series in 1897. Intuitively, the Kendall correlation between two variables will be high when observations have a similar (or identical for a correlation of 1) rank (i.e. relative position label of the observations within the variable: 1st, 2nd, 3rd, etc.) between the two variables, and low when observations have a dissimilar (or fully different for a correlation of −1) rank between the two variables. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rank Correlation
In statistics, a rank correlation is any of several statistics that measure an ordinal association—the relationship between rankings of different ordinal variables or different rankings of the same variable, where a "ranking" is the assignment of the ordering labels "first", "second", "third", etc. to different observations of a particular variable. A rank correlation coefficient measures the degree of similarity between two rankings, and can be used to assess the significance of the relation between them. For example, two common nonparametric methods of significance that use rank correlation are the Mann–Whitney U test and the Wilcoxon signed-rank test. Context If, for example, one variable is the identity of a college basketball program and another variable is the identity of a college football program, one could test for a relationship between the poll rankings of the two types of program: do colleges with a higher-ranked basketball program tend to have a higher-ranked f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Microsoft Excel
Microsoft Excel is a spreadsheet developed by Microsoft for Microsoft Windows, Windows, macOS, Android (operating system), Android and iOS. It features calculation or computation capabilities, graphing tools, pivot tables, and a macro (computer science), macro programming language called Visual Basic for Applications (VBA). Excel forms part of the Microsoft Office suite of software. Features Basic operation Microsoft Excel has the basic features of all spreadsheets, using a grid of ''cells'' arranged in numbered ''rows'' and letter-named ''columns'' to organize data manipulations like arithmetic operations. It has a battery of supplied functions to answer statistical, engineering, and financial needs. In addition, it can display data as line graphs, histograms and charts, and with a very limited three-dimensional graphical display. It allows sectioning of data to view its dependencies on various factors for different perspectives (using ''pivot tables'' and the ''sce ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Percentile Rank
In statistics, the percentile rank (PR) of a given score is the percentage of scores in its frequency distribution that are less than that score. Its mathematical formula is : PR = \frac \times 100, where ''CF''—the cumulative frequency—is the count of all scores less than or equal to the score of interest, ''F'' is the frequency for the score of interest, and ''N'' is the number of scores in the distribution. Alternatively, if ''CF'' is the count of all scores less than the score of interest, then : PR = \frac \times 100. The figure illustrates the percentile rank computation and shows how the 0.5 × ''F'' term in the formula ensures that the percentile rank reflects a percentage of scores less than the specified score. For example, for the 10 scores shown in the figure, 60% of them are below a score of 4 (five less than 4 and half of the two equal to 4) and 95% are below 7 (nine less than 7 and half of the one equal to 7). Occasionally the percentile rank of a score is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fractional Ranking ("1 2
A fraction is one or more equal parts of something. Fraction may also refer to: * Fraction (chemistry), a quantity of a substance collected by fractionation * Fraction (floating point number), an (ambiguous) term sometimes used to specify a part of a floating point number * Fraction (politics), a subgroup within a parliamentary party * Fraction (radiation therapy), one unit of treatment of the total radiation dose of radiation therapy that is split into multiple treatment sessions * Fraction (religion), the ceremonial act of breaking the bread during Christian Communion People with the surname * Matt Fraction, a comic book author See also * Algebraic fraction, an indicated division in which the divisor, or both dividend and divisor, are algebraic expressions ** Irrational fraction, a type of algebraic fraction * Faction (other) * ''Frazione'', a type of administrative division of an Italian ''commune'' * Free and Independent Fraction, a Romanian political party * Part (d ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Power Law
In statistics, a power law is a Function (mathematics), functional relationship between two quantities, where a Relative change and difference, relative change in one quantity results in a proportional relative change in the other quantity, independent of the initial size of those quantities: one quantity varies as a Exponentiation, power of another. For instance, considering the area of a square in terms of the length of its side, if the length is doubled, the area is multiplied by a factor of four. Empirical examples The distributions of a wide variety of physical, biological, and man-made phenomena approximately follow a power law over a wide range of magnitudes: these include the sizes of craters on the moon and of solar flares, the foraging pattern of various species, the sizes of activity patterns of neuronal populations, the frequencies of words in most languages, frequencies of family names, the species richness in clades of organisms, the sizes of power outages, volcanic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Van Der Waerden Test
Named after the Dutch mathematician Bartel Leendert van der Waerden, the Van der Waerden test is a statistical test that ''k'' population distribution functions are equal. The Van der Waerden test converts the ranks from a standard Kruskal-Wallis one-way analysis of variance to quantiles of the standard normal distribution (details given below). These are called normal scores and the test is computed from these normal scores. The ''k'' population version of the test is an extension of the test for two populations published by Van der Waerden (1952,1953). Background Analysis of Variance (ANOVA) is a data analysis technique for examining the significance of the factors (independent variables) in a multi-factor model. The one factor model can be thought of as a generalization of the two sample t-test. That is, the two sample t-test is a test of the hypothesis that two population means are equal. The one factor ANOVA tests the hypothesis that ''k'' population means are equal. The stan ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Wilcoxon Signed-rank Test
The Wilcoxon signed-rank test is a non-parametric statistical hypothesis test used either to test the location of a population based on a sample of data, or to compare the locations of two populations using two matched samples., p. 350 The one-sample version serves a purpose similar to that of the one-sample Student's ''t''-test. For two matched samples, it is a paired difference test like the paired Student's ''t''-test (also known as the "''t''-test for matched pairs" or "''t''-test for dependent samples"). The Wilcoxon test can be a good alternative to the ''t''-test when population means are not of interest; for example, when one wishes to test whether a population's median is nonzero, or whether there is a better than 50% chance that a sample from one population is greater than a sample from another population. History The test is named for Frank Wilcoxon (1892–1965) who, in a single paper, proposed both it and the rank-sum test for two independent samples. The test was p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
