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Ranked
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] |
Borda Count
The Borda count is a family of positional voting rules which gives each candidate, for each ballot, a number of points corresponding to the number of candidates ranked lower. In the original variant, the lowest-ranked candidate gets 0 points, the next-lowest gets 1 point, etc., and the highest-ranked candidate gets ''n'' − 1 points, where ''n'' is the number of candidates. Once all votes have been counted, the option or candidate with the most points is the winner. The Borda count is intended to elect broadly acceptable options or candidates, rather than those preferred by a majority, and so is often described as a consensus-based voting system rather than a majoritarian one. The Borda count was developed independently several times, being first proposed in 1435 by Nicholas of Cusa (see History below), but is named for the 18th-century French mathematician and naval engineer Jean-Charles de Borda, who devised the system in 1770. It is currently used to elect two ethnic minority ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Strict Weak Ordering
In mathematics, especially order theory, a weak ordering is a mathematical formalization of the intuitive notion of a ranking of a set, some of whose members may be tied with each other. Weak orders are a generalization of totally ordered sets (rankings without ties) and are in turn generalized by partially ordered sets and preorders.. There are several common ways of formalizing weak orderings, that are different from each other but cryptomorphic (interconvertable with no loss of information): they may be axiomatized as strict weak orderings (partially ordered sets in which incomparability is a transitive relation), as total preorders (transitive binary relations in which at least one of the two possible relations exists between every pair of elements), or as ordered partitions ( partitions of the elements into disjoint subsets, together with a total order on the subsets). In many cases another representation called a preferential arrangement based on a utility function i ... [...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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ordinal Measurement
Level of measurement or scale of measure is a classification that describes the nature of information within the values assigned to variables. Psychologist Stanley Smith Stevens developed the best-known classification with four levels, or scales, of measurement: nominal, ordinal, interval, and ratio. This framework of distinguishing levels of measurement originated in psychology and is widely criticized by scholars in other disciplines. Other classifications include those by Mosteller and Tukey, and by Chrisman. Stevens's typology Overview Stevens proposed his typology in a 1946 '' Science'' article titled "On the theory of scales of measurement". In that article, Stevens claimed that all measurement in science was conducted using four different types of scales that he called "nominal", "ordinal", "interval", and "ratio", unifying both " qualitative" (which are described by his "nominal" type) and "quantitative" (to a different degree, all the rest of his scales). The co ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Spearman's Rank Correlation Coefficient
In statistics, Spearman's rank correlation coefficient or Spearman's ''ρ'', named after Charles Spearman and often denoted by the Greek letter \rho (rho) or as r_s, is a nonparametric measure of rank correlation ( statistical dependence between the rankings of two variables). It assesses how well the relationship between two variables can be described using a monotonic function. The Spearman correlation between two variables is equal to the Pearson correlation between the rank values of those two variables; while Pearson's correlation assesses linear relationships, Spearman's correlation assesses monotonic relationships (whether linear or not). If there are no repeated data values, a perfect Spearman correlation of +1 or −1 occurs when each of the variables is a perfect monotone function of the other. Intuitively, the Spearman correlation between two variables will be high when observations have a similar (or identical for a correlation of 1) rank (i.e. relative position la ... [...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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ordinal Scale
Ordinal data is a categorical, statistical data type where the variables have natural, ordered categories and the distances between the categories are not known. These data exist on an ordinal scale, one of four levels of measurement described by S. S. Stevens in 1946. The ordinal scale is distinguished from the nominal scale by having a ''ranking''. It also differs from the interval scale and ratio scale by not having category widths that represent equal increments of the underlying attribute. Examples of ordinal data A well-known example of ordinal data is the Likert scale. An example of a Likert scale is: Examples of ordinal data are often found in questionnaires: for example, the survey question "Is your general health poor, reasonable, good, or excellent?" may have those answers coded respectively as 1, 2, 3, and 4. Sometimes data on an interval scale or ratio scale are grouped onto an ordinal scale: for example, individuals whose income is known might be grouped into ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Friedman Test
The Friedman test is a non-parametric statistical test developed by Milton Friedman. Similar to the parametric repeated measures ANOVA, it is used to detect differences in treatments across multiple test attempts. The procedure involves ranking each row (or ''block'') together, then considering the values of ranks by columns. Applicable to complete block designs, it is thus a special case of the Durbin test. Classic examples of use are: * ''n'' wine judges each rate ''k'' different wines. Are any of the ''k'' wines ranked consistently higher or lower than the others? * ''n'' welders each use ''k'' welding torches, and the ensuing welds were rated on quality. Do any of the ''k'' torches produce consistently better or worse welds? The Friedman test is used for one-way repeated measures analysis of variance by ranks. In its use of ranks it is similar to the Kruskal–Wallis one-way analysis of variance by ranks. The Friedman test is widely supported by many statistical software ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Non-parametric Statistics
Nonparametric statistics is the branch of statistics that is not based solely on parametrized families of probability distributions (common examples of parameters are the mean and variance). Nonparametric statistics is based on either being distribution-free or having a specified distribution but with the distribution's parameters unspecified. Nonparametric statistics includes both descriptive statistics and statistical inference. Nonparametric tests are often used when the assumptions of parametric tests are violated. Definitions The term "nonparametric statistics" has been imprecisely defined in the following two ways, among others: Applications and purpose Non-parametric methods are widely used for studying populations that take on a ranked order (such as movie reviews receiving one to four stars). The use of non-parametric methods may be necessary when data have a ranking but no clear numerical interpretation, such as when assessing preferences. In terms of levels o ... [...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 varia ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rank Product
The rank product is a biologically motivated test for the detection of differentially expressed genes in replicated microarray experiments. It is a simple non-parametric statistical method based on ranks of fold changes. In addition to its use in expression profiling, it can be used to combine ranked lists in various application domains, including proteomics, metabolomics, statistical meta-analysis, and general feature selection. Calculation of the rank product Given ''n'' genes and ''k'' replicates, let r_ the rank of gene ''g'' in the ''i''-th replicate. Compute the rank product via the geometric mean: : RP(g)=(\Pi_^kr_)^ Determination of significance levels Simple permutation-based estimation is used to determine how likely a given RP value or better is observed in a random experiment. # generate ''p'' permutations of ''k'' rank lists of length ''n''. # calculate the rank products of the ''n'' genes in the ''p'' permutations. # count how many times the rank products of ... [...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] |
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