|
Tschuprow's T
In statistics, Tschuprow's ''T'' is a measure of association between two nominal variables, giving a value between 0 and 1 (inclusive). It is closely related to Cramér's V, coinciding with it for square contingency tables. It was published by Alexander Tschuprow (alternative spelling: Chuprov) in 1939.Tschuprow, A. A. (1939) ''Principles of the Mathematical Theory of Correlation''; translated by M. Kantorowitsch. W. Hodge & Co. Definition For an ''r'' × ''c'' contingency table with ''r'' rows and ''c'' columns, let \pi_ be the proportion of the population in cell (i,j) and let :\pi_=\sum_^c\pi_ and \pi_=\sum_^r\pi_. Then the mean square contingency is given as : \phi^2 = \sum_^r\sum_^c\frac , and Tschuprow's ''T'' as : T = \sqrt . Properties ''T'' equals zero if and only if independence holds in the table, i.e., if and only if \pi_=\pi_\pi_. ''T'' equals one if and only there is perfect dependence in the table, i.e., if and only if for each ''i'' there is onl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Statistics
Statistics (from German language, German: ''wikt:Statistik#German, Statistik'', "description of a State (polity), state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a scientific, industrial, or social problem, it is conventional to begin with a statistical population or a statistical model to be studied. Populations can be diverse groups of people or objects such as "all people living in a country" or "every atom composing a crystal". Statistics deals with every aspect of data, including the planning of data collection in terms of the design of statistical survey, surveys and experimental design, experiments.Dodge, Y. (2006) ''The Oxford Dictionary of Statistical Terms'', Oxford University Press. When census data cannot be collected, statisticians collect data by developing specific experiment designs and survey sample (statistics), samples. Representative sampling as ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Association (statistics)
In statistics, correlation or dependence is any statistical relationship, whether causal or not, between two random variables or bivariate data. Although in the broadest sense, "correlation" may indicate any type of association, in statistics it usually refers to the degree to which a pair of variables are ''linearly'' related. Familiar examples of dependent phenomena include the correlation between the height of parents and their offspring, and the correlation between the price of a good and the quantity the consumers are willing to purchase, as it is depicted in the so-called demand curve. Correlations are useful because they can indicate a predictive relationship that can be exploited in practice. For example, an electrical utility may produce less power on a mild day based on the correlation between electricity demand and weather. In this example, there is a causal relationship, because extreme weather causes people to use more electricity for heating or cooling. However ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nominal Data
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 conc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cramér's V
In statistics, Cramér's V (sometimes referred to as Cramér's phi and denoted as φ''c'') is a measure of association between two nominal variables, giving a value between 0 and +1 (inclusive). It is based on Pearson's chi-squared statistic and was published by Harald Cramér in 1946. Usage and interpretation φ''c'' is the intercorrelation of two discrete variablesSheskin, David J. (1997). Handbook of Parametric and Nonparametric Statistical Procedures. Boca Raton, Fl: CRC Press. and may be used with variables having two or more levels. φ''c'' is a symmetrical measure: it does not matter which variable we place in the columns and which in the rows. Also, the order of rows/columns doesn't matter, so φ''c'' may be used with nominal data types or higher (notably, ordered or numerical). Cramér's V may also be applied to goodness of fit chi-squared models when there is a 1 × ''k'' table (in this case ''r'' = 1). In this case ''k'' is taken as the number of optional ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Contingency Tables
In statistics, a contingency table (also known as a cross tabulation or crosstab) is a type of table in a matrix format that displays the (multivariate) frequency distribution of the variables. They are heavily used in survey research, business intelligence, engineering, and scientific research. They provide a basic picture of the interrelation between two variables and can help find interactions between them. The term ''contingency table'' was first used by Karl Pearson in "On the Theory of Contingency and Its Relation to Association and Normal Correlation", part of the ''Drapers' Company Research Memoirs Biometric Series I'' published in 1904. A crucial problem of multivariate statistics is finding the (direct-)dependence structure underlying the variables contained in high-dimensional contingency tables. If some of the conditional independences are revealed, then even the storage of the data can be done in a smarter way (see Lauritzen (2002)). In order to do this one can use ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Alexander Alexandrovich Chuprov
Alexander Alexandrovich Chuprov (or Tschuprov) (Russian: Алекса́ндр Алекса́ндрович Чупро́в) ( Mosal'sk, February 18, 1874 - Geneva, April 19, 1926) Russian Empire statistician who worked on mathematical statistics, sample survey theory and demography. Chuprov was born in Mosal'sk but grew up and was educated in Moscow where his father, Alexander Ivanovich (1842–1908), a distinguished economist and statistician, was a professor. Alexander Alexandrovich graduated from the physico-mathematical faculty of Moscow University in 1896 with a dissertation on "The theory of probability as the foundation of theoretical statistics." He spent the years 1897-1901 studying political economy in Germany, in Berlin and Strasbourg. His doctoral dissertation, supervised by Georg Friedrich Knapp (1842–1926) '' Die Feldgemeinschaft, eine morphologische Untersuchung'' was published in 1902. The most important result of his stay in Germany was his friendship with the st ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mean Square Contingency
In statistics, the phi coefficient (or mean square contingency coefficient and denoted by φ or rφ) is a measure of association for two binary variables. In machine learning, it is known as the Matthews correlation coefficient (MCC) and used as a measure of the quality of binary (two-class) classifications, introduced by biochemist Brian W. Matthews in 1975. Introduced by Karl Pearson, and also known as the ''Yule phi coefficient'' from its introduction by Udny Yule in 1912 this measure is similar to the Pearson correlation coefficient in its interpretation. In fact, a Pearson correlation coefficient estimated for two binary variables will return the phi coefficient. Two binary variables are considered positively associated if most of the data falls along the diagonal cells. In contrast, two binary variables are considered negatively associated if most of the data falls off the diagonal. If we have a 2×2 table for two random variables ''x'' and ''y'' where ''n''11, ''n''10 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Empirical Value
Empirical evidence for a proposition is evidence, i.e. what supports or counters this proposition, that is constituted by or accessible to sense experience or experimental procedure. Empirical evidence is of central importance to the sciences and plays a role in various other fields, like epistemology and law. There is no general agreement on how the terms ''evidence'' and ''empirical'' are to be defined. Often different fields work with quite different conceptions. In epistemology, evidence is what justifies beliefs or what determines whether holding a certain belief is rational. This is only possible if the evidence is possessed by the person, which has prompted various epistemologists to conceive evidence as private mental states like experiences or other beliefs. In philosophy of science, on the other hand, evidence is understood as that which '' confirms'' or ''disconfirms'' scientific hypotheses and arbitrates between competing theories. For this role, it is important that ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pearson's Chi-squared Test
Pearson's chi-squared test (\chi^2) is a statistical test applied to sets of categorical data to evaluate how likely it is that any observed difference between the sets arose by chance. It is the most widely used of many chi-squared tests (e.g., Yates, likelihood ratio, portmanteau test in time series, etc.) – statistical procedures whose results are evaluated by reference to the chi-squared distribution. Its properties were first investigated by Karl Pearson in 1900. In contexts where it is important to improve a distinction between the test statistic and its distribution, names similar to ''Pearson χ-squared'' test or statistic are used. It tests a null hypothesis stating that the frequency distribution of certain events observed in a sample is consistent with a particular theoretical distribution. The events considered must be mutually exclusive and have total probability 1. A common case for this is where the events each cover an outcome of a categorical variable. A ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Phi Coefficient
In statistics, the phi coefficient (or mean square contingency coefficient and denoted by φ or rφ) is a measure of association for two binary variables. In machine learning, it is known as the Matthews correlation coefficient (MCC) and used as a measure of the quality of binary (two-class) classifications, introduced by biochemist Brian W. Matthews in 1975. Introduced by Karl Pearson, and also known as the ''Yule phi coefficient'' from its introduction by Udny Yule in 1912 this measure is similar to the Pearson correlation coefficient in its interpretation. In fact, a Pearson correlation coefficient estimated for two binary variables will return the phi coefficient. Two binary variables are considered positively associated if most of the data falls along the diagonal cells. In contrast, two binary variables are considered negatively associated if most of the data falls off the diagonal. If we have a 2×2 table for two random variables ''x'' and ''y'' where ''n''11, ''n' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Uncertainty Coefficient
In statistics, the uncertainty coefficient, also called proficiency, entropy coefficient or Theil's U, is a measure of nominal association. It was first introduced by Henri Theil and is based on the concept of information entropy. Definition Suppose we have samples of two discrete random variables, ''X'' and ''Y''. By constructing the joint distribution, , from which we can calculate the conditional distributions, and , and calculating the various entropies, we can determine the degree of association between the two variables. The entropy of a single distribution is given as: : H(X)= -\sum_x P_X(x) \log P_X(x) , while the conditional entropy is given as: : H(X, Y) = -\sum_ P_(x,~y) \log P_(x, y) . The uncertainty coefficient or proficiency is defined as: : U(X, Y) = \frac = \frac , and tells us: given ''Y'', what fraction of the bits of ''X'' can we predict? In this case we can think of ''X'' as containing the total information, and of ''Y'' as allowing one to pred ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Goodman And Kruskall's Lambda
In probability theory and statistics, Goodman & Kruskal's lambda (\lambda) is a measure of proportional reduction in error in cross tabulation analysis. For any sample with a nominal independent variable and dependent variable (or ones that can be treated nominally), it indicates the extent to which the modal categories and frequencies for each value of the independent variable differ from the overall modal category and frequency, i.e., for all values of the independent variable together. \lambda is defined by the equation :\lambda = \frac. where :\varepsilon_1 is the overall non-modal frequency, and :\varepsilon_2 is the sum of the non-modal frequencies for each value of the independent variable. Values for lambda range from zero (no association between independent and dependent variables) to one (perfect association). Weaknesses Although Goodman and Kruskal's lambda is a simple way to assess the association between variables, it yields a value of 0 (no association) whenever ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
