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Level Of 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 has since had a complex history, being adopted and extended in some disciplines and by some scholars, and criticized or rejected by others. 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" ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Classifying
Classification is the activity of assigning objects to some pre-existing classes or categories. This is distinct from the task of establishing the classes themselves (for example through cluster analysis). Examples include diagnostic tests, identifying spam emails and deciding whether to give someone a driving license. As well as 'category', synonyms or near-synonyms for 'class' include 'type', 'species', 'order', 'concept', 'taxon', 'group', 'identification' and 'division'. The meaning of the word 'classification' (and its synonyms) may take on one of several related meanings. It may encompass both classification and the creation of classes, as for example in 'the task of categorizing pages in Wikipedia'; this overall activity is listed under taxonomy. It may refer exclusively to the underlying scheme of classes (which otherwise may be called a taxonomy). Or it may refer to the label given to an object by the classifier. Classification is a part of many different kinds of activ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dependent And Independent Variables
A variable is considered dependent if it depends on (or is hypothesized to depend on) an independent variable. Dependent variables are studied under the supposition or demand that they depend, by some law or rule (e.g., by a mathematical function), on the values of other variables. Independent variables, on the other hand, are not seen as depending on any other variable in the scope of the experiment in question. Rather, they are controlled by the experimenter. In pure mathematics In mathematics, a function (mathematics), function is a rule for taking an input (in the simplest case, a number or set of numbers)Carlson, Robert. A concrete introduction to real analysis. CRC Press, 2006. p.183 and providing an output (which may also be a number). A symbol that stands for an arbitrary input is called an independent variable, while a symbol that stands for an arbitrary output is called a dependent variable. The most common symbol for the input is , and the most common symbol for the o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Range (statistics)
In descriptive statistics, the range of a set of data is size of the narrowest interval which contains all the data. It is calculated as the difference between the largest and smallest values (also known as the sample maximum and minimum). It is expressed in the same units as the data. The range provides an indication of statistical dispersion. Closely related alternative measures are the Interdecile range and the Interquartile range. Range of continuous IID random variables For ''n'' independent and identically distributed continuous random variables ''X''1, ''X''2, ..., ''X''''n'' with the cumulative distribution function G(''x'') and a probability density function g(''x''), let T denote the range of them, that is, T= max(''X''1, ''X''2, ..., ''X''''n'')- min(''X''1, ''X''2, ..., ''X''''n''). Distribution The range, T, has the cumulative distribution function ::F(t)= n \int_^\infty g(x) (x+t)-G(x) \, \textx. Gumbel notes that the "beauty of this formula is com ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Globally Unique Identifier
A Universally Unique Identifier (UUID) is a 128-bit label used to uniquely identify objects in computer systems. The term Globally Unique Identifier (GUID) is also used, mostly in Microsoft systems. When generated according to the standard methods, UUIDs are, for practical purposes, unique. Their uniqueness does not depend on a central registration authority or coordination between the parties generating them, unlike most other numbering schemes. While the probability that a UUID will be duplicated is not zero, it is generally considered close enough to zero to be negligible. Thus, anyone can create a UUID and use it to identify something with near certainty that the identifier does not duplicate one that has already been, or will be, created to identify something else. Information labeled with UUIDs by independent parties can therefore be later combined into a single database or transmitted on the same channel, with a negligible probability of duplication. Adoption of UUIDs is wi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Constructivist Epistemology
Constructivism is a view in the philosophy of science that maintains that scientific knowledge is constructed by the scientific community, which seeks to measure and construct models of the natural world. According to constructivists, natural science consists of mental constructs that aim to explain sensory experiences and measurements, and that there is no single valid methodology in science but rather a diversity of useful methods. They also hold that the world is independent of human minds, but knowledge of the world is always a human and social construction. Constructivism opposes the philosophy of objectivism, embracing the belief that human beings can come to know the truth about the natural world not mediated by scientific approximations with different degrees of validity and accuracy. Constructivism and sciences Social constructivism in sociology One version of ''social constructivism'' contends that categories of knowledge and reality are actively created by soci ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dichotomy
A dichotomy () is a partition of a set, partition of a whole (or a set) into two parts (subsets). In other words, this couple of parts must be * jointly exhaustive: everything must belong to one part or the other, and * mutually exclusive: nothing can belong simultaneously to both parts. If there is a concept A, and it is split into parts B and not-B, then the parts form a dichotomy: they are mutually exclusive, since no part of B is contained in not-B and vice versa, and they are jointly exhaustive, since they cover all of A, and together again give A. Such a partition is also frequently called a bipartition. The two parts thus formed are Complement (set theory), complements. In logic, the partitions are dual (category theory), opposites if there exists a proposition such that it holds over one and not the other. Treating continuous variables or multicategorical variables as binary variables is called discretization, dichotomization. The discretization error inherent in dichoto ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Studentized Range
In statistics, the studentized range, denoted ''q'', is the difference between the largest and smallest data in a sample normalized by the sample standard deviation. It is named after William Sealy Gosset (who wrote under the pseudonym "''Student''"), and was introduced by him in 1927. The concept was later discussed by Newman (1939), Keuls (1952), and John Tukey in some unpublished notes. Its statistical distribution is the '' studentized range distribution'', which is used for multiple comparison procedures, such as the single step procedure Tukey's range test, the Newman–Keuls method, and the Duncan's step down procedure, and establishing confidence intervals that are still valid after data snooping has occurred. Description The value of the studentized range, most often represented by the variable ''q'', can be defined based on a random sample ''x''1, ..., ''x''''n'' from the ''N''(0, 1) distribution of numbers, and another random variable ''s'' that is ind ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Coefficient Of Variation
In probability theory and statistics, the coefficient of variation (CV), also known as normalized root-mean-square deviation (NRMSD), percent RMS, and relative standard deviation (RSD), is a standardized measure of dispersion of a probability distribution or frequency distribution. It is defined as the ratio of the standard deviation \sigma to the mean \mu (or its absolute value, , and often expressed as a percentage ("%RSD"). The CV or RSD is widely used in analytical chemistry to express the precision and repeatability of an assay. It is also commonly used in fields such as engineering or physics when doing quality assurance studies and ANOVA gauge R&R, by economists and investors in economic models, in epidemiology, and in psychology/neuroscience. Definition The coefficient of variation (CV) is defined as the ratio of the standard deviation \sigma to the mean \mu, CV = \frac. It shows the extent of variability in relation to the mean of the population. The coefficien ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Harmonic Mean
In mathematics, the harmonic mean is a kind of average, one of the Pythagorean means. It is the most appropriate average for ratios and rate (mathematics), rates such as speeds, and is normally only used for positive arguments. The harmonic mean is the multiplicative inverse, reciprocal of the arithmetic mean of the reciprocals of the numbers, that is, the generalized f-mean with f(x) = \frac. For example, the harmonic mean of 1, 4, and 4 is :\left(\frac\right)^ = \frac = \frac = 2\,. Definition The harmonic mean ''H'' of the positive real numbers x_1, x_2, \ldots, x_n is :H(x_1, x_2, \ldots, x_n) = \frac = \frac. It is the reciprocal of the arithmetic mean of the reciprocals, and vice versa: :\begin H(x_1, x_2, \ldots, x_n) &= \frac, \\ A(x_1, x_2, \ldots, x_n) &= \frac, \end where the arithmetic mean is A(x_1, x_2, \ldots, x_n) = \tfrac1n \sum_^n x_i. The harmonic mean is a Schur-concave function, and is greater than or equal to the minimum of its arguments: for positive a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Geometric Mean
In mathematics, the geometric mean is a mean or average which indicates a central tendency of a finite collection of positive real numbers by using the product of their values (as opposed to the arithmetic mean which uses their sum). The geometric mean of numbers is the Nth root, th root of their product (mathematics), product, i.e., for a collection of numbers , the geometric mean is defined as : \sqrt[n]. When the collection of numbers and their geometric mean are plotted in logarithmic scale, the geometric mean is transformed into an arithmetic mean, so the geometric mean can equivalently be calculated by taking the natural logarithm of each number, finding the arithmetic mean of the logarithms, and then returning the result to linear scale using the exponential function , :\sqrt[n] = \exp \left( \frac \right). The geometric mean of two numbers is the square root of their product, for example with numbers and the geometric mean is \textstyle \sqrt = The geometric mean o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ratio
In mathematics, a ratio () shows how many times one number contains another. For example, if there are eight oranges and six lemons in a bowl of fruit, then the ratio of oranges to lemons is eight to six (that is, 8:6, which is equivalent to the ratio 4:3). Similarly, the ratio of lemons to oranges is 6:8 (or 3:4) and the ratio of oranges to the total amount of fruit is 8:14 (or 4:7). The numbers in a ratio may be quantities of any kind, such as counts of people or objects, or such as measurements of lengths, weights, time, etc. In most contexts, both numbers are restricted to be Positive integer, positive. A ratio may be specified either by giving both constituting numbers, written as "''a'' to ''b''" or "''a'':''b''", or by giving just the value of their quotient Equal quotients correspond to equal ratios. A statement expressing the equality of two ratios is called a ''proportion''. Consequently, a ratio may be considered as an ordered pair of numbers, a Fraction (mathematic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Deviation (statistics)
In mathematics and statistics, deviation serves as a measure to quantify the disparity between an observed value of a variable and another designated value, frequently the mean of that variable. Deviations with respect to the sample mean and the population mean (or "true value") are called errors and residuals, ''errors'' and ''residuals'', respectively. The Sign (mathematics), sign of the deviation reports the direction of that difference: the deviation is positive when the observed value exceeds the reference value. The absolute value of the deviation indicates the size or magnitude of the difference. In a given sample (statistics), sample, there are as many deviations as sample points. Summary statistics can be derived from a set of deviations, such as the ''standard deviation'' and the ''mean absolute deviation'', measures of statistical dispersion, dispersion, and the ''mean signed deviation'', a measure of bias of an estimator, bias. The deviation of each data point is calc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
