correlation

[‚kär·ə′lā·shən] (atomic physics) electron correlation (geology) The determination of the equivalence or contemporaneity of geologic events in separated areas. As a step in seismic study, the selecting of corresponding phases, taken from two or more separated seismometer spreads, of seismic events seemingly developing at the same geologic formation boundary. (physics) They tendency of two or more systems that independently exhibit simple behavior to show complex and novel behavior together because of their interaction. (statistics) The interdependence or association between two variables that are quantitative or qualitative in nature.

correlation

the association between two VARIABLES such that when one changes in magnitude the other one does also, i.e. there is a CONCOMITANT VARIATION. Correlation may be positive or negative. Positive correlation describes the situation in which, if one variable increases, so also does the other. Negative correlation describes the situation in which the variables vary inversely, one increasing when the other decreases.

Correlation can be measured by a statistic, the CORRELATION COEFFICIENT or coefficient of association, of which there exist several forms. Most of these focus on a linear relationship (i.e. a relationship in which the variation in one variable is directly proportional to the variation in the other). When presented graphically, for a perfect relationship between variables a straight line can be drawn through all points on the graph. Correlation coefficients are constructed essentially as measures of departure from this straight line. Curvilinear correlation occurs when the variation of the variables is nonlinear, the rate of change of one being faster than the other.

When no association is found between variables they are said to have statistical independence. The technique of correlation analysis is mainly used on interval level data (see CRITERIA AND LEVELS OF MEASUREMENT), but tests also exist for other levels of data (see SPEARMAN RANK CORRELATION COEFFICIENT).

Finding a correlation does not imply causation. Spurious relationships can be found between variables so there has to be other evidence to support the inference of one variable influencing the other. It also must be remembered that the apparent association may be caused by a third factor influencing both variables systematically For situations in which three or more variables are involved, techniques of MULTIVARIATE ANALYSIS exist. See also REGRESSION, CAUSAL MODELLING, PATH ANALYSIS.

Correlation

in biology, the interdependence of the structure and functions of the cells, tissues, organs, and systems of the body, manifested in the body’s development and in its life activities.

The development and existence of the organism as an integral whole is dependent on correlation. The concept was introduced by G. Cuvier (1800–05); however, since he did not accept the theory of evolution, his idea of correlation had a static character, holding that it was evidence of the permanent coexistence of organs. Evolutionary theory gave correlation a dynamic, historical character: the interconnection of the parts of the body is as much the result of their phylogenic development as of their ontogenic development. The problem of correlation was developed from an evolutionary point of view by A. N. Severtsov, and a more profound understanding of it was offered by I. I. ShmaPgauzen.

Several forms of correlation are distinguished. Genomic correlation is a function of the multiple action of hereditary factors (pleiotropy) and of the action of genes that are more closely interrelated (chromosomal correlation). Morphogenetic correlation is the interdependence among the internal factors of individual development. There may be a connection between two or more morphogenetic processes. Thus, it has been shown that the rudiment of the chordamesoderm becomes the inductor that determines the development of the central nervous system and that the optic cup induces the crystalline lens of the eye. Correlation determines the locus and dimensions of a developing organ. Since morphogenetic processes lead to changes in organic inter-relationships, new morphogenetic correlations develop. Thus, a sequential system of morphogenetic correlations gradually un-folds in the course of individual development, becoming one of the chief factors in ontogeny, maintaining the integrity of the organism throughout its development. The data accumulated by developmental biology have enabled some authors to subdivide these correlations into developmental correlations, which de-pend on the activity of the nervous system; functional (ergontic) correlations; and hormonal correlations. Phylogenetic, or phyletic, correlations—the relational changes of the organs during the course of evolution—were considered by Severtsov to be an independent phenomenon, called coordination.

REFERENCES

Shmal’gauzen, 1.1. Osnovy sravnitel’noi anatomii pozvonochnykh, 4th ed. Moscow, 1947.
Shmal’gauzen, 1.1. Organizm, kak tseloe v individual’nom i istoricheskom razvitii. Moscow-Leningrad, 1942.
Severtsov, A. N. Morfologicheskie zakonomernosti evoliutsii. Moscow, 1949. (Sobr. soch., vol. 5.)
Balinsky, B. I. An Introduction to Embryology, 2nd ed. Philadelphia-London, 1965.

A. A. MAKHOTIN

Correlation

in linguistics, the opposition or convergence of linguistic units according to specific features (on all levels of a linguistic system).

Most well developed is the theory of phonological correlation (a phoneme alternation associated with some morphological difference, or forming correlative series that are in opposition according to some one distinctive feature). The notions distinguished include correlative pair (French ã-a, õ-o, ẽ-e, œ̃-œ), feature (nasalization in French, labiovelarization in the Shona languages of the Bantu family), series (ã, õ, ẽ, œ̃), and bundles (in the Archi language, the six-membered bundle z-s-ts-ts’-t̄s-s̄).

Correlation

in mathematical statistics, a probabilistic or statistical relationship, which, generally speaking, does not have a rigorously functional character. In contrast to a functional relationship, a correlative relationship arises either when one of the random variables depends not only on a given second variable but also on a number of random factors or when, among the conditions upon which one and the other variable depend, there exist some that are common to both of them. A correlation table provides an example of this type of dependence. From Table 1 it is evident that, on the average, an increase in the height of pine trees is accompanied by an increase in the diameter of their trunks; however, pines of a given height (for example, 23 m) possess a distribution of diameters with a fairly large scatter. If, on the average, 23-m pines are thicker than 22-m ones, this relation may be violated to a noticeable extent for individual pines. The statistical correlation in a finite sample being studied is more interesting when it indicates the existence of a link between the phenomena under investigation that conforms to some rule.

Correlation theory is based on the assumption that the phenomena being studied obey some definite probabilistic laws (seePROBABILITY; PROBABILITY THEORY). The relationship between two random events is manifested by the conditional probability of one of the events, given that the other has occurred, being different from the unconditional probability. Similarly, the influence of one random quantity on another is characterized by the laws for the conditional distributions of the first at fixed values of the second. For each possible value X = x, let the conditional expectation y(x) = E(yǀX = x) of the quantity Y be defined. The function y (x) is called the regression of the quantity Y on X, and its graph is called the regression line of Y on X. The dependence of Y on X is manifested in the change in the mean value of Y with a change in X, although for each X = x the quantity Y is still a random quantity with a definite scatter. Let m_y =E(Y) be the unconditional expectation of Y. If the quantities are independent, then all the conditional expectations of Y are independent of x and coincide with the unconditional expectations:

y(x) = E(YǀX = x) = E(Y) = m_Y

The converse is not always true. In order to find out how well the regression gives the change in Y with a change in Xt we use the conditional variance of y at a given value of X = x or its mean—the variance of Y relative to the regression line (a measure of the scatter near the regression line):

For a strictly functional relationship, the quantity y at a given X = x assumes only one specific value, that is, the variance near the regression line equals zero.

The regression line may be approximately reconstructed from a sufficiently extensive correlation table: one takes for an approximate value of y (x) the mean of those observed values of Y that correspond to the valued = x. Figure 1 depicts the approximate regression line corresponding to data in Table 1 for the dependence of the mean diameter of pine trees on height. In the central part this line is obviously a good expression of the actual dependence. If the number of observations corresponding to certain

Table 1. Correlation between the diameters and heights of 624 northern pine trunks
Height (m)
Diameter (cm)	17	18	19	20	21	22	23	24	25	26	27	28	29	30	Total
14–17	2	2	5	1											10
18–21	1	3	3	12	15	9	4								47
22–25	1	1	1	3	18	24	29	14	7						98
26–29					7	18	30	43	31	3	2				134
30–33					1	5	18	29	35	18	7	1			114
34–37						1	3	17	33	26	12	6			98
38–41							2	2	10	19	16	4			53
42–45									4	13	6	8		1	32
46–49								3	3	7	6	2	1		22
50–53									1	4	4	2	1		12
54–57										1	1	1			3
58 and greater											1				1
Total..........	4	6	9	16	41	57	86	108	124	91	55	24	2	1	624
Mean diameter.....	18.5	18.6	17.7	20.0	22.9	25.0	27.2	30.1	32.7	38.3	40.0	41.8	49.5	43.5	31.2

values of X is insufficiently large, then this method may lead to completely random results. Thus, the points of the line corresponding to heights of 29 and 30 m are unreliable because of the small number of observations.

Figure 1. Approximate regression line for dependence of mean diameter of northern pine trunks on height

In the case of correlation of two random variables, the usual indicator of the concentration of the distribution near the regression line is the correlation ratio

where σ²y is the variance of Y (the correlation ratio η²XǀY is analogously defined, but there is no simple relation between ηYǀX and ηXǀY).The quantity η²YǀX, which varies from 0 to 1, is equal to zero if and only if the regression has the form y(x) = m_y, in which case Y is said to be uncorrelated with X η²Xǀy is equal to unity in the case of an exact functional dependence of Y on X. The most frequently used measure of the degree of dependence between X and Y is the correlation coefficient between X and Y

where −1 ≤ ρ ≤ 1. However, the practical use of the correlation coefficient as a measure of dependence is justified only when the joint distribution of (X, Y) pairs is normal or approximately normal; the use of p as a measure of dependence between arbitrary Y and X sometimes leads to erroneous deductions, since p can equal zero even when Y depends strictly on X. If the two-dimensional distribution of X and Y is normal, then the regression line of Y on X and that of X on Y are straight lines:

y = m_y + β_y(x − m_x) and x = m_x + β_x(y − m_y)

where βY = δ(σy/σx) and βx = ρ(σx/σy); β_y and β_x called the regression coefficients. Moreover,

Since in this case

E(Y − y(x))² = (1 − ρ²)

and

E(Y − x(y))² = (1 − ρ²)

it is evident that p (the correlation ratios coincide with ρ²) completely determines the degree of concentration of the distribution near the regression line: in the limiting case ρ = ±1, the regression lines coalesce into one, which corresponds to the strict linear relationship between Y and X when ρ = 0, the quantities are not correlated.

In the study of the relationship between several random variables X₁, . . . , X_n, multiple and partial correlation ratios and correlation coefficients are used (the latter primarily in the case of linear relationships). A fundamental characteristic of the dependence is the set of coefficients ρ_ij —the simple correlation coefficients between X_i and X_j —which form the correlation matrix (ρ_ij) (obviously, ρ_ij = ρ_ij and ρ_kk = 1). The multiple correlation coefficient serves as a measure of the linear correlation between X and the set of all the remaining variables X₂ . . . , X_n for n = 3, it is

If it is assumed that a change in the variables X₁ and X₂ is determined to some extent by a change in the remaining variables X₃, . . . , X_n, then the partial correlation coefficient of X₁ and X₁ relative to X₃, . . . , X_n is an indicator of the linear relationship between X₁ and X₂ with the effects of X₃, . . . , X_n excluded; for n = 3, it is

Multiple and partial correlation ratios have somewhat more complex expressions.

In mathematical statistics, methods have been developed for estimating the aforementioned coefficients as well as for testing hypotheses concerning their values by using their sample analogs (sample correlation coefficients, correlation ratios). See.

REFERENCES

Dunin-Barkovskii, I. V., and N. V. Smirnov. Teoriia veroiatnostei i matematicheskaia statistika v tekhnike (the general section). Moscow, 1955.
Cramér, H. Matematicheskie metody statistiki. Moscow, 1948. (Translated from English.)
Hald, A. Matematicheskaia statistika s tekhnicheskimi prilozheniiami. Moscow, 1956. (Translated from English.)
Van der Waerden, B. L. Matematicheskaia statistika. Moscow, 1960. (Translated from German.)
MitropoPskii, A. K. Tekhnika statisticheskikh vychislenii, 2nd ed. Moscow, 1971.

A. V. PROKHOROV

correlation

A confirmation that the target blip seen on radarscope or the track plotted on a plotting board is the same aircraft on which information is being received.

correlation

In statistics, a measure of the strength of the relationship between two variables. It is used to predict the value of one variable given the value of the other. For example, a correlation might relate distance from urban location to gasoline consumption. Expressed on a scale from -1.0 to +1.0, the strongest correlations are at both extremes and provide the best predictions. See regression analysis.

correlation

coefficient

[ko″ĕ-fish´ent] 1. an expression of the change or effect produced by the variation in certain variables, or of the ratio between two different quantities.2. in chemistry, a number or figure put before a chemical formula to indicate how many times the formula is to be multiplied.absorption coefficient absorptivity.1. linear absorption coefficient.2. mass absorption coefficient.Bunsen coefficient the number of milliliters of gas dissolved in a milliliter of liquid at atmospheric pressure (760 mm Hg) and a specified temperature. Symbol, α.confidence coefficient the probability that a interval" >confidence interval will contain the true value of the population parameter. For example, if the confidence coefficient is 0.95, 95 per cent of the confidence intervals so calculated for a large number of random samples would contain the parameter.correlation coefficient a numerical value that indicates the degree and direction of relationship between two variables; the coefficients range in value from +1.00 (perfect positive relationship) to 0.00 (no relationship) to −1.00 (perfect negative or inverse relationship).diffusion coefficient see diffusion coefficient.coefficient of digestibility the proportion of a food that is digested compared to what is absorbed, expressed as a percentage.dilution coefficient a number that expresses the effectiveness of a disinfectant for a given organism. It is calculated by the equation tcⁿ = k, where t is the time required for killing all organisms, c is the concentration of disinfectant, n is the dilution coefficient, and k is a constant. A low coefficient indicates the disinfectant is effective at a low concentration.linear absorption coefficient the fraction of a beam of radiation absorbed per unit thickness of absorber.mass absorption coefficient the linear absorption coefficient divided by the density of the absorber.phenol coefficient see phenol coefficient.sedimentation coefficient the velocity at which a particle sediments in a centrifuge divided by the applied centrifugal field, the result having units of time (velocity divided by acceleration), usually expressed in Svedberg units (S), which equal 10⁻¹³ second. Sedimentation coefficients are used to characterize the size of macromolecules; they increase with increasing mass and density and are higher for globular than for fibrous particles.

cor·re·la·tion

(kōr'ĕ-lā'shŭn), 1. The mutual or reciprocal relation of two or more items or parts. 2. The act of bringing into such a relation. 3. The degree to which variables change together.

correlation

The degree to which two or more variables are related in some fashion. A linear relationship between variables can be measured with Pearson's correlation or Spearman's rho.
Correlation may not mean causation.

correlation

Statistics The degree to which an event, factor, phenomenon, or variable is associated with, related to, or can be predicted from another; the degree to which a linear relationship exists between variables, measured by a correlation coefficient. See Cervical biopsy-cytology correlation, Clinical correlation, Correlation coefficient, Intertemporal correlation, Pearson correlation, Rank correlation.

correlation

The degree to which changes in variables reflect, or fail to reflect one another. Correlations are said to be positive when the variables change in the same direction and negative when they move in opposite directions. A common fault in statistics is to assume that correlations are significant when they are not, that is, to assume unjustifiably that changes in variables are causally related.

correlation

a statistical association between two variables, calculated as the correlation coefficient r . The coefficient can range from r = 1.0 (a perfect positive correlation) to r = -1.0 (a perfect negative correlation), with an r value of 0 indicating no relationship between the two variables. Height and weight in humans are positively correlated (as values for height increase so do values for weight), whereas other variables give a negative correlation, e.g. as human age increases so mental agility tends to decrease.

cor·re·la·tion

(kōr'ĕ-lā'shŭn) 1. The mutual or reciprocal relation of two or more items or parts. 2. The act of bringing into such a relation. 3. The degree to which variables change together.

Patient discussion about correlation

Q. I have chronic hayfever problems in the mornings for the first hour.Seems to be a correlation with dairy produ I also got asthma 8 years ago at age 69, after having 2 pet cats. It is controlled with 2 puffs of Symbicord daily, am & pm.Anyone managed a complete cure?A. Hey lixuri,you mean to tell me after after 25yrs as a therapist,All my patients had to do is drink water all day.i love it,how long does it take to work,an what does the patient do in the mean time if they have a asthmatic attack(drink WAter while you cant breath?-PLEASE SEND ME AN AANSWER.---mrfoot56.

Q. What correlation is there between Diet and Fitness? do i attain those two in a similar way? do i have to attain one in order to complete/gain the other ? A. agree with dominicus. if you want to be healthier, you should keep your eye on what you eat and how often/how regular you do the exercise.
the result will be best if you can combine those two in balance portion and in healthy and wise manner.
Good luck, and stay healthy always..

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noun correspondence

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noun a logical or natural association between two or more things

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noun a reciprocal relation between two or more things

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noun a statistic representing how closely two variables co-vary

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noun a statistical relation between two or more variables such that systematic changes in the value of one variable are accompanied by systematic changes in the other

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