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Correlation and dependence
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This article is about correlation and dependence in statistical data. For other uses, see correlation (disambiguation).
In statistics, dependence or association is any statistical relationship, whether causal or not, between two random variables or bivariate data. Correlation is any of a broad class of statistical relationships involving dependence, though in common usage it most often refers to how close two variables are to having a linear relationship with each other. Familiar examples of dependent phenomena include the correlation between the physical statures of parents and their offspring, and the correlation between the demand for a limited supply product and its price.
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, in general, the presence of a correlation is not sufficient to infer the presence of a causal relationship (i.e., correlation does not imply causation).
Formally, random variables are dependent if they do not satisfy a mathematical property of probabilistic independence. In informal parlance, correlation is synonymous with dependence. However, when used in a technical sense, correlation refers to any of several specific types of relationship between mean values. There are several correlation coefficients, often denoted ρ or r, measuring the degree of correlation. The most common of these is the Pearson correlation coefficient, which is sensitive only to a linear relationship between two variables (which may be present even when one variable is a nonlinear function of the other). Other correlation coefficients have been developed to be more robust than the Pearson correlation – that is, more sensitive to nonlinear relationships.[1][2][3] Mutual information can also be applied to measure dependence between two variables.
Several sets of (x, y) points, with the Pearson correlation coefficient of x and y for each set. Note that the correlation reflects the noisiness and direction of a linear relationship (top row), but not the slope of that relationship (middle), nor many aspects of nonlinear relationships (bottom). N.B.: the figure in the center has a slope of 0 but in that case the correlation coefficient is undefined because the variance of Y is zero.
Contents
[hide]
1 Pearson's product-moment coefficient
2 Rank correlation coefficients
3 Other measures of dependence among random variables
4 Sensitivity to the data distribution
5 Correlation matrices
6 Common misconceptions
6.1 Correlation and causality
6.2 Correlation and linearity
7 Bivariate normal distribution
8 See also
9 References
10 Further reading
11 External links
Pearson's product-moment coefficient[edit]
Main article: Pearson product-moment correlation coefficient
The most familiar measure of dependence between two quantities is the Pearson product-moment correlation coefficient, or "Pearson's correlation coefficient", commonly called simply "the correlation coefficient". It is obtained by dividing the covariance of the two variables by the product of their standard deviations. Karl Pearson developed the coefficient from a similar but slightly different idea by Francis Galton.[4]
The population correlation coefficient ρX,Y between two random variables X and Y with expected values μX and μY and standard deviations σX and σY is defined as
ρ X , Y = c o r r ( X , Y ) = c o v ( X , Y ) σ X σ Y = E [ ( X − μ X ) ( Y − μ Y ) ] σ X σ Y , {\displaystyle \rho _{X,Y}=\mathrm {corr} (X,Y)={\mathrm {cov} (X,Y) \over \sigma _{X}\sigma _{Y}}={E[(X-\mu _{X})(Y-\mu _{Y})] \over \sigma _{X}\sigma _{Y}},}
where E is the expected value operator, cov means covariance, and corr is a widely used alternative notation for the correlation coefficient.
External video
Lecture 21: Covariance and Correlation, Statistics 110, Harvard University, 49:25, April 29, 2013
The Pearson correlation is defined only if both of the standard deviations are finite and nonzero. It is a corollary of the Cauchy–Schwarz inequality that the correlation cannot exceed 1 in absolute value. The correlation coefficient is symmetric: corr(X,Y) = corr(Y,X).
The Pearson correlation is +1 in the case of a perfect direct (increasing) linear relationship (correlation), −1 in the case of a perfect decreasing (inverse) linear relationship (anticorrelation),[5] and some value in the open interval (−1, 1) in all other cases, indicating the degree of linear dependence between the variables. As it approaches zero there is less of a relationship (closer to uncorrelated). The closer the coefficient is to either −1 or 1, the stronger the correlation between the variables.
If the variables are independent, Pearson's correlation coefficient is 0, but the converse is not true because the correlation coefficient detects only linear dependencies between two variables. For example, suppose the random variable X is symmetrically distributed about zero, and Y = X2. Then Y is completely determined by X, so that X and Y are perfectly dependent, but their correlation is zero; they are uncorrelated. However, in the special case when X and Y are jointly normal, uncorrelatedness is equivalent to independence.
If we have a series of n measurements of X and Y written as xi and yi for i = 1, 2, ..., n, then the sample correlation coefficient can be used to estimate the population Pearson correlation r between X and Y. The sample correlation coefficient is written as
r x y = ∑ i = 1 n ( x i − x ¯ ) ( y i − y ¯ ) ( n − 1 ) s x s y = ∑ i = 1 n ( x i − x ¯ ) ( y i − y ¯ ) ∑ i = 1 n ( x i − x ¯ ) 2 ∑ i = 1 n ( y i − y ¯ ) 2 , {\displaystyle r_{xy}={\frac {\sum \limits _{i=1}^{n}(x_{i}-{\bar {x}})(y_{i}-{\bar {y}})}{(n-1)s_{x}s_{y}}}={\frac {\sum \limits _{i=1}^{n}(x_{i}-{\bar {x}})(y_{i}-{\bar {y}})}{\sqrt {\sum \limits _{i=1}^{n}(x_{i}-{\bar {x}})^{2}\sum \limits _{i=1}^{n}(y_{i}-{\bar {y}})^{2}}}},}
where x and y are the sample means of X and Y, and sx and sy are the corrected sample standard deviations of X and Y.
The uncorrected form of r (not standard) can be written as
r x y = ∑ x i y i − n x ¯ y ¯ n s x s y = n ∑ x i y i − ∑ x i ∑ y i n ∑ x i 2 − ( ∑ x i ) 2 n ∑ y i 2 − ( ∑ y i ) 2 . {\displaystyle {\begin{aligned}r_{xy}&={\frac {\sum x_{i}y_{i}-n{\bar {x}}{\bar {y}}}{ns_{x}s_{y}}}\\&={\frac {n\sum x_{i}y_{i}-\sum x_{i}\sum y_{i}}{{\sqrt {n\sum x_{i}^{2}-(\sum x_{i})^{2}}}~{\sqrt {n\sum y_{i}^{2}-(\sum y_{i})^{2}}}}}.\end{aligned}}}
where sx and sy are now the uncorrected sample standard deviations of X and Y.
If x and y are results of measurements that contain measurement error, the realistic limits on the correlation coefficient are not −1 to +1 but a smaller range.[6] For the case of a linear model with a single independent variable, the coefficient of determination (R squared) is the square of r, Pearson's product-moment coefficient.
Rank correlation coefficients[edit]
Main articles: Spearman's rank correlation coefficient and Kendall tau rank correlation coefficient
Rank correlation coefficients, such as Spearman's rank correlation coefficient and Kendall's rank correlation coefficient (τ) measure the extent to which, as one variable increases, the other variable tends to increase, without requiring that increase to be represented by a linear relationship. If, as the one variable increases, the other decreases, the rank correlation coefficients will be negative. It is common to regard these rank correlation coefficients as alternatives to Pearson's coefficient, used either to reduce the amount of calculation or to make the coefficient less sensitive to non-normality in distributions. However, this view has little mathematical basis, as rank correlation coefficients measure a different type of relationship than the Pearson product-moment correlation coefficient, and are best seen as measures of a different type of association, rather than as alternative measure of the population correlation coefficient.[7][8]
To illustrate the nature of rank correlation, and its difference from linear correlation, consider the following four pairs of numbers (x, y):
(0, 1), (10, 100), (101, 500), (102, 2000).
As we go from each pair to the next pair x increases, and so does y. This relationship is perfect, in the sense that an increase in x is always accompanied by an increase in y. This means that we have a perfect rank correlation, and both Spearman's and Kendall's correlation coefficients are 1, whereas in this example Pearson product-moment correlation coefficient is 0.7544, indicating that the points are far from lying on a straight line. In the same way if y always decreases when x increases, the rank correlation coefficients will be −1, while the Pearson product-moment correlation coefficient may or may not be close to −1, depending on how close the points are to a straight line. Although in the extreme cases of perfect rank correlation the two coefficients are both equal (being both +1 or both −1), this is not generally the case, and so values of the two coefficients cannot meaningfully be compared.[7] For example, for the three pairs (1, 1) (2, 3) (3, 2) Spearman's coefficient is 1/2, while Kendall's coefficient is 1/3.
Other measures of dependence among random variables[edit]
See also: Pearson product-moment correlation coefficient § Variants
The information given by a correlation coefficient is not enough to define the dependence structure between random variables.[9] The correlation coefficient completely defines the dependence structure only in very particular cases, for example when the distribution is a multivariate normal distribution. (See diagram above.) In the case of elliptical distributions it characterizes the (hyper-)ellipses of equal density; however, it does not completely characterize the dependence structure (for example, a multivariate t-distribution's degrees of freedom determine the level of tail dependence).
Distance correlation[10][11] was introduced to address the deficiency of Pearson's correlation that it can be zero for dependent random variables; zero distance correlation implies independence.
The Randomized Dependence Coefficient[12] is a computationally efficient, copula-based measure of dependence between multivariate random variables. RDC is invariant with respect to non-linear scalings of random variables, is capable of discovering a wide range of functional association patterns and takes value zero at independence.
The correlation ratio is able to detect almost any functional dependency,[citation needed][clarification needed] and the entropy-based mutual information, total correlation and dual total correlation are capable of detecting even more general dependencies. These are sometimes referred to as multi-moment correlation measures,[citation needed] in comparison to those that consider only second moment (pairwise or quadratic) dependence.
The polychoric correlation is another correlation applied to ordinal data that aims to estimate the correlation between theorised latent variables.
One way to capture a more complete view of dependence structure is to consider a copula between them.
The coefficient of determination generalizes the correlation coefficient for relationships beyond simple linear regression.
Sensitivity to the data distribution[edit]
Further information: Pearson product-moment correlation coefficient § Sensitivity to the data distribution
The degree of dependence between variables X and Y does not depend on the scale on which the variables are expressed. That is, if we are analyzing the relationship between X and Y, most correlation measures are unaffected by transforming X to a + bX and Y to c + dY, where a, b, c, and d are constants (b and d being positive). This is true of some correlation statistics as well as their population analogues. Some correlation statistics, such as the rank correlation coefficient, are also invariant to monotone transformations of the marginal distributions of X and/or Y.
Pearson/Spearman correlation coefficients between X and Y are shown when the two variables' ranges are unrestricted, and when the range of X is restricted to the interval (0,1).
Most correlation measures are sensitive to the manner in which X and Y are sampled. Dependencies tend to be stronger if viewed over a wider range of values. Thus, if we consider the correlation coefficient between the heights of fathers and their sons over all adult males, and compare it to the same correlation coefficient calculated when the fathers are selected to be between 165 cm and 170 cm in height, the correlation will be weaker in the latter case. Several techniques have been developed that attempt to correct for range restriction in one or both variables, and are commonly used in meta-analysis; the most common are Thorndike's case II and case III equations.[13]
Various correlation measures in use may be undefined for certain joint distributions of X and Y. For example, the Pearson correlation coefficient is defined in terms of moments, and hence will be undefined if the moments are undefined. Measures of dependence based on quantiles are always defined. Sample-based statistics intended to estimate population measures of dependence may or may not have desirable statistical properties such as being unbiased, or asymptotically consistent, based on the spatial structure of the population from which the data were sampled.
Sensitivity to the data distribution can be used to an advantage. For example, scaled correlation is designed to use the sensitivity to the range in order to pick out correlations between fast components of time series.[14] By reducing the range of values in a controlled manner, the correlations on long time scale are filtered out and only the correlations on short time scales are revealed.
Correlation matrices[edit]
"Correlation matrix" redirects here. For correlation matrices in quantum physics, see Quark–lepton complementarity.
See also: Covariance matrix § Correlation matrix
The correlation matrix of n random variables X1, ..., Xn is the n × n matrix whose i,j entry is corr(Xi, Xj). If the measures of correlation used are product-moment coefficients, the correlation matrix is the same as the covariance matrix of the standardized random variables X i / σ ( X i ) {\displaystyle X_{i}/\sigma (X_{i})} for i = 1 , … , n {\displaystyle i=1,\dots ,n} . This applies both to the matrix of population correlations (in which case σ is the population standard deviation), and to the matrix of sample correlations (in which case σ denotes the sample standard deviation). Consequently, each is necessarily a positive-semidefinite matrix. Moreover, the correlation matrix is strictly positive definite if no variable can have all its values exactly generated as a linear function of the values of the others.
The correlation matrix is symmetric because the correlation between Xi and Xj is the same as the correlation between Xj and Xi.
A correlation matrix appears, for example, in one formula for the coefficient of multiple determination, a measure of goodness of fit in multiple regression.
In statistical modelling, correlation matrices representing the relationships between variables are categorized into different correlation structures, which are distinguished by factors such as the number of parameters required to estimate them. For example, in an exchangeable correlation matrix, all pairs of variables are modelled as having the same correlation, so all non-diagonal elements of the matrix are equal to each other. On the other hand, an autoregressive matrix is often used when variables represent a time series, since correlations are likely to be greater when measurements are closer in time. Other examples include independent, unstructured, M-dependent, and Toeplitz.
Common misconceptions[edit]
Correlation and causality[edit]
Main article: Correlation does not imply causation
See also: Normally distributed and uncorrelated does not imply independent
The conventional dictum that "correlation does not imply causation" means that correlation cannot be used to infer a causal relationship between the variables.[15] This dictum should not be taken to mean that correlations cannot indicate the potential existence of causal relations. However, the causes underlying the correlation, if any, may be indirect and unknown, and high correlations also overlap with identity relations (tautologies), where no causal process exists. Consequently, establishing a correlation between two variables is not a sufficient condition to establish a causal relationship (in either direction).
A correlation between age and height in children is fairly causally transparent, but a correlation between mood and health in people is less so. Does improved mood lead to improved health, or does good health lead to good mood, or both? Or does some other factor underlie both? In other words, a correlation can be taken as evidence for a possible causal relationship, but cannot indicate what the causal relationship, if any, might be.
Correlation and linearity[edit]
Four sets of data with the same correlation of 0.816
The Pearson correlation coefficient indicates the strength of a linear relationship between two variables, but its value generally does not completely characterize their relationship.[16] In particular, if the conditional mean of Y given X, denoted E(Y | X), is not linear in X, the correlation coefficient will not fully determine the form of E(Y | X).
The image on the right shows scatter plots of Anscombe's quartet, a set of four different pairs of variables created by Francis Anscombe.[17] The four y variables have the same mean (7.5), variance (4.12), correlation (0.816) and regression line (y = 3 + 0.5x). However, as can be seen on the plots, the distribution of the variables is very different. The first one (top left) seems to be distributed normally, and corresponds to what one would expect when considering two variables correlated and following the assumption of normality. The second one (top right) is not distributed normally; while an obvious relationship between the two variables can be observed, it is not linear. In this case the Pearson correlation coefficient does not indicate that there is an exact functional relationship: only the extent to which that relationship can be approximated by a linear relationship. In the third case (bottom left), the linear relationship is perfect, except for one outlier which exerts enough influence to lower the correlation coefficient from 1 to 0.816. Finally, the fourth example (bottom right) shows another example when one outlier is enough to produce a high correlation coefficient, even though the relationship between the two variables is not linear.
These examples indicate that the correlation coefficient, as a summary statistic, cannot replace visual examination of the data. Note that the examples are sometimes said to demonstrate that the Pearson correlation assumes that the data follow a normal distribution, but this is not correct.[4]
Bivariate normal distribution[edit]
If a pair (X, Y) of random variables follows a bivariate normal distribution, the conditional mean E(X|Y) is a linear function of Y, and the conditional mean E(Y|X) is a linear function of X. The correlation coefficient r between X and Y, along with the marginal means and variances of X and Y, determines this linear relationship:
E ( Y ∣ X ) = E ( Y ) + r σ y X − E ( X ) σ x , {\displaystyle E(Y\mid X)=E(Y)+r\sigma _{y}{\frac {X-E(X)}{\sigma _{x}}},}
where E ( X ) {\displaystyle E(X)} and E ( Y ) {\displaystyle E(Y)} are the expected values of X and Y, respectively, and σx and σy are the standard deviations of X and Y, respectively.
See also[edit]
Statistics portal
Further information: Correlation (disambiguation)
Autocorrelation
Canonical correlation
Coefficient of determination
Cointegration
Concordance correlation coefficient
Cophenetic correlation
Copula
Correlation function
Correlation gap
Covariance
Covariance and correlation
Cross-correlation
Ecological correlation
Fraction of variance unexplained
Genetic correlation
Goodman and Kruskal's lambda
Illusory correlation
Interclass correlation
Intraclass correlation
Lift (data mining)
Mean dependence
Modifiable areal unit problem
Multiple correlation
Point-biserial correlation coefficient
Quadrant count ratio
Spurious correlation
Statistical arbitrage
Subindependence
References[edit]
Jump up ^ Croxton, Frederick Emory; Cowden, Dudley Johnstone; Klein, Sidney (1968) Applied General Statistics, Pitman. ISBN 9780273403159 (page 625)
Jump up ^ Dietrich, Cornelius Frank (1991) Uncertainty, Calibration and Probability: The Statistics of Scientific and Industrial Measurement 2nd Edition, A. Higler. ISBN 9780750300605 (Page 331)
Jump up ^ Aitken, Alexander Craig (1957) Statistical Mathematics 8th Edition. Oliver & Boyd. ISBN 9780050013007 (Page 95)
^ Jump up to: a b Rodgers, J. L.; Nicewander, W. A. (1988). "Thirteen ways to look at the correlation coefficient". The American Statistician. 42 (1): 59–66. doi:10.1080/00031305.1988.10475524. JSTOR 2685263.
Jump up ^ Dowdy, S. and Wearden, S. (1983). "Statistics for Research", Wiley. ISBN 0-471-08602-9 pp 230
Jump up ^ Francis, DP; Coats AJ; Gibson D (1999). "How high can a correlation coefficient be?". Int J Cardiol. 69 (2): 185–199. doi:10.1016/S0167-5273(99)00028-5.
^ Jump up to: a b Yule, G.U and Kendall, M.G. (1950), "An Introduction to the Theory of Statistics", 14th Edition (5th Impression 1968). Charles Griffin & Co. pp 258–270
Jump up ^ Kendall, M. G. (1955) "Rank Correlation Methods", Charles Griffin & Co.
Jump up ^ Mahdavi Damghani B. (2013). "The Non-Misleading Value of Inferred Correlation: An Introduction to the Cointelation Model". Wilmott Magazine. doi:10.1002/wilm.10252.
Jump up ^ Székely, G. J. Rizzo; Bakirov, N. K. (2007). "Measuring and testing independence by correlation of distances". Annals of Statistics. 35 (6): 2769–2794. arXiv:0803.4101v1  . doi:10.1214/009053607000000505.
Jump up ^ Székely, G. J.; Rizzo, M. L. (2009). "Brownian distance covariance". Annals of Applied Statistics. 3 (4): 1233–1303. arXiv:1010.0297  . doi:10.1214/09-AOAS312.
Jump up ^ Lopez-Paz D. and Hennig P. and Schölkopf B. (2013). "The Randomized Dependence Coefficient", "Conference on Neural Information Processing Systems" Reprint
Jump up ^ Thorndike, Robert Ladd (1947). Research problems and techniques (Report No. 3). Washington DC: US Govt. print. off.
Jump up ^ Nikolić, D; Muresan, RC; Feng, W; Singer, W (2012). "Scaled correlation analysis: a better way to compute a cross-correlogram". European Journal of Neuroscience: 1–21. doi:10.1111/j.1460-9568.2011.07987.x.
Jump up ^ Aldrich, John (1995). "Correlations Genuine and Spurious in Pearson and Yule". Statistical Science. 10 (4): 364–376. doi:10.1214/ss/1177009870. JSTOR 2246135.
Jump up ^ Mahdavi Damghani, Babak (2012). "The Misleading Value of Measured Correlation". Wilmott. 2012 (1): 64–73. doi:10.1002/wilm.10167.
Jump up ^ Anscombe, Francis J. (1973). "Graphs in statistical analysis". The American Statistician. 27: 17–21. doi:10.2307/2682899. JSTOR 2682899.
Further reading[edit]
Cohen, J.; Cohen P.; West, S.G. & Aiken, L.S. (2002). Applied multiple regression/correlation analysis for the behavioral sciences (3rd ed.). Psychology Press. ISBN 0-8058-2223-2.
Hazewinkel, Michiel, ed. (2001) [1994], "Correlation (in statistics)", Encyclopedia of Mathematics, Springer Science+Business Media B.V. / Kluwer Academic Publishers, ISBN 978-1-55608-010-4
Oestreicher, J. & D. R. (February 26, 2015). Plague of Equals: A science thriller of international disease, politics and drug discovery. California: Omega Cat Press. p. 408. ISBN 978-0963175540.
External links[edit]
Look up correlation or dependence in Wiktionary, the free dictionary.
Wikimedia Commons has media related to Correlation and dependence.
Wikiversity has learning resources about Correlation
MathWorld page on the (cross-)correlation coefficient/s of a sample
Compute significance between two correlations, for the comparison of two correlation values.
A MATLAB Toolbox for computing Weighted Correlation Coefficients
[1] Proof-that-the-Sample-Bivariate-Correlation-has-limits-plus-or-minus-1
Interactive Flash simulation on the correlation of two normally distributed variables by Juha Puranen.
Correlation analysis. Biomedical Statistics
R-Psychologist Correlation visualization of correlation between two numeric variables
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text:
History of chocolate
From Wikipedia, the free encyclopedia
Jump to: navigation, search
"Traités nouveaux & curieux du café du thé et du chocolate", by Philippe Sylvestre Dufour, 1685.
The history of chocolate begins in Mesoamerica. Fermented beverages made from chocolate date back to 350 BC.[1] The Aztecs believed that cacao seeds were the gift of Quetzalcoatl, the god of wisdom, and the seeds once had so much value that they were used as a form of currency. Originally prepared only as a drink, chocolate was served as a bitter, from a liquid, mixed with spices or corn puree. It was believed to have aphrodisiac powers and to give the drinker strength. Today, such drinks are also known as "Chilate" and are made by locals in the South of Mexico. After its arrival to Europe in the sixteenth century, sugar was added to it, rendering it an aphrodisiac, and it became popular throughout society, first among the ruling classes and then among the common people. In the 20th century, chocolate was considered essential in the rations of United States soldiers at war.[2]
The word "chocolate" comes from the Classical Nahuatl word chocolātl, and entered the English language from the Spanish language.[3]
Contents
[hide]
1 History
2 History in Europe
2.1 Early history
2.2 Expansion
3 Modern usage
4 See also
5 References
6 External links
History[edit]
An Aztec woman generates foam by pouring chocolate from one vessel to another in the Codex Tudela
Cultivation, consumption, and cultural use of cacao were extensive in Mesoamerica where the cacao tree is native.[4] When pollinated, the seed of the cacao tree eventually forms a kind of sheath, or ear, 20" long, hanging from the tree trunk itself. Within the sheath are 30 to 40 brownish-red almond-shaped beans embedded in a sweet viscous pulp. While the beans themselves are bitter due to the alkaloids within them, the sweet pulp may have been the first element consumed by humans. Evidence suggests that it may have been fermented and served as an alcoholic beverage as early as 1400 BC.[5]
While researchers do not agree which Mesoamerican culture first domesticated the cacao tree, the use of the fermented bean in a drink seems to have arisen in North America (Mexico). Scientists have been able to confirm its presence in vessels around the world by evaluating the "chemical footprint" detectable in the microsamples of contents that remain.[1] Ceramic vessel with residues from the preparation of chocolate beverages have been found at archaeological sites dating back to the Early Formative (1900–900 BC) period. For example, one such vessel found at an Olmec archaeological site on the Gulf Coast of Veracruz, Mexico dates chocolate's preparation by pre-Olmec peoples as early as 1750 BC.[6] On the Pacific coast of Chiapas, Mexico, a Mokayanan archaeological site provides evidence of cacao beverages dating even earlier, to 1900 BC.[6]
Earliest evidence of domestication of the cacao plant dates to the Olmec culture from the Preclassic period.[7] The Olmecs used it for religious rituals or as a medicinal drink, with no recipes for personal use. Little evidence remains of how the beverage was processed.
The Mayan people, by contrast, do leave some surviving writings about cacao which confirm the identification of the drink with the gods. The Dresden Codex specifies that it is the food of the rain deity Kon, the Madrid Codex that gods shed their blood on the cacao pods as part of its production.[8] The consumption of the chocolate drink is also depicted on pre-Hispanic vases. The Mayans seasoned their chocolate by mixing the roasted cacao seed paste into a drink with water, chile peppers and cornmeal, transferring the mixture repeatedly between pots until the top was covered with a thick foam.[2]
By 1400, the Aztec empire took over a sizable part of Mesoamerica. They were not able to grow cacao themselves, but were forced to import it.[2] All of the areas that were conquered by the Aztecs that grew cacao beans were ordered to pay them as a tax, or as the Aztecs called it, a "tribute". The cacao bean became a form of currency. The Spanish conquistadors left records of the value of the cacao bean, noting for instance that 100 beans could purchase a canoe filled with fresh water or a turkey hen.[5][9] The Aztecs associated cacao with the god Quetzacoatl, whom they believed had been condemned by the other gods for sharing chocolate with humans.[2] Unlike the Maya of Yucatán, the Aztecs drank chocolate cold. It was consumed for a variety of purposes, as an aphrodisiac or as a treat for men after banquets, and it was also included in the rations of Aztec soldiers.[10]
Pueblo people, who lived in an area that is now the U.S. Southwest, imported cacao from Mesoamerican cultures in southern Mexico or Central America between 900 and 1400. They used it in a common beverage consumed by everyone in their society.[1]
History in Europe[edit]
See also: History of chocolate in Spain
Early history[edit]
Until the 16th century, the cacao tree was wholly unknown to Europeans.[2]
Christopher Columbus encountered the cacao bean on his fourth mission to the Americas on August 15, 1502, when he and his crew seized a large native canoe that proved to contain among other goods for trade, cacao beans.[11] His son Ferdinand commented that the natives greatly valued the beans, which he termed almonds, "for when they were brought on board ship together with their goods, I observed that when any of these almonds fell, they all stooped to pick it up, as if an eye had fallen."[11] But while Columbus took cacao beans with him back to Spain,[11] it made no impact until Spanish friars introduced chocolate to the Spanish court.[2]
A Lady Pouring Chocolate by Jean-Étienne Liotard (1744)
Spanish conquistador Hernán Cortés may have been the first European to encounter chocolate when he observed it in the court of Montezuma in 1519.[12] In 1568, Bernal Diaz, who accompanied Cortés in the conquest of Mexico, wrote of this encounter which he witnessed:
From time to time they served him [Montezuma] in cups of pure gold a certain drink made from cacao. It was said that it gave one power over women, but this I never saw. I did see them bring in more than fifty large pitchers of cacao with froth in it, and he drank some of it, the women serving with great reverence.[13]
Jose de Acosta, a Spanish Jesuit missionary who lived in Peru and then Mexico in the later 16th century, described its use more generally:
Loathsome to such as are not acquainted with it, having a scum or froth that is very unpleasant taste. Yet it is a drink very much esteemed among the Indians, where with they feast noble men who pass through their country. The Spaniards, both men and women that are accustomed to the country are very greedy of this Chocolate. They say they make diverse sorts of it, some hot, some cold, and some temperate, and put therein much of that "chili"; yea, they make paste thereof, the which they say is good for the stomach and against the catarrh.
After the Spanish conquest of the Aztecs, chocolate was imported to Europe. There, it quickly became a court favorite. It was still served as a beverage, but the Spanish added sugar or honey to counteract the natural bitterness.[5] The Spaniards initially intended to recreate the original taste of the Mesoamerican chocolate by adding similar spices, but this habit had faded away by the end of the eighteenth century.[14] Within about a hundred years, chocolate established a foothold throughout Europe.[2]
How the word "chocolate" came into Spanish is not certain. The authority on the Spanish language, the Royal Spanish Academy, derives it from the Nahuatl word "xocolatl" (pronounced [ ʃoˈkolaːtɬ]) made up from the words "xococ" meaning sour or bitter, and "atl" meaning water or drink.[15] However, as William Bright noted[16] the word "chocolatl" doesn't occur in central Mexican colonial sources making this an unlikely derivation. Santamaria[17] gives a derivation from the Yucatec Maya word "chokol" meaning hot, and the Nahuatl "atl" meaning water. More recently Dakin and Wichman derive it from another Nahuatl term, "chicolatl" from Eastern Nahuatl meaning "beaten drink".[18] They derive this term from the word for the frothing stick, "chicoli". The word xocoatl means beverage of maize.[19] The words "cacaua atl" mean drink of cacao.[19] The word "xocolatl" does not appear in Molina's dictionary.[19]
Expansion[edit]
An early 20th century chocolate advert
The new craze for chocolate brought with it a thriving slave market, as between the early 17th and late 19th centuries the laborious and slow processing of the cacao bean was manual.[2] Cacao plantations spread, as the English, Dutch, and French colonized and planted. With the depletion of Mesoamerican workers, largely to disease, cacao production was often the work of poor wage laborers and African slaves. Wind-powered and horse-drawn mills were used to speed production, augmenting human labor. Heating the working areas of the table-mill, an innovation that emerged in France in 1732, also assisted in extraction.[20] The Chocolaterie Lombart, created in 1760, claimed to be the first chocolate company in France, ten years before Pelletier et Pelletier.[21]
New processes that speed the production of chocolate emerged early in the Industrial Revolution. In 1815, Dutch chemist Coenraad van Houten introduced alkaline salts to chocolate, which reduced its bitterness.[2] A few years thereafter, in 1828, he created a press to remove about half the natural fat (cacao butter) from chocolate liquor, which made chocolate both cheaper to produce and more consistent in quality. This innovation introduced the modern era of chocolate.[11] Known as "Dutch cocoa", this machine-pressed chocolate was instrumental in the transformation of chocolate to its solid form when in 1847 Joseph Fry learned to make chocolate moldable by adding back melted cacao butter.[5] Milk had sometimes been used as an addition to chocolate beverages since the mid-17th century, but in 1875 Daniel Peter invented milk chocolate by mixing a powdered milk developed by Henri Nestlé with the liquor.[2][11] In 1879, the texture and taste of chocolate was further improved when Rodolphe Lindt invented the conching machine.[22]
Lindt & Sprüngli AG, a Swiss-based concern with global reach, had its start in 1845 as the Sprüngli family confectionery shop in Zurich that added a solid-chocolate factory the same year the process for making solid chocolate was developed and later bought Lindt's factory. Besides Nestlé, several chocolate companies had their start in the late 19th and early 20th centuries. Cadbury was manufacturing boxed chocolates in England by 1868.[2] In 1893, Milton S. Hershey purchased chocolate processing equipment at the World's Columbian Exposition in Chicago and soon began the career of Hershey's chocolates with chocolate-coated caramels.
Modern usage[edit]
Main article: Cocoa production in Côte d'Ivoire
Roughly two-thirds of the world's cocoa is produced in Western Africa, with Côte d'Ivoire being the largest source, producing a total crop of 1,448,992 tonnes[23]. Ghana, Nigeria, and Cameroon are other West African countries among the top 5 cocoa producing countries in the world. Like many food industry producers, individual cocoa farmers are at the mercy of volatile world markets. The price can vary from between £500 ($945) and £3,000 ($5,672) per ton in the space of just a few years.[citation needed] While investors trading in cocoa can dump shares at will, individual cocoa farmers can not ramp up production and abandon trees at anywhere near that pace.
Only three to four percent of "cocoa futures" contracts traded in the cocoa markets ever end up in the physical delivery of cocoa. Every year seven to nine times more cocoa is bought and sold on the exchange than exists.
It has been alleged that an estimated 90% of cocoa farms in Côte d'Ivoire have used some form of slave labor in order to remain viable.[24][unreliable source?] When cocoa prices drop, farmers in West Africa sometimes cut costs by resorting to slave labor.[dubious – discuss][25]
See also[edit]
Food portal
History portal
Alonso de Molina's dictionary of 1571 and of 1555
Food history
History of yerba mate
List of English words of Nahuatl origin
References[edit]
^ Jump up to: a b c Watson, Traci (22 January 2013). "Earliest Evidence of Chocolate in North America". Science. Retrieved 3 March 2014.
^ Jump up to: a b c d e f g h i j k Kerr, Justin (2007). "History of Chocolate". Field Museum. Retrieved 2014-03-03.
Jump up ^ "The American Heritage Dictionary". Archived from the original on October 11, 2008. Retrieved 2009-05-09.
Jump up ^ Kiple, Kenneth F.; Kriemhild Coneè Ornelas (2000). The Cambridge world history of food. Cambridge University Press. pp. 635–638. ISBN 978-0-521-40214-9.
^ Jump up to: a b c d Bensen, Amanda (March 1, 2008). "A Brief History of Chocolate". Smithsonian Magazine. Retrieved 3 March 2014.
^ Jump up to: a b Terry G. Powis; W. Jeffrey Hurst; María del Carmen Rodríguez; Ponciano Ortíz C.; Michael Blake; David Cheetham; Michael D. Coe; John G. Hodgson (December 2007). "Oldest chocolate in the New World". Antiquity. 81 (314). ISSN 0003-598X. Retrieved 2011-02-15.
Jump up ^ Coe, Sophie Dobzhansky; Coe, Michael D. (2007). The True History of Chocolate. Thames and Hudson. ISBN 978-0-500-28696-8.
Jump up ^ Thompson, J. Eric S. (1956). "Notes on the use of cacao in Middle America". Middle American Archaeology. Cambridge Mass. 128: 95–116.
Jump up ^ Keoke, Emory Dean; Porterfield, Kay Marie (1 January 2009). Encyclopedia of American Indian Contributions to the World: 15,000 Years of Inventions and Innovations. Infobase Publishing. p. 43. ISBN 978-1-4381-0990-9.
Jump up ^ Szogyi, Alex (1 January 1997). Chocolate: Food of the Gods. Greenwood Publishing Group. pp. 149–151. ISBN 978-0-313-30506-1.
^ Jump up to: a b c d e Spadaccini, Jim. "The Sweet Lure of Chocolate". Exploratorium. Retrieved 2014-03-03.
Jump up ^ Burleigh, Robert (2002). Chocolate: Riches from the Rainforest. Harry N. Abrams, Ins., Publishers. ISBN 0-8109-5734-5.
Jump up ^ The Bernal Diaz Chronicles, translated and edited by Albert Idell, published by Doubleday Dolphin, 1956, p.160
Jump up ^ Norton, Marcy (April 2004). "Conquests of Chocolate". OAH Magazine of History. 18 (3): 16. Retrieved 5 December 2017.
Jump up ^ "Diccionario de la lengua española, Real Academia Española". rae.es.
Jump up ^ Campbell, Lyle. Quichean Linguistic Prehistory; University of California Publications in Linguistics No. 81. Berkeley, California: University of California Press. p. 104.
Jump up ^ Santamaria, Francisco. Diccionario de Mejicanismos. Mexico: Editorial Porrúa S. A. pp. 412–413.
Jump up ^ Dakin, Karen; Wichmann, Soren (2000). "Cacao and Chocolate A Uto-Aztecan perspective". Ancient Mesoamerica. Cambridge: Cambridge University Press. 11 (1): 55–75. doi:10.1017/S0956536100111058.
^ Jump up to: a b c Molina, Fray Alonso de (1977). Vocabulario en Lengua Castellana y Mexicana y Mexicana y Castellana. Edicion Facsimile. Mexico: Editorial Porrua, S.A. p. 10.
Jump up ^ Wilson & Hurst, "Chocolate and Health: Chemistry, Nutrition and Therapy", p. 219, Royal Society of Chemistry, 2015
Jump up ^ Clarence-Smith, William Gervase (2003-09-02), Cocoa and Chocolate, 1765-1914, Routledge, p. 48, ISBN 978-1-134-60778-5, retrieved 2017-09-12
Jump up ^ Klein, Christopher (February 14, 2014). "The Sweet History of Chocolate". History. Retrieved 2014-03-03.
Jump up ^ "Top 10 Cocoa Producing Countries". WorldAtlas. Retrieved 2017-10-09.
Jump up ^ "Truevision TV Slavery - a global investigation". Archived from the original on April 22, 2006. Retrieved 2006-06-27.
Jump up ^ "Bittersweet Chocolate". Archived from the original on 2007-02-10. Retrieved 2006-06-27.
External links[edit]
Gutenberg’s “Chocolate: or, An Indian Drinke”
LibriVox’s Audio Book “Chocolate: or, An Indian Drinke”
The Chocolate and Ancient Maya
A Brief History of Chocolate. Smithsonian.com
Chocolate: Food of the Gods. Cornell University, Mann Library
"Chocolate. From Mesoamerica To Modern Master Chocolatiers", ICEX
[hide]
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Chocolate
Overview
Outline
History (in Spain)
Theobroma
Theobroma
Theobroma cacao
Theobroma grandiflorum
Theobroma bicolor
Components
Cocoa bean
Cocoa butter
Cocoa solids
Chocolate liquor
Drugs
Anandamide
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