Correlation (Geology)

The nature of sedimentary strata

Physical correlation

Interpreting Earth history within a stratum

Fossil correlation

Absolute vs. relative ages of strata

In geology, the term correlation refers to the methods by which the age relationship between various strata of Earth’s crust is established. Such relationships can be established, in general, in one of two ways: by comparing the physical characteristics of strata with each other (physical correlation); and by comparing the type of fossils found in various strata (fossil correlation).

Correlation is an important geological technique because it provides information with regard to changes that have taken place at various times in Earth history. It also provides information about the times at which such changes have occurred. One result of correlation studies has been the development of a geologic time scale that separates Earth history into a number of discrete time blocks known as eras, periods, and epochs.

The nature of sedimentary strata

Sedimentary rocks provide information about Earth history that is generally not available from igneous or metamorphic rocks. To understand why this is so, imagine a region in which sediments have been deposited for millions of years. For example, suppose that for many millions of years a river has emptied into an ocean, laying down, or depositing, sediments eroded from the land. During that period of time, layers of sediments would have collected one on top of the other at the mouth of the river.

These layers of sediments are likely to be very different from each other, depending on a number of factors, such as the course followed by the river, the climate of the area, the rock types exposed along the river course, and many other geological factors in the region. One of the most obvious differences in layers is thickness. Layers of sedimentary rock may range in thickness from less than an inch to many feet.

Sedimentary layers that are identifiably different from each other are called beds or strata. In many places on Earth, many of strata are stacked one on top of each other and commonly separated from each other by relatively well-defined surfaces known as bedding planes.

In 1669, the Danish physician and theologian Nicolaus Steno made a seemingly obvious assertion about the nature of sedimentary strata. Steno stated that in any sequence of sedimentary rocks, any one layer (stratum) is older than the layer below it and younger than the layer above it. Steno’s discovery is now known as the Law of Superposition.

The Law of Superposition applies only to sedimentary rocks that have not been overturned by geologic forces, for example during episodes of mountain building. Igneous rocks, by comparison, may form in any horizontal sequence whatsoever. A flow of magma may force itself, for example, underneath, in the middle or, on top of an existing rock stratum. It is difficult to look back millions of years and determine the age of the igneous rock compared to rock layers around it.

Physical correlation

Using sedimentary rock strata it is possible, at least in theory, to write the geological history of the continents for the last billion or so years. Some important practical problems, however, prevent the full realization of this goal. For example, in many areas, erosion has removed much or most of the sedimentary rock that once existed there. In other places, strata are not clearly exposed to view but, instead, are buried hundreds or thousands of feet beneath the thin layer of soil that covers most of Earth’s surface.

A few exceptions exist. A familiar example is the Grand Canyon, where the Colorado River has cut through dozens of strata, exposing them to view and making them available for study by geologists. Within the Grand Canyon, a geologist can follow a particular stratum for many miles, noting changes within the stratum and changes between that stratum and its neighbors above and below.

One of the characteristics observable in such a case is that a stratum often changes in thickness from one edge to another. At the edge where the thickness approaches zero, the stratum may merge into another stratum. The principle of lateral continuity states that strata are three-dimensional features that extend outward in all directions and merge with adjacent deposits at their edges.

Human activity also exposes strata to view. When a highway is constructed through a mountainous area, for example, parts of a mountainside may be excavated, revealing sedimentary rock strata. These strata can then be studied to discover the correlation among them and with strata in other areas.

Another problem is that strata are sometimes disrupted by earth movements. For example, an earthquake may lift one block of Earth’s crust over an adjacent block or may shift it horizontally in comparison to the second block. The correlation between adjacent strata may then be difficult to determine.

Physical correlation is accomplished by using a number of criteria. For example, the color, texture, and type of minerals contained within a stratum make it possible for geologists to classify a particular stratum quite specifically. This allows them to match up portions of that stratum in regions that are physically separated from each other. In the American West, for example, some strata have been found to cover large parts of two or more states although they are physically exposed in only a few specific regions.

Interpreting Earth history within a stratum

Rocks with a particular set of characteristics are called facies. Facies changes, which are changes in the characteristics of a stratum or series of strata, are important clues to Earth history. Suppose that a geologist finds that the facies in a particular stratum change from a limestone to a shale to a sandstone over a distance of a few miles. The geologist knows that limestone is laid down on a sea bottom, shale is formed from compacted mud, and sandstone is formed when sand is compressed. The limestone to shale to sandstone facies pattern may allow an astute geologist to reconstruct what Earth’s surface looked like when this particular stratum was formed. For example, knowing these rocks were laid down in adjacent environments, the geologist might consider that the limestone was deposited on a coral reef, the shale in a quiet lagoon or coastal swamp, and the sandstone in a nearby beach. So facies changes indicate differences in the environments in which adjacent facies were deposited.

Fossil correlation

One of the most important discoveries in the science of correlation was made by the English engineer William Smith in the 1810s. One of Smith’s jobs involved the excavation of land for canals being constructed outside of London. As sedimentary rocks were exposed during this work, Smith found that any given stratum always contained the same set of fossils. Even if the stratum were physically separated by a relatively great distance, the same fossils could always be found in all parts of the stratum.

In 1815, Smith published a map of England and Wales showing the geologic history of the region based on his discovery. The map was based on what Smith called his law of faunal succession. That law says simply that it is possible to identify the sequence in which strata are laid down by examining the fossils they contain. The simplest fossils are the oldest and, therefore, strata that contain simple fossils are older than strata that contain more complex fossils.

KEY TERMS

Bedding plane— The top of a layer of rock.

Deposition— The accumulation of sediments after transport by wind, water, ice, or gravity.

Facies— A body of rock with distinctive characteristics.

Fossil correlation— The matching of sedimentary strata based on fossils present in the strata.

Lateral continuity— The principle that sedimentary strata are three-dimensional features that extend horizontally in all directions and that eventually terminate against the margin of other strata.

Physical correlation— The matching of sedimentary strata based on the physical characteristics of rocks that make up the strata.

Radiometric dating— A process by which the age of a rock can be determined by studying the relative concentrations of a radioactive isotope and the products formed by its decay.

Superposition— The principle that a layer of rocks is older than any other layer that lies above it and younger than any other layer that lies below it.

The remarkable feature of Smith’s discovery is that it appears to be valid over very great distances. That is, suppose that a geologist discovers a stratum of rock in southwestern California that contains fossils A, B, and C. If another stratum of rock in eastern Texas is also discovered that contains the same fossils, the geologist can conclude that it is probably the same stratum—or at least of the same age—as the southwestern California stratum.

Absolute vs. relative ages of strata

The correlation studies described so far allow scientists to estimate the relative ages of strata. If stratum B lies above stratum A, B is the younger of the two. However determining the actual, or absolute, age of strata (for example, 3.5 million years old) is often difficult since the age of a fossil cannot be determined directly. The most useful tool in dating strata is radio-metric dating of materials. A radioactive isotope such as uranium-238 decays at a very regular and well-known rate. That rate is known as its half-life, the time it takes for one-half of a sample of the isotope to decay. The half-life of uranium-238, for example, is 4.5 billion years. By measuring the concentration of uranium-238 in comparison with the products of its decay (especially lead-206), a scientist can estimate the age of the rock in which the uranium was found. This kind of radioactive dating has made it possible to place specific dates on the ages of strata that have been studied and correlated by other means.

See also Dating techniques; Deposit; Fossil and fossilization; Sediment and sedimentation.

David E. Newton

Correlation (geology)

In geology , the term correlation refers to the methods by which the age relationship between various strata of Earth's crust is established. Such relationships can be established, in general, in one of two ways: by comparing the physical characteristics of strata with each other (physical correlation); and by comparing the type of fossils found in various strata (fossil correlation).

Correlation is an important geological technique because it provides information with regard to changes that have taken place at various times in Earth history. It also provides clues as to the times at which such changes have occurred. One result of correlational studies has been the development of a geologic time scale that separates Earth history into a number of discrete time blocks known as eras, periods, and epochs.

The nature of sedimentary strata

Sedimentary rocks provide information about Earth history that is generally not available from igneous or metamorphic rocks. To understand why this is so, imagine a region in which sediments have been laid down for millions of years. For example, suppose that for many millions of years a river has emptied into an ocean , laying down, or depositing, sediments eroded from the land. During that period of time, layers of sediments would have collected one on top of the other at the mouth of the river.

These layers of sediments are likely to be very different from each other, depending on a number of factors, such as the course followed by the river, the climate of the area, the rock types exposed along the river course, and many other geological factors in the region. One of the most obvious differences in layers is thickness. Layers of sedimentary rock may range in thickness from less than an inch to many feet.

Sedimentary layers that are identifiably different from each other are called beds or strata. In many places on Earth's surface, dozens of strata are stacked one on top of each other. Strata are often separated from each other by relatively well-defined surfaces known as bedding planes.

In 1669, the Danish physician and theologian Nicolaus Steno made a seemingly obvious assertion about the nature of sedimentary strata. Steno stated that in any sequence of sedimentary rocks, any one layer (stratum) is older than the layer below it and younger than the layer above it. Steno's discovery is now known as the law of superposition.

The law of superposition applies only to sedimentary rocks that have not been overturned by geologic forces. Igneous rocks , by comparison, may form in any horizontal sequence whatsoever. A flow of magma may force itself, for example, underneath, in the middle or, or on top of an existing rock stratum. It is very difficult to look back millions of years later, then, and determine the age of the igneous rock compared to rock layers around it.

Physical correlation

Using sedimentary rock strata it should be possible, at least in theory, to write the geological history of the continents for the last billion or so years. Some important practical problems, however, prevent the full realization of this goal. For example, in many areas, erosion has removed much or most of the sedimentary rock that once existed there. In other places, strata are not clearly exposed to view but, instead, are buried hundreds or thousands of feet beneath the thin layer of soil that covers most of Earth's surface.

A few remarkable exceptions exist. A familiar example is the Grand Canyon, where the Colorado River has cut through dozens of strata, exposing them to view and making them available for study by geologists. Within the Grand Canyon, a geologist can follow a particular stratum for many miles, noting changes within the stratum and changes between that stratum and its neighbors above and below.

One of the characteristics observable in such a case is that a stratum often changes in thickness from one edge to another. At the edge where the thickness approaches zero , the stratum may merge into another stratum. This phenomenon is understandable when one considers the way the sediment in the rocks was laid down. At the mouth of a river, for example, the accumulation of sediments is likely to be greatest at the mouth itself, with decreasing thickness at greater distances into the lake or ocean. The principle of lateral continuity describes this phenomenon, namely that strata are three-dimensional features that extend outward in all directions, merging with adjacent deposits at their edges.

Human activity also exposes strata to view. When a highway is constructed through a mountainous (or hilly) area, for example, parts of a mountainside may be excavated, revealing various sedimentary rock strata. These strata can then be studied to discover the correlation among them and with strata in other areas.

Another problem is that strata are sometimes disrupted by earth movements. For example, an earthquake may lift one block of Earth's crust over an adjacent block or may shift it horizontally in comparison to the second block. The correlation between adjacent strata may then be difficult to determine.

Physical correlation is accomplished by using a number of criteria. For example, the color , grain size, and type of minerals contained within a stratum make it possible for geologists to classify a particular stratum quite specifically. This allows them to match up portions of that stratum in regions that are physically separated from each other. In the American West, for example, some strata have been found to cover large parts of two or more states although they are physically exposed in only a few specific regions.

Interpreting Earth history within a stratum

Imagine that geologists a million years from now began studying Earth's surface within a 3 mi (5 kilometer) radius of your home. What would they find? They would probably discover considerable variation in the sediment deposits that are accumulating in your region today. They might find the remains of a river bed, a swamp, a lake, and other features. Geologists living today who study strata laid down millions of years ago make similar discoveries. As they follow an individual stratum for many kilometers, they find that its characteristics change. The stratum tends to have one set of characteristics in one region, which gradually changes into another set of characteristics farther along in the stratum. Those characteristics also change, at some distance farther along, into yet another set of characteristics.

Rocks with a particular set of characteristics are called a facies. Facies changes, changes in the characteristics of a stratum or series of strata, are important clues to Earth history. Suppose that a geologist finds that the facies in a particular stratum change from a limestone to a shale to a sandstone over a distance of a few miles. The geologist knows that limestone is laid down on a sea bottom, shale is formed from compacted mud, and sandstone is formed when sand is compressed. The limestone to shale to sandstone facies pattern may allow an astute geologist to reconstruct what Earth's surface looked like when this particular stratum was formed. For example, knowing these rocks were laid down in adjacent environments, the geologist might consider that the limestone was deposited on a coral reef, the shale in a quiet lagoon or coastal swamp, and the sandstone in a nearby beach. So facies changes indicate differences in the environments in which adjacent facies were deposited.

Fossil correlation

One of the most important discoveries in the science of correlation was made by the English surveyor William Smith in the 1810s. One of Smith's jobs involved the excavation of land for canals being constructed outside of London. As sedimentary rocks were exposed during this work, Smith found that any given stratum always contained the same set of fossils. Even if the stratum were physically separated by a relatively great distance, the same fossils could always be found in all parts of the stratum.

In 1815, Smith published a map of England and Wales showing the geologic history of the region based on his discovery. The map was based on what Smith called his law of faunal succession . That law says simply that it is possible to identify the sequence in which strata are laid down by examining the fossils they contain. The simplest fossils are the oldest and, therefore, strata that contain simple fossils are older than strata that contain more complex fossils.

The remarkable feature of Smith's discovery is that it appears to be valid over very great distances. That is, suppose that a geologist discovers a stratum of rock in southwestern California that contains fossils A, B, and C. If another stratum of rock in eastern Texas is also discovered that contains the same fossils, the geologist can conclude that it is probably the same stratum—or at least of the same age—as the southwestern California stratum.

Absolute vs. relative ages of strata

The correlational studies described so far allow scientists to estimate the relative ages of strata. If stratum B lies above stratum A, B is the younger of the two. However determining the actual, or absolute, age of strata (for example, 3.5 million years old) is often difficult since the age of a fossil cannot be determined directly. The most useful tool in dating strata is radiometric dating of materials. A radioactive isotope such as uranium-238 decays at a very regular and well-known rate . That rate is known as its half-life , the time it takes for one-half of a sample of the isotope to decay. The half-life of uranium-238, for example, is 4.5 billion years. By measuring the concentration of uranium-238 in comparison with the products of its decay (especially lead-206), a scientist can estimate the age of the rock in which the uranium was found. This kind of radioactive dating has made it possible to place specific dates on the ages of strata that have been studied and correlated by other means.

See also Dating techniques; Deposit; Fossil and fossilization; Sediment and sedimentation.

David E. Newton

KEY TERMS

Bedding plane

—The top of a layer of rock.

Deposition

—The accumulation of sediments after transport by wind, water, ice, or gravity.

Facies

—A body of sedimentary rock with distinctive characteristics.

Fossil correlation

—The matching of sedimentary strata based on fossils present in the strata.

Lateral continuity

—The principle that sedimentary strata are three-dimensional features that extend horizontally in all directions and that eventually terminate against the margin of other strata.

Physical correlation

—The matching of sedimentary strata based on the physical characteristics of rocks that make up the strata.

Radiometric dating

—A process by which the age of a rock can be determined by studying the relative concentrations of a radioactive isotope and the products formed by its decay.

Superposition

—The principle that a layer of rocks is older than any other layer that lies above it and younger than any other layer that lies below it.

Correlation (geology)

In geology , the term correlation refers to the methods by which the age relationship between various strata of Earth's crust is established. Such relationships can be established, in general, in one of two ways: by comparing the physical characteristics of strata with each other (physical correlation); and by comparing the type of fossils found in various strata (fossil correlation).

Correlation is an important geological technique because it provides information with regard to changes that have taken place at various times in Earth history. It also provides clues as to the times at which such changes have occurred. One result of correlational studies has been the development of a geologic time scale that separates Earth history into a number of discrete time blocks known as eras, periods, and epochs.

Sedimentary rocks provide information about Earth history that is generally not available from igneous or metamorphic rocks. For example, suppose that for many millions of years a river has emptied into an ocean, laying down, or depositing, sediments eroded from the land. During that period of time, layers of sediments would have collected one on top of the other at the mouth of the river. These layers of sediments are likely to be very different from each other, depending on a number of factors, such as the course followed by the river, the climate of the area , the rock types exposed along the river course, and many other geological factors in the region. One of the most obvious differences in layers is thickness. Layers of sedimentary rock may range in thickness from less than an inch to many feet.

Sedimentary layers that are identifiably different from each other are called beds or strata. In many places on Earth's surface, dozens of strata are stacked one on top of each other. Strata are often separated from each other by relatively well-defined surfaces known as bedding planes.

In 1669, the Danish physician and theologian Nicolaus Steno (1638–1686) made a seemingly obvious assertion about the nature of sedimentary strata. Steno stated that in any sequence of sedimentary rocks, any one layer (stratum) is younger than the layer below it and older than the layer above it. Steno's discovery is now known as the law of superposition .

The law of superposition applies only to sedimentary rocks that have not been overturned by geologic forces. Igneous rocks , by comparison, may form in any horizontal sequence whatsoever. A flow of magma may force itself, for example, underneath, in the middle or, or on top of an existing rock stratum. It is very difficult to look back millions of years later, then, and determine the age of the igneous rock compared to rock layers around it.

Using sedimentary rock strata it should be possible, at least in theory, to write the geological history of the continents for the last billion or so years. Some important practical problems, however, prevent the full realization of this goal. For example, in many areas, erosion has removed much or most of the sedimentary rock that once existed there. In other places, strata are not clearly exposed to view but, instead, are buried hundreds or thousands of feet beneath the thin layer of soil that covers most of Earth's surface.

A few remarkable exceptions exist. A familiar example is the Grand Canyon , where the Colorado River has cut through dozens of strata, exposing them to view and making them available for study by geologists. Within the Grand Canyon, a geologist can follow a particular stratum for many miles, noting changes within the stratum and changes between that stratum and its neighbors above and below. One of the characteristics observable in such a case is that a stratum often changes in thickness from one edge to another. At the edge where the thickness approaches zero, the stratum may merge into another stratum. This phenomenon is understandable when one considers the way the sediment in the rocks was laid down. At the mouth of a river, for example, the accumulation of sediments is likely to be greatest at the mouth itself, with decreasing thickness at greater distances into the lake or ocean. The principle of lateral continuity describes this phenomenon, namely that strata are three-dimensional features that extend outward in all directions, merging with adjacent deposits at their edges.

Human activity also exposes strata to view. When a highway is constructed through a mountainous (or hilly) area, for example, parts of a mountainside may be excavated, revealing various sedimentary rock strata. These strata can then be studied to discover the correlation among them and with strata in other areas.

Another problem is that strata are sometimes disrupted by earth movements. For example, an earthquake may lift one block of Earth's crust over an adjacent block or may shift it horizontally in comparison to the second block. The correlation between adjacent strata may then be difficult to determine.

Physical correlation is accomplished by using a number of criteria. For example, the color, grain size, and type of minerals contained within a stratum make it possible for geologists to classify a particular stratum quite specifically. This allows them to match up portions of that stratum in regions that are physically separated from each other. In the American West, for example, some strata have been found to cover large parts of two or more states although they are physically exposed in only a few specific regions.

The stratum tends to have one set of characteristics in one region, which gradually changes into another set of characteristics farther along in the stratum. Those characteristics also change, at some distance farther along, into yet another set of characteristics. Rocks with a particular set of characteristics are called a facies. Facies changes, changes in the characteristics of a stratum or series of strata, are important clues to Earth history. If, for example, a geologist finds that the facies in a particular stratum change from a limestone to a shale to a sandstone over a distance of a few miles, the geologist knows that limestone is laid down on a sea bottom, shale is formed from compacted mud, and sandstone is formed when sand is compressed. The limestone to shale to sandstone facies pattern may allow an astute geologist to reconstruct what Earth's surface looked like when this particular stratum was formed. For example, knowing these rocks were laid down in adjacent environments, the geologist might consider that the limestone was deposited on a coral reef, the shale in a quiet lagoon or coastal swamp, and the sandstone in a nearby beach. So facies changes indicate differences in the environments in which adjacent facies were deposited.

One of the most important discoveries in the science of correlation was made by the English surveyor William Smith (1769–1839) in the 1810s. One of Smith's jobs involved the excavation of land for canals being constructed outside of London. As sedimentary rocks were exposed during this work, Smith found that any given stratum always contained the same set of fossils. Even if the stratum were physically separated by a relatively great distance, the same fossils could always be found in all parts of the stratum.

In 1815, Smith published a map of England and Wales showing the geologic history of the region based on his discovery. The map was based on what Smith called his law of faunal succession. That law says simply that it is possible to identify the sequence in which strata are laid down by examining the fossils they contain. The simplest fossils are the oldest and, therefore, strata that contain simple fossils are older than strata that contain more complex fossils.

The remarkable feature of Smith's discovery is that it appears to be valid over very great distances. That is, suppose that a geologist discovers a stratum of rock in southwestern California that contains fossils A, B, and C. If another stratum of rock in eastern Texas is also discovered that contains the same fossils, the geologist can conclude that it is probably the same stratum—or at least of the same age—as the southwestern California stratum.

The correlational studies described so far allow scientists to estimate the relative ages of strata. If stratum B lies above stratum A, B is the younger of the two. However determining the actual, or absolute, age of strata (for example, 3.5 million years old) is often difficult because the age of a fossil cannot be determined directly. The most useful tool in dating strata is radiometric dating of materials. A radioactive isotope such as uranium-238 decays at a very regular and well-known rate. That rate is known as its half-life , the time it takes for one-half of a sample of the isotope to decay. The half-life of uranium-238, for example, is 4.5 billion years. By measuring the concentration of uranium-238 in comparison with the products of its decay (especially lead-206), a scientist can estimate the age of the rock in which the uranium was found. This kind of radioactive dating has made it possible to place specific dates on the ages of strata that have been studied and correlated by other means.

See also Cross cutting; Dating methods; Field methods in geology; Landscape evolution; Strike and dip

Correlation

As used in mathematics, correlation is a measure of how closely two variables change in relationship to each other. For example, consider the variables height and age for boys and girls. In general, one could predict that the older a child is, the taller he or she will be. A baby might be 12 inches long; an 8-year-old, 36 inches; and a 15-year old, 60 inches. This relationship is called a positive correlation because both variables change in the same direction: as age increases, so does height.

A negative correlation is one in which variables change in the opposite direction. An example of a negative correlation might be grades in school and absence from class. The more often a person is absent from class, the poorer his or her grades are likely to be.

The two variables compared to each other in a correlation are called the independent variable and the dependent variable. As the names suggest, an independent variable is one whose change tends to be beyond human control. Time is often used as an independent variable because it goes on whether we like it or not. In the simplest sense, time always increases, it never decreases.

A dependent variable is one that changes as the result of changes in the independent variable. In a study of plant growth, plant height might be a dependent variable. The amount by which a plant grows depends on the amount of time that has passed.

Correlation coefficient

Statisticians have invented mathematical devices for measuring the amount by which two variables are correlated with each other. The correlation coefficient, for example, ranges in value from −1 to +1. A correlation coefficient of +1 means that two variables are perfectly correlated with each other. Each distinct increase or decrease in the independent variable is accompanied by an exactly similar increase or decrease in the dependent variable. A correlation coefficient of +0.75 means that a change in the independent variable will be accompanied by a comparable increase in the dependent variable a majority of the time. A correlation coefficient of 0 means that changes in the independent and dependent variable appear to be random and completely unrelated to each other. And a negative correlation coefficient (such as −0.69) means that two variables respond in opposite directions. When one increases, the other decreases, and vice versa.

Understanding the meaning of correlation

It is easy to misinterpret correlational measures. They tell us nothing at all about cause and effect. For example, suppose that you measured the annual income of people from age 5 to age 25. You would probably find the two variables—income and age—to be positively correlated. The older people become, the more money they are likely to earn.

Words to Know

Correlation coefficient: A numerical index of a relationship between two variables.

Negative correlation: Changes in one variable are reflected by changes in the second variable in the opposite direction.

Positive correlation: Changes in one variable are reflected by similar changes in the second variable.

The wrong way to interpret that correlation is to say that growing older causes people to earn more money. Of course, that isn't true. The correlation can be explained in other ways. Obviously, a 5-year-old child can't earn money the way an 18-year-old or a 25-year-old can. Measures of correlation, such as the correlation coefficient, simply tell whether two variables change in the same way or not without providing any information as to the reason for that relationship.

Of course, scientists often design an experiment so that a measure of correlation will have some meaning. A nutrition experiment might be designed to test the effect of feeding rats a certain kind of food. The experimenter may arrange conditions so that only one factor—the amount of that kind of food—changes in the experiment. Every other condition is left the same throughout the experiment. In such a case, the amount of food is the independent variable and changes in the rat (such as weight changes) are considered the dependent variable. Any correlation between these two variables might then suggest (but would not prove) that the food being tested caused weight changes in the rat.

correlation If a change in the amount of one variable is accompanied by a comparable change in the amount of another variable, and the latter change does not occur in the absence of the former change, then the variables are said to be correlated. This is sometimes called the method of concomitant variation, after the terminology devised by John Stuart Mill, who spelled out many of the basic designs of logical proof in the nineteenth century (see A System of Logic, Ratiocinative and Deductive, 1843
). Correlations may be linear (where there is a constant ratio between the rates of change in each of the variables) or curvilinear (where the rate of change of one variable is at an increasing or decreasing ratio to the rate of change in the other variable). They may be positive (increase in one variable is associated with increase in the other) or negative (increase in one variable is associated with decrease in the other). Negative correlations are sometimes termed inverse correlations; positive correlations are occasionally referred to as direct correlations. When two (or more) variables are correlated, but there is no causal link between them, then the correlation is said to be spurious: both may be affected by a third (antecedent) variable. See also ASSOCIATION COEFFICIENTS; CAUSAL MODELLING; CURVILINEAR RELATIONSHIP; MULTIVARIATE ANALYSIS.