Stereology
Stereology is the science of estimating or measuring geometric quantities. A geometric quantity is something like length or surface area. Other common geometric quantities are volume and the number of objects. Estimation is a way to get an idea of how much there is without actually having to measure the value.
A few examples should make this easier to understand. Suppose that the question is, "How many trees are in a forest?" There might very well be millions of trees in any given forest. It does not make sense to count every tree. What does it matter if the answer is 23 million trees or 23 million and 5 trees? Besides, who is going to be able to count every single tree. It is too much work. The solution is estimate the number of trees and get a good idea of how many trees there are.
An important question might be, "How much copper can be retrieved by mining a given deposit?" Another important question might be, "If a drug is given to a patient, do any cells die?" Another interesting question to answer might be, "Even though these two ancient pots look alike, were they made from the same raw materials?"
Each of these questions is fairly difficult to directly measure. Can the entire deposit be evaluated without mining it in the first place? Is it possible to count the millions or billions of cells found in many tissues in an organism? Is it possible to determine the materials that make up a pot without destroying it?
The work to complete tasks may be too arduous, too dangerous, too expensive, or destructive of the objects being studied. For that reason sampling is performed. A sample is a piece taken from the original object or group of objects and used to represent the bigger group. For example, one or more rocks may be chosen as sampled of the rocks found in an ore deposit. A piece of tissue may be chosen or removed from a large organ to determine what is inside of the organ. A small piece of a pot may be removed and used to study the pot.
As you might expect the manner in which the sample is chosen is important. Getting the sampling correct is the second big step in this process. The first step was deciding what is to be studied. The most common approach in stereological studies is the systematic sampling approach. This is where the first sample is chosen at random and the rest of the samples are chosen systematically. An example should make this clear.
Suppose a class of students is lined up. The teacher flips a coin. If it is heads then the first student is chosen. If tails the second student is chosen. The teacher begins with the first chosen student and then walks down the line of students touching every other students' head. This picks half the class. No one student can predict if they will be picked or not although students can line up knowing that if they are picked, then their friends are also picked.
Clearly, using systematic sampling is not as random as independent random sampling. The importance of systematic sampling is not in a situation where the objects can be rearranged such as a group of students. It is more useful when the objects are fixed in position such as grains of temper in a ceramic, trees in a forest, cells in an organ, or metals in an alloy.
One of the more difficult microscopic questions is the number of particles in a solid. The number of grains of a mineral or the number of cells in an organ are typical questions to answer. The first unbiased counting method was developed in 1984. This method employed 2 concepts: a method of counting objects of varying size, shape, orientation, and distribution seen on a surface along with a method that allowed counting in 3-dimensions. The method was improved over the years and has recently seen a jump in efficiency. The new method is known as the proportionator. The proportionator improves counting by directly addressing the issue of variance. This is the difference seen between samples. The proportionator is able to significantly reduce the work involved in situations where the variance is high. The greater the differences in samples the better the proportionator works. This is one of those counter intuitive situations in which the method "thrives when the situation deteriorates." The proportionator is a must for any research having difficulties managing the variance, and any group that has to deal with a large amount of sampling, i.e. hundreds or thousands of research animals.
A common definition given for stereology is that it infers 3-dimensional information from 2-dimensional images. This is an outdated definition that frankly covers little of classical stereology or modern research. Consider point counting which is so often mistakenly claimed as a method developed by geologists. This method was developed for land management purposes. It was applied to the fields of forestry and ecology well before its use in geology. These 3 fields do not infer 3-dimensional information. The application was 2-dimensional information from 2-dimensional sampling. The same is true of line probes. These probes were originally intended to determine 3-dimensional information, but quickly found use in studies in geography, land management, forestry, and ecology.
Stereology is used in many diverse fields including paleontology, forest science, medicine, pathology , archaeology, petrology, dentistry, anatomy, aquaculture, etc.