Archive for the ‘Observational bias’ Category

Shand Recording Micrometer

April 10, 2012

I’ll have to check and see if that is the correct name for the device.

The Shand device was an important invention. For the first time it was possible to perform stereological procedures in an efficient manner. It transformed geology from a descriptive science into a quantitative science.

What was fascinating about the device was the difficulty in finding a drawing of it. Numerous references to the device did not lead to a drawing or photograph or a detailed description of how it worked. The original device was built to assist in the modal analysis of rocks. Once reported the device was copied and improved on by many others.

The device was an implementation of the Rosiwal lineal analysis. It allowed a number of different rock minerals to be analyzed at the same time.

One of the interesting issues that came out of the device was an interest in the conditions that allowed the work to be unbiased. There was quite a bit of dispute over the necessary conditions for an unbiased result with many people ascribing to the original conditions set out by Rosiwal. There were also people that thought, and correctly, that the conditions proposed by Rosiwal were too restrictive and that relaxing the sampling conditions did not introduce bias.

Now that data was being collected the next important step in sampling was addressed. How much sampling was needed to get a “good” result. Much of the analysis of the Rosiwal method was performed using desktop simulations in which known paper samples were analyzed. This work continued well into the 1930s in the US by Proudfoot. The recommendations for sampling were soon to be eclipsed by the invention of Glagolev device.

The need to understand bias issues and the variance of the estimator did not exist until data was generated. The Shand and other devices quickly drove the need to understand these issues and as history showed, the understandings were not easy to develop.


Cavalieri is attached to point counting due to a 100 year old mistake

April 10, 2012

Your posts are ridiculous and simply add unnecessary confusion to the field. “Rosival” vs “Rosiwal” is a joke since languages without “w” use a “v” so the name appears both ways. No one but you claims Cavalieri did stereology, the term was not even invented until 1962, centuries after he died. The work he did forms the theoretical basis for the method used today, in combination with point counting, to estimate total volume of 3-D objects. If you want to be taken seriously, you need to tone down the vitriolic rhetoric, which is out of place for scholarly scientific exchanges.

You have called me a creep multiple times. That is vitriolic.

Rosiwal was Austrian.  The German language has a ‘w’. Not sure what language you are talking about.

I have never stated that Cavalieri did stereology. That is a straw man argument.

Regardless of when the term stereology was coined, stereology was done long before that time. Rosiwal traverses, quadrats, bayonet probes, Shand micrometer, Ford’s device, Glagolev’s device, Steinhaus’s work, and many more methods and devices were in use before the coining of stereology. The term was coined to provide a description of the methods long in use by many disciples.

Cavalieri’s work does not form the theoretical basis for stereology. It has nothing whatsoever to do with point counting. It involves the comparison of objects of equal volume or area. You might want to check with a mathematician to learn why Cavalieri’s theorem is not related to point counting.

Point counting was not developed from Cavalieri’s theorem. It was invented at least 2 independent times, neither of which deal with anything remotely involving Cavalieri. The reason that the name Cavalieri appears in the literature is a mistake in 1902 in which a geological paper improperly applied the Cavalieri theorem in a model based analysis of Manhattan rocks. The name stuck even though it is a misnomer. Chayes explains the mistake quite well. One of the inventions of point counting, the second invention time I am aware of, took place at the NIH. The first invention took place years before Glagolev published his implementation. The first invention was not proved although the mathematician involved with the group had pledged to provide a proof. The second invention has a rather shaky proof. A good example of a proof showing that point counting works is in DeHoff’s book. That proof shows that the estimator is unbiased.

There really isn’t anyway to connect Cavalieri with point counting. Cavalieri compares two objects A and B and then declares that if the comparison holds, then A and B have the same volume or area. That isn’t anything at all like point counting. It doesn’t even have anything at all to do with the Delesse principle or Rosiwal’s work.

Early and Late Recognition

July 23, 2010

Each observer is different when it comes to doing stereological research. The reason for this is the way that the researchers interpret what they see. One of the basic issues in recognition is deciding whether or not something is a part of the population being counted. A cell or structure seen in the microscope is something to count or something not to count. After a decision is reached about whether or not something should be counted, comes the issue about the intersection of the probes and the item of interest.

The easiest decision is whether or not an object is intersected by a line. A counting frame is composed of 2 types of lines. The green or dashed lines are the inclusion lines and the red or solid lines are the exclusion lines. Touching a line seems to be a simple rule. In fact, there are many cases that becomes gray issues. Whatever decision is made in one place has to be used at all times. The decision that a certain fuzzy condition is a touch or not needs to be used in all similar conditions. The same conditions need to be used for both the inclusion and exclusion lines. If the rules are not applied in a consistent manner then a bias is introduced. This bias may be quite small if the counting frame is small. The bias becomes more pronounced as the counting frame decreases in size.

The most difficult decision is the decision about the z-position of an object. Some observers tend to be early recognizers. The tendency is to see something in focus before others. The idea is that the researcher is focusing through the material and decides that something is in focus before other people. A late recognizer is someone that decides later than other people that an object is in focus. Near the top of the optical disector an early recognizer might say that a cell is not counted, while a later recognizer might decide that the cell is indeed counted. Problems occur when late and early recognition are used consistently across the height of the disector.

If someone uses early recognition at the top of an optical disector and late recognition near the bottom of the optical disector it is as if the optical disector is smaller than it is. The result is that fewer counts are made and the population is underestimated. The opposite can happen as well if someone uses late recognition at the top and early recognition at the bottom, then the result is that more cells are accepted and an over projection occurs.

It does not matter if a person is an early or late recognizer. What matters is being consistent in the application of counting rules regardless of the position where counts are made.