Snedecor

Snedecor was a statistician that helped lay out the design of many experiments through his book on the subject. Many references to his 1902 book can be found in the stereological literature. His work saw a recent rejuvenation when one of his formulas was inappropriately used to compute the coefficient of error. Some of Snedecor's work was mentioned in a book by Scheaffer et al. This work is based on the notion that the samples are independent, which is clearly not the case.

One of the earliest formulas for the coefficient of error was the binomial distribution formula which was suggested for use in point counting. The geologists and later other scientists realized the inadequacy of the formula for their work. The same was true of the Snedecor formula. In both cases, the problem was linked to the lack of independence between samples. The solutions offered to counter this problem was to take samples far enough away to avoid problems. The same can be seen in Rosiwal's work where it is recommended that no two traversal lines cross the same crystal. One of the early studies that realized that the Snedecor formula was not appropriate studied sugar beets in agriculture.

The problem had been identified by hundreds of researchers across the globe. A solution to the problem was eventually worked out by reexamining the problem from the position of developing a method to calculate the coefficient of error when the samples were known to be related to each other. The pioneering work was done by Matheron. He started with the assumption that the samples were taken in a systematic manner and used this to determine a formula for the measure of dispersion.

For unknown reasons an old formula that was not applicable was resurrected. The lessons of hundreds of researchers from many different scientific fields from metallurgy, to geology, to biology was forgotten. Their incite into the cause of the problem and the success of Matheron to develop a formula which was applicable to systematic sampling was overlooked.

Fortunately, the resurrection of this old and inapplicable method appears to have been just a brief stumble in the advancement of stereological research.

The best means of estimating the coefficient of error today is the extension of the Matheron technique. This technique has been extended to point counting and to counting of objects. Important research continues to be done by Garcia-Finana, Cruz-Orive, Gundersen, and Baddeley.

Failure to understand stereology

A few years back there was a presentation on stereology in which the speaker claimed you could break the rules and still get a "good" answer. The speaker came to this conclusion because they had done an experiment using proper protocols and then did an experiment with sloppy methods. The two answers they decided were good enough and then deiced that being sloppy and being a good scientist were the same thing. Ok. Those are not the words used in the presentation, but that is what the person was saying. So a real stereologist stands up and suggests that the speaker "Didn't look hard enough to find a difference."

This was exchange between sloppy work is no different than using a method known to get a wrong result. There are many reasons given to use methods than are known to be biased.
1. The person running the lab says "Worked for me, it'll work for you"
2. It's simpler to get the wrong answer.
3. Claim it's just as good without knowing the answer.

Cavalieri misnomer

The Cavalieri estimator is a bit of a misnomer. Cavalieri did not do estimates. Cavalieri did not point count.

Back in 1902 two geologists were trying to determine the size of crystals viewed through a microscope. They modeled the crystals as rectangular prisms and made use of the Cavalieri principle to determine the volume of the crystals. A mistake made in the application of the Cavalieri principle was that two objects must have the same height. This was not true in the work done. This misuse of the Cavalieri principle has not stopped the name from being used.

One of the odd things of stereological papers is making reference to Cavalieri's 1536 book when stating that point counting is being used. The reference has nothing whatsoever to do with stereological methods.

The citation of a 450 year old work that is an improper citation has fortunately become less of a fad.

Stereology Let's Us Measure the World Correctly

Stereology is more than counting cells although that is the most common use of stereological principles in the eyes of neuroscientists. Stereology is used in a great number of biological disciplines other than tissue level studies.

One of the interesting parts of the biological studies that employs proper stereological principles is ecology. One of the questions that is studied is some measure of biological diversity. A great number of measures have been conceived and many have fallen to the side as their weaknesses have been revealed.

Stereological measures were developed that provided information needed to answer questions such as biological diversity, and available forage. Many of these methods use techniques that are the same as the methods that are performed under the microscope. In fact, very similar problems exist such as the edge effect.

The importance of stereological methods, whether under the microscope or macroscopic analyses of large land areas, is that the methods have been develoepd that provide the right answer.