Bias is an important issue in science because it can lead to misleading results and conclusions.

The theoretical foundation of design-free (unbiased) stereology is emphasis on avoiding the wide variety of sources of stereological and non-sterelogical bias that can cause estimates to deviate in a systematic way from the true or expected value.

Terminology

Persons unfamiliar with the mathematical definition of bias often confuse this term with the common-language definition: a conscious preference or partiality for one outcome over another.

Stereologists use the term bias (systematic error) for its mathematical meaning: biased formulas and models can generate biased estimates that diverge from the true parameter value.

In stereology the term "unbiased," refers to formulas that yield accurate estimates that converge on the true parameter value. This accuracy is based on the use of sampling and geomtetric probes that avoid all known assumptions and models that cannnot be verified.

In an effort to avoid the distractions of the "biased vs. unbiased" debate, stereologists frequently use "design-based" or "assumption- and model free" to refer to mathematically unbiased methods of modern stereology.

A third category is "unbiased for all practical purposes," the designation that can apply to the application of theoretically unbiased stereology to actual biological tissue. In this case practical aspects of the design may introduce an insignificant amount of bias that has a negligible effect on the results.

Stereological bias

Bias causes the central tendency (e.g., mean) of an estimate to deviate from the true value.

For example, consider the scenario where biological objects are assumed to have the shapes of classical (Euclidean) objects, a so-called biased or assumption- and model-based method.

Imagine estimating the mean cell volume of a population of cells under the assumption that a cell is a sphere. In this scenario, measuring the "radius" of 1, 10, or 100 cells and applying the formula for the volume of a sphere will generate a result; however, the result will never converge on the true value.

Because the quantity of bias in this case cannot be measured, there are no correction formulas or other approaches to remove it.

The problem is obvious: Cells are not spheres. Spheres are classical structures from Euclidean geometry, while cells are natural objects that exist in 3-D tissue and develop under complex selection forces that cause variability in size, shape, and orientation.

Formula from Euclidean geometry using the radius or diameter assume that these values are the same, regardless of their direction in space.

When we observe 3-D cells on 2-D sections, we do not observe cells, but rather a single profile through each cell. For biological cells, the "radius" of a cell varies with a number of factors, including the angle of the section, the actual profile of the cell observed, and the direction of measurement to the profile border.

Stereological bias from false models and unverifiable assumptions cannot be measured or removed from sample estimates. So-called correction factors (e.g., Abercrombie, 1946) simply add further bias by introducing more assumptions and models into the process.

Bias from assumptions, models, and correction factors is well known in the field of stereology; nevertheless, every day biological data based on these false and model-based assumptions are submitted to major peer review journals for publication.

While model- and assumption-based approaches are useful in theoretical mathematics, engineering, and in the construction of man-made objects (tables, walls, books, clocks, etc.), they generate inaccurate results when applied to naturally occurring, non-classically shaped objects found in biological tissue.

Non-stereological bias

In practice, there is no single approach, no brand of software, and no "one size fits all" design that can guarantee unbiased results from unbiased formula.

Applying unbiased formula to biological tissue offers many opportunities for introducing non-stereological bias resulting from tissue fixation, tissue shrinkage, staining artifacts, calculation errors, clerical mistakes, etc.

Both stereological and non-stereological bias result in the deviation of the sample estimate from the true value, however, there is an important difference: Non-stereological bias can be identified and eliminated; once present, stereological bias cannot be measured or removed. For example, poor tissue penetration causes incomplete staining of all cells in the section. Once identified, increasing the tissue penetration will stain all cells as required for accurate stereological estimates.

Computer software eliminates the many common calculation errors that can cause non-stereological bias; however, computerized systems rely 100% on trained users for precise recognition of the biological features of interest.

In summary, assumption-based, model-based, and correction-based formula introduce unknown and unremovable bias when applied to biological tissue. The relative "unbiasedness" of estimates using mathematically unbiased formula depends on how well investigators succeed in avoiding sources of non-stereological bias when applying unbiased methods to biological tissue. When all major sources of stereological and non-stereological bias have been eliminated, results are considered "unbiased for all practical purposes."