ABSTRACT
Contents 1.1 Sampling and bias 2 1.2 Why unbiasedness is desirable 3 1.3 Sources of bias in microscopy 4 1.4 The hierarchical nature of microscopical investigations 6 1.5 Stereology-geometrical quantification in 3D 7 1.6 Think in three dimensions-a macroscopic analogy by thought
experiment 7 1.7 Dimensions and sectioning 9 1.8 Geometrical probes 11 1.9 Ratios and densities 12 1.10 The reference space 12
Box 1.1 Dimensionality and scaling effects 14
A quantitative scientific analysis of any sort requires a higher level of objectivity and rigor in methodology than a comparable qualitative assessment. This rigor should extend from the planning of a study, through sampling of fundamental units and sub-samples to the actual measurements made. Perhaps counterintuitively the need for rigor increases in importance as the proportion of the total object being studied decreases. If a microscope is used to resolve the structures of interest it is almost inevitable that only a tiny fraction of the original object will actually be analyzed. For example, consider what proportion of an object is actually examined when a light microscope is employed in a histopathological analysis. An object the size of a neo-natal human kidney (about 12000 mm3 in volume) will often be used to generate three or four blocks from each of which a single 5-µmthick section will be microtomed and mounted. On each of these sections a small number of fields of view will be examined. This sampling regime would therefore involve the examination of a few hundreds of cubic microns of tissue, which is a million millionth (10-12th) of the volume of the original organ. Whilst such a tiny fraction may suffice to give a reasonable qualitative feel for the condition of the organ it is unsuitable for quantitative analysis unless it has been obtained with a statistically sound sampling method.
