I have copied here the methods used by Gerd Geyer in his revision of the Moroccan fallotapidids. Initially, I had intended to simply summarize, but the integrity of the original text is best treated verbatim :

"Stastitical studies are an important tool in the interpretation of morphology and taxonomic status of trilobites. They have become increasingly popular within the last decade but are less well established compared with that completed on most other major fossil groups. However, quantitative studies not only supplement qualitative morphological studies and can "further attest to or refute a hypothesis based on qualitative observations" (BRIGHT, 1959). Morphological measurements help constrain the morphologic variations, and permits separation of close relatives. Without precise knowledge of the morphological variability, the introduction of new taxa is merely a guess. Nontheless, it should always kept in mind that trilobitologists -perhaps even more than most other paleontologists - always deal with morphospecies rather than "real" biospecies.

The intrinsic problem of quantitative studies starts with collecting. All paleontologists are aware that any collection of macrofossil is biased. Collecting means a selection of specimens from the available material. Outcrops are usually limited and present a limited slice of the fossil-bearing beds. Moreover, preservation depends on lithology. As a result, certain sizes and, hence, growth stages are usually favored. Collecting is also a function of personnal attitude, and large or complete specimens are usually sampled in a more poorly preserved state than small cephala. In addition, are only well preserved specimens retained or does the collection include only those specimens with certain features ? Finally, collecting depends on local conditions, such as weather, exposure, and distance to neighbouring settlements [...]. The result is always an arbitrary selection even when the worker tries to attain a valid representation of the population.

However, the key question is wether or not the collection is usable as an indicator for the morphology of the represented taxa, rather than wether the sample does mirror the total population. As soon as diagnostic features are known and statistical methods are able to give a reliable sketch of the morphological development during ontogney, deficiencies in sampling will become evident. In other words : a graph that depicts a clear morphological trend is able to characterize ontogenic development and in turn to indicate specimens, which possible belongs to different taxa. Hence, collection bias may not affect the particular objective of the studies.

Graphic analysis should, however, distinguish between characterization of 1) populations and 2) taxa. A valid sample has to depict in all probability the morphological structure of the living population. in turn, taxa in paleontology are merely an interpretation of the relationships of populations. One of the main problems is that samples usually start at a specific size of the individuals, and small specimens are poorly represented or absent. This is due to general preservational vagaries as well as the inability to collect small specimens that are well enough preserved for recognition or use. As a result, the curves of morphology are affected by the range of the values in question." (GEYER, 1996).

As you can see, Dr Geyer made an excellent summary of the problems we will be facing. He used for his study two methods (regression analysis and non-metric multidimensional scaling), but the regression analysis is the most accessible to our study (the multidimensional scaling being beyond our capacity). In order to use regression analysis, we will need well-standardized and accurate measurement methods (cf. photography guide). The following illustrations depict the measures proposed (at least at the beginning of the study).

Here are several figures adapted from Sam Gon III's initial drawings, in order to illustrate the measurements proposed for statistical analysis :

The Cephalon :

 

 

Cephalic angles may be difficult to obtain consistently, since the selection of angles is based on choosing tangents along continuous curves.

The Pygidium :

In addition to the metrics indicated in the figure and table below, the number of axial rings (including the number of rings of the terminal piece) and the number of pleural ribs will be recorded.

 

In the long-term, we might not need all these measures. But at the beginning of the study, it is best to collect more characters than ultimately needed, to assess their utility in distinguishing morphotaxa. Please see next the page about data collection.

GEYER G. 1996. The Moroccan Fallostapidid trilobites revisited. Beringeria 18 : pp. 89 - 199.