## 4.2 Analysis of quantitative (scoring) results

### Estimation of error associated with scoring

Although the descriptions for the thin-sections detailed in Markham (2000) Appendix 5.5 were written over a period of time, the scoring of all thin-sections took place over a period of seven days. This was done to minimise human bias in assessing the score for each thin-section. The empirical quantitative system was developed on examination of approximately 20 thin-sections that had been viewed approximately 18 months previously, and the scores allocated at that time were deliberately re-estimated as part of the seven-day scoring activity in order to see if the length of time that had elapsed had contributed to any human bias. It was found that the majority of the 'new' and 'old' scores agreed within ±1 scoring unit (apart from 'opaques' scores, which are not incremental), hence leading to the conclusion that the potential error on assigning scores is ±1 of the given score. The devised system was easy to use and, once practised, scores could be assigned within minutes.

### Presentation of results

Markham (2000) examined the results in three ways; bivariate plots, multiple parameter plots and quantitative arithmetical comparison (analysis of residuals). Space dictates only the latter is reported here.

### Quantitative arithmetical comparison

The degree of similarity between graphical profiles can be arithmetically measured by adding together the moduli of the differences between each average score from two profiles, ignoring the opaque scores for reasons discussed above, and amphibole and mica scores as they are largely similar throughout. For example, if there are two profiles consisting of average scores (colour, grain size, pyroxene, feldspar, epidote and apatite) of 5, 7, 5, 8, 6 and 3 and 7, 3, 8, 6, 7 and 4 respectively, then the sum of the modulus of the difference is obtained by the expression (|5-7| + |7-3| + |5-8| + |8-6| +|6-7| + |3-4|), giving 13 as the sum of the moduli of the differences, called the residue. Therefore a perfect match in profiles would result in a zero residue, while a low residue indicates a close match and a high residue indicates a poor match in at least one of the scoring categories. This method can be used to investigate the degree of similarity within and between axe sub-groups and exposure sub-groups.