Comparing Frequency-Distribution Curves

In this chapter, we consider the form of simple frequency distributions and the means by which they may be compared. In most earth-science applications, our observations will not correspond closely to the Normal distribution, nor to any other theoretical distribution, but that does not necessarily prevent description and characterisation with a few statistics. However, sometimes a direct comparison with the Normal distribution may be helpful and, in a few instances, it may be important, for example, to satisfy the requirements for ANOVA (Chap. 4). Therefore, this chapter commences with methods that compare observations to a Normal distribution. The discussion commences with simple arithmetical and graphic methods and then continues with the process of transforming observations by standardisation to facilitate direct comparison with the Normal distribution. The cumulative version of the frequency distribution sometimes expedites a cursory visual comparison of samples, and cumulative frequency distributions of grain size may reveal underlying processes.