Abstract
An ordinal scale is one which comprises rank-ordered data, where the differences between the ranks are not (and commonly cannot be) specified. Examples include the Mohs' hardness scale, biostratigraphic stages and zones, metamorphic grade, and absent-rare-common-abundant estimates of lithologic components. Correlations and trends in ordinal information can be investigated in a manner analogous to linear regression using a measure of association, the gamma statistic. A significance test for gamma is provided. These statistical measures are applied to the following illustrative examples: distribution and correlation of mineral components in some modern lake sediments, variation of grain size with distance in some detrital limestones, and the distribution in time of sedimentary structure assemblages in a deltaic succession. Use of gamma (and in certain cases multivariate techniques such as cluster analysis) is valuable if time or other limitations prevent the acquisition of data on an interval or ratio scale. For many types of data, ordinal statistics are the only type suitable but have been largely ignored by geologists in the past.
