Introduction

Earth scientists sometimes collect data for which the sampling or experimental units can be assigned to two or more discrete and mutually exclusive categories that are contingent on each other. Consider a paleomagnetic study of the orientation of Earth's magnetic field using cores collected from the sea floor on a traverse perpendicular to the mid-ocean ridge. Roughly 55% of the core samples show the magnetic field pointing north and the remaining 45% show the magnetic field pointing south. These directions are discrete and mutually exclusive categories: a rock may be magnetized to point to the north or the south, but it cannot ever be both (the case of an in-between magnetization recorded during a reversal is so rare that it can be considered negligible). These two possibilities, north vs. south, also make up the entire set of possible outcomes and are therefore contingent upon each other: for a sample of 100 cores, a decrease in the number in one category (e.g. north-polarized rocks) must be accompanied by an increase in the number in the other (south-polarized rocks) and vice versa.

These are nominal scale data (Chapter 3). The questions researchers ask about these data are the sort asked about any sample(s) from a population.

First, you may want to know the probability that a sample has been taken from a population with a known or expected proportion within each of two or more categories.