Statistics Explained: Non-parametric tests for nominal scale data

Introduction Life scientists often collect data that can be assigned to two or more discrete and mutually exclusive categories. For example, a sample of 20 humans can be partitioned into two categories of ‘right-handed’ or ‘left-handed’ (because even people who claim to be ambidextrous still perform a greater proportion of actions with one hand and can be classified as having a dominant right or left hand). These two categories are discrete, because there is no intermediate state, and mutually exclusive, because a person cannot be assigned to both. They also make up the entire set of possible outcomes within the sample and are therefore contingent upon each other, because for a fixed sample size a decrease in the number in one category must be accompanied by an increase in the number in the other 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 need to know the probability a sample has been taken from a population having a known or expected proportion within each category. For example, the proportion of left-handed people in the world is close to 0.1 (10%), which can be considered the proportion in the population because it is from a sample of several million people. A biomedical scientist, who suspected the proportion of left- and right-handed people showed some variation among occupations, sampled 20 statisticians and found that four were left handed and 16 right handed. The question is whether the proportions in the sample were significantly different from the expected proportions of 0.1 and 0.9 respectively. The difference between the population and the sample might be solely due to chance or also reflect career choice.