We test the hypothesis that the choice by traditional people of species of plants for medicinal use does or does not depend on the families to which those species belong. Our geographic context is continental North America north of the Rio Grande River. Our plant context is flowering plants. Our ethnological context is Native American traditions. Our null hypothesis is that the probability of any species being medicinal is the fraction of all species that are medicinal, no matter the family to which that species may belong. Classical statistical techniques and the experience of ethnobiologists had already made it clear that among very large plant families, most have either very many or very few medicinal species. Here we use intense computation to simulate thousands of data sets to create predictions to compare with the observed data for medium and small families. Our results clearly show that a surprising number of medium and small families also have very many or very few medicinal species. Recent molecular, fossil and cytological studies have confirmed the evolutionary naturalness of most plant families. This suggests that species in the same family may have inherited from common ancestors similar ecological adaptations, such as ways to protect themselves from herbivores, pathogens or decomposers. Some of these adaptations affect the physiology of the attacking organisms, suggesting an explanation for the clear preferences of Native American traditions to choose medicinal species from some families much more than from others, regardless of the size of those families.