Types of false paternal events include but are not limited to:
Pregnancy outside of a marriage
Pregnant female married man who was not father of child
Adoption
Man married pregnant widow
Children known by step-father's name
Man took wife's name and/or children given the wife's surname
Man changed name for various reasons
Clerical error in recording administrative data such as assigning a name to the wrong person
It should be stressed that adoptions were quite common in every age: parents died by disease or war and a relative took in the children and raised them with their name, daughters had children out of wedlock and the grandparents (or other relatives) raised the children as their own. A teen-age girl who gets pregnant by one boy and marries another - for whatever reason - might be a more frequent occurence than maternal infidelity in earlier generations. Taking into consideration the strong pressure against "unwed mothers" until the last generation or so, one might expect such cases to account for some of the paternal irregularity indicated by Y-chromosome testing. Mothers, under 18, of first-child sons in the line could be indicators for a higher probability of this phenomenon.
A result indicating a "false paternal event" would certainly be a disappointment to most participants. But your name is legally your name and a small sample size could be misleading. A DNA sequence suggesting a "false paternal event" could be that of the original bloodline - e.g., 20 people are tested, 19 are very similar and yours is clearly different. It could be that the 19 descend from the same person 300 years ago who was adopted while your line links to the original blood line going back 800 years.
If you are a male Dawkins or a female Dawkins with access to a male Dawkins DNA, please consider joining the project. Clicking this
link will take you to the registration page.