Final answer:
The nurse researchers used network sampling by having parents who consented to participate refer other potential participants, creating a network of subjects. Network sampling, also known as snowball sampling, is a nonrandom sampling method where initial subjects are identified and then asked to refer other individuals who may also meet the criteria for the study. In this case, the nurse researchers initially identified parents who have abused their children, and then they asked these subjects to identify other individuals who might participate in the study.
Step-by-step explanation:
The sampling method used by nurse researchers who wanted to study the characteristics of parents who have abused their children in the described study is network sampling. This is because initially identified parents were asked to provide referrals to identify other individuals who could participate in the study, forming a network of participants based on their connections to each other. This method relies on the social networks of individuals rather than random selection.