"To conduct the mediation" means taking the role of a neutral person who helps two or more parties who are in conflict to communicate and find a mutually agreeable solution. Full definition
If private sessions are not conducted the mediation sessions can take longer. (danddfamilylaw.com)
(9) A person who conducts a mediation under this section shall not be required to testify in a civil proceeding or in a proceeding before any tribunal respecting the mediation. (ontario.ca)
Moreover, the sample size was rather small to conduct the mediation analyses. (link.springer.com)