Data from a published study was deposited on the Harvard Dataverse abiding by the replication policy of a scientific journal. I have no connections with the scholars who collected the data and published the study, but I am conducting related work so I downloaded the "replication" data and used it to also conduct some new analyses. I have now found some interesting results, and since my new tests are not part of the original publication, I would like to publish them in new articles (I will also use some original data that I have collected).
Question: is it appropriate to use data collected by other researchers and made public for replication purposes in other to provide new scientific insights? Should I ask permission to use the replication data for a new publication? In particular, shall I contact these authors and, eventually, agree with data restrictions or co-authorship requests?
Existing questions cover related cases where the same author(s) re-use old data, a case of scanning data from an existing publication, and a case where replication (apparently without extensions) is used to connect with the author(s), and a similar case where a database becomes available upon publication.