Disappointed so far.

In the essay "Early Nineteenth-Century Welsh Immigrants in Upper New York State" based on the description of a Welsh community in the town of Freedom, NY, found in Franklin Ellis’, History of Cattaraugus County, New York, Philadelphia, 1879, on page 392:
“In 1841, Robert Williams, John Higgins, Thomas Rees, Daniel Morgans, H. O. Roberts, John Lewis, and others came in from Oneida Co., N. Y., and formed the nucleus of a Welsh settlement,,,” Dr. Henry says that, “In addition to listing the names of these six immigrants, the same article mentions Ebenezer Baptist Church (Welsh), organized May 2, 1843, with forty-two members, and Salem Church (Welsh Calvinistic Methodist, first meeting in 1851)."

Dr. Henry explains that “By comparing ages and family makeup it is possible in some cases to be reasonably certain of a match between a family in Cattaraugus County in 1850 and in Oneida County in 1840.”

Reasonably certain?

First, while those six persons may have originated in Oneida County, they are described as forming only the nucleus of the Welsh settlement. At least some of the Welsh settlers came by way of other counties but they came with the same names: Evans, Jones, Griffith, Thomas, Richards, Owen, Pugh, etc.

The 1840 Census does not list names or exact ages of all family members, only the head of the household. Knowing only the name of the head of the household and the age ranges of the remaining family members is hardly enough information to say that John Jones in Oneida County in 1840 is the same John Jones who is residing in Cattaraugus County in 1850. I would never use the words “reasonably certain” based on that information.

In any case, some significant percentage of the congregation of the Salem Church in Freedom came from Newport, Herkimer County. It is documented in the National Register of Historic Places that they named their church after the older Salem Church located in Herkimer County which they had attended before moving west to Cattaraugus County.