In the absence of comparative method reconstruction, high rate of lexical cognate candidates is often used as evidence for relationships between languages. This paper uses the Oswalt Monte Carlo Shift test (a variant of Oswalt 1970) to explore the statistical basis of the claim that the four Papuan languages of the Solomon Islands have greater than chance levels of lexical similarity. The results of this test initially appear to show that the lexical similarities between the Central Solomons Papuan languages are statistically significant, but the effect disappears when known Oceanic loanwords are removed. The Oswalt Monte Carlo test is a useful technique to test a claim of greater than chance similarity between any two word lists — with the proviso that undetected loanwords strongly increase the chance of spurious identification.