This is the author accepted manuscript. The final version is available from the publisher via the DOI in this record. ; Transfer functions are valuable tools in palaeoecology, but their output may not always be meaningful. A recently-developed statistical test ('randomTF') offers the potential to distinguish among reconstructions which are more likely to be useful, and those less so. We applied this test to a large number of reconstructions of peatland water table depth based on testate amoebae. Contrary to our expectations, a substantial majority (25 of 30) of these reconstructions gave non-significant results (P > 0.05). The underlying reasons for this outcome are unclear. We found no significant correlation between randomTF P-value and transfer function performance, the properties of the training set and reconstruction, or measures of transfer function fit. These results give cause for concern but we believe it would be extremely premature to discount the results of non-significant reconstructions. We stress the need for more critical assessment of transfer function output, replication of results and ecologically-informed interpretation of palaeoecological data. ; Elements of this project were supported by various funding agencies including: grant PSPB-013/2010 through the Swiss Contribution to the enlarged EU; project 017008 through EU FP6 (Millenium); grant 14-14-00891 from the Russian Scientific Fund; grant IE150173 from the Royal Society; NERC doctoral training grant NE/G52398X/1; NERC research grants NE/I022809/1, NE/I022981/1, NE/I022833/1 and NE/I023104/1; a DEL-NI doctoral training grant and the Worldwide Universities Network (project: Arctic Environments, Vulnerabilities and Opportunities). RJP is supported by the Leverhulme Trust through project RPG-2015-162.