Response to Macnaughton’s ‘Comment on 'A low-uncertainty measurement of the Boltzmann constant'’

In his comment on our 2013 paper ‘A low-uncertainty measurement of the Boltzmann constant’ [1] Macnaughton claims that his re-analysis “…reveals systematic non-random patterns in residuals of the key fitted model equation”. He claims that “these patterns violate the assumptions underlying the analysis” and “raise questions about the validity of [our] estimate of kB”. He also claims that we deleted “troublesome” data in a “somewhat arbitrary” manner. While we are grateful to Macnaughton for his attention to our freely accessible data, we disagree with his conclusions. The dataset we analysed consists of 263 data points, while the ‘trends’ in the data to which he refers constitute at most 12 points. Concerning the improper removal of data points to which he alludes we note that all 324 data points that we acquired were included in the supplementary data, but some data were excluded from the analysis for the reasons stated in the original text. Macnaughton was able to determine the effect of including or excluding these data but did not do so. In this paper we demonstrate that none of the issues to which Macnaughton draws attention could conceivably have any significant effect on our final estimate for the Boltzmann constant or its uncertainty.