Hans Erren brought to my notice a study he did on artifacts in the Quelccaya ice core record, first observed by Steve McIntyre (of climateaudit.org). I thought I would run this through benford() to see if it could pick up the problem. The study is here at Hans’ home site and the dataset is here at the NOAA data archive.
According to Hans’ study the artifact is caused by rounding up of the accumulation results to whole centimeters. This form of ‘result management’ reduces the degrees of freedom of results, reducing essentially real numbers to a more limited integer domain, clearly seen in Hans’ figure.
I created a little space between some abutting numbers, trimmed off the header and footer of the file and ran the benford() time series analysis from the Audit-0.1 package on the 6th and 7th column, the O18 and the accumulation results. Below is the code in R:
d< -read.table("q83cor1.txt") benford(d[,6]+10,plot=TRUE,n=50) benford(d[,7],plot=TRUE,n=50)
Results management is indicated by the red line falling below the green
line along the series. This red line is the probability of the second digit frequency being consistent with Benford’s Law. The accumulation figures show a clear deviation with increasing depth, consistent with the figure produced by Hans Erren above. The O18 also show signs of results management at greater depths, though to a lesser degree than the accumulation.
The package used to perform these analyses is freely available here