Randomly sampling Wikipedia entries and then using it to predict h-index scores may mean nothing. This is a play on the title of , but serves as a good, one-sentence critique of .
The authors of  suggest that personal profiles of scientists on Wikipedia should correspond with scientific impact (measured using the h-index). If they do not, then it suggests that Wikipedia is the source of distortion, artificially giving attention to lesser mortals (as it were).
However, this assumes two things: that the properties of Wikipedia entries should reflect the scoring of citation indices, and that random samples of Wikipedia entries will correspond to the distributions of h-index values.
The first assumption is only valid if h-indices capture all possible information about scientific impact. Clearly, this is not the case, as many different indicies have been developed  to characterize the various nuances inherent in scientific output and influence.
The authors of  present a systematic review of various citation indices. Importantly, none of which produce a normal distribution centered around a mean. So when the mean h-index value of the Wikipedia sample is compared to the h-indices of different scientific fields, it does not mean as much as one would assume at first glance.
The brings us to the second assumption, which regards the underlying distribution of scientific impact. While this is not clearly discussed in , we know from other studies  that scientific impact can be explained using Lotka’s Law (which can be characterized using a Pareto distribution).
While this long-tail can be mitigated using specialized metrics such as the x-index , this was not considered in . In fact, one could argue that Wikipedia profiles and citation indices are statistically independent of one another.
 Meyer, R. Does Your Professor Have a Wikipedia Entry? Congrats! It Means Nothing. Maybe they even wrote it themselves. The Atlantic, November 7 (2013).
 Samoilenko, A. and Yasseri, T. The distorted mirror of Wikipedia: a quantitative analysis of Wikipedia coverage of academics. arXiv:1310. 8508 (2013).
 Alonso, S., Cabrerizo, F.J., Herrera-Viedma, E., and Herrera, F. h-index: a review focused in its variants, computation and standardization for different scientific fields. Journal of Informetrics, 3(4), 273-289 (2009). doi:10.1016/j.joi.2009.04.001.
 MacRoberts, M.H. and MacRoberts, B.R. A Re-Evaluation of Lotka’s Law of Scientific Productivity. Social Studies of Science, 12(3), 443-450 (1982).
 Rodriguez-Navarro, A. A Simple Index for the High-Citation Tail of Citation Distribution to Quantify Research Performance in Countries and Institutions. PLoS One, 6(5), e20510 (2011).