Mean Normalised Log-transformed Citation Score (MNLCS): A field normalised average citation impact indicator for sets of articles from multiple fields and years

The Mean Normalised Log-transformed Citation Score (MNLCS) is a variant of the Mean Normalised Citation Score (MNLCS) to assess the average citation impact of a set of articles. This formula compares the average citation impact of articles within a group to the average citation impact of all articles in the fields and year of the group’s articles. A score of above 1 indicates that the group’s articles have a higher average citation impact than normal for the fields and years in which they were published. The MNLCS uses a log transformation to citation counts before processing them because sets of citation counts are typically highly skewed and this transformation prevents individual articles from having too much influence on the results. The MNLCS calculation is as follows.
1.  Log transformation: For each article A in the group to be assessed, replace its citation count c by a log-transformed version, ln(1+c).
2.  Field normalisation: Divide the log transformed citation count ln(1+c) of each article A in the group by the average (arithmetic mean) log transformed citation count ln(1+x) for all articles x in the same field and year as A.
3. Calculation: MNLCS is the arithmetic mean of all the field-normalised, log-transformed citation counts of articles in the group.

The MNLCS calculations are illustrated below in Excel for a group publishing articles A,C, H and J in a single field containing articles A to K.

And here is an example of MNLCS calculations for a group that is split between two fields, X and Y, with articles A,C, H and J in field X and O, S, U in field Y.

Confidence intervals can be calculated for MNLCS to assess whether two different MNLCS values are statistically significantly different from each other. The formulae use the means and standard errors of the log transformed citation counts (note: not the field normalised versions) for the articles in the group and the world’s articles in the same field and year as the group. The formula is more complicated if the group publishes in multiple fields and years – this post just discusses the simplest case, with formula below.

The confidence interval calculations are illustrated below in Excel. In this case the group MNLCS is 0.885 but its 95% confidence interval is (0.119, 2.081) so the group average is not statistically significantly different from the world MNLCS value, which is always 1.

All of the above calculations (including confidence intervals) are also built into the free software Webometric Analyst for sets of citation counts from Scopus, the Web of Science as well as for web indicators.
More details are given in this paper:
Thelwall, M. (in press). Three practical field normalised alternative indicator formulae for research evaluation Journal of Informetrics. 10.1016/j.joi.2016.12.002