Average Citation and Alternative Indicator Values for Groups of Documents

These instructions explain how to gather citation and alternative indicator data, calculate arithmetic and geometric means and the proportion cited for the data, and (if wanted) calculate world normalised average citation MNLCS and average proportion cited NPC indicators. Jump straight to the instructions.

Indicators for groups of articles

Arithmetic mean: The per document usual average of all the indicator data (e.g., citation counts, Mendeley reader counts, web citation counts) - not really appropriate because indicator data is highly skewed

Geometric mean: The per document geometric mean average of all the indicator data (e.g., citation counts, Mendeley reader counts, web citation counts) - better than the arithmetic mean for citation data because of skewing.

Mean of ln(1+raw data): The arithmetic mean after a transformation of ln(1+x) to eliminate skewing - better than the arithmetic mean for citation data because of skewing and just as good as the geometric mean.

Proportion cited: The proportion of all documents with at least one positive indicator value (e.g., a citation count of at least 1). This can be more useful than the geometric mean if a very low proportion of the documents are cited because it has narrower confidence intervals.

Here is an example of the report that Webometric Analyst will give you for each set of documents:

File: Biochemistry Molecular Biology Alcohol 2012
Records                      : 500
Arithmetic mean of raw data  : 16.844000
Geometric mean (95%CI) of raw data   : 7.991652 (7.036911, 9.059811)
Mean (95%CI) of ln(1+raw data)   : 2.196297 (2.084045, 2.308548)
Proportion (95%CI) non-zero      : 0.836000 (0.801005, 0.865871)

World normalised indicators for groups of articles

MNLCS (Mean Log-transformed Normalised Citation Score) is the average number of log-transformed citations for the group, divided by the average number of log-transformed citations for the corresponding world set. Values higher than 1 indicate that the citation counts for the group tend to be above the world average and values below 1 indicate that citation counts for the group tend to be below the world average. Two confidence intervals are reported for MNLCS but the sample confidence intervals should always be used unless making the assumption that the world file contains a complete set of all the world’s articles from the field and year. Blog post describing MNLCS calculations and MNLCS worked example spreadsheet, including confidence limits.

EMNPC and MNPC (Equalised/Mean-based Normalised Proportion Cited) is the proportion of articles cited for the group, divided by the corresponding world proportion of cited articles for the same field and year. Values higher than 1 indicate that the proportion of cited articles for the group is above the world average and values below 1 indicate that the proportion of cited articles for the group is below the world average. These figures can be ignored for the World groups because they are always 1. EMNPC and MNPC worked example spreadsheet, including confidence limits.

Here is an example of the report that Webometric Analyst will give you for a group of documents from the same field and year:

Group file: Spain. In set: Biochemistry Molecular Biology Alcohol 2012
Records   :  193
Arithmetic mean     : 16.663212
Geometric mean (95%CI) of raw data   : 8.162284 (6.598901, 10.047313)
Mean (95%CI) of ln(1+raw data)   : 2.215095 (2.028004, 2.402187)
Proportion non-zero (95%CI)      : 0.808290 (0.746954, 0.857593)
MNLCS - mean (95%CI) of world normalised ln(1+raw  data) [population version] : 1.008559 (0.923374, 1.093744)
MNLCS - mean (95%CI) of world normalised ln(1+raw  data)     [sample version] : 1.008559 (0.911468, 1.110933)
NPC - world normalised proportion (95%CI) cited  (non-zero): 0.966854 (0.893995, 1.045651)

And here is an example of a combined report for multiple documents from the same group (Spanish research in this case) spanning different fields and years.

MNLCS calculations for all files.

==============================================================
Group N     MNLCS L95Sample   U95Sample   L95Pop      U95Pop
World 1000  1     0.940734    1.064616    0.956326    1.043673
Spain 475   0.989 0.913058    1.069826    0.9245527   1.052597
==============================================================

Field equalised proportion non-zero calculations.

==========================================================================
Group N     PropNonzero Lower95     Upper95     NPC   Lower95     Upper95
world 1000  0.767000    0.739807    0.792149    1.000 0.952902    1.049426
Spain 475   0.744571    0.703499    0.781719    0.971 0.911822    1.033502
==========================================================================

Step by step instructions for gathering data and calculating the indicators

Choose which option path to follow, depending on the indicators to be calculated. If you prefer, try a workshop run through of all these tasks instead.

Here are the steps needed to gather data and calculate indicators, with worked examples in most. Please try the worked examples first and then repeat with your own data or queries.