Why with bibliometrics the Humanities does not need to be the weakest link

Abstract

In this study an attempt is made to establish new bibliometric indicators for the assessment of research in the Humanities. Data from a Dutch Faculty of Humanities was used to provide the investigation a sound empirical basis. For several reasons (particularly related to coverage) the standard citation indicators, developed for the sciences, are unsatisfactory. Target expanded citation analysis and the use of oeuvre (lifetime) citation data, as well as the addition of library holdings and productivity indicators enable a more representative and fair assessment. Given the skew distribution of population data, individual rankings can best be determined based on log transformed data. For group rankings this is less urgent because of the central limit theorem. Lifetime citation data is corrected for professional age by means of exponential regression.

Appendix: mathematics of PA-correction for citations

Starting from the data as it is plotted in the scatter diagram of citation rates per author over PA (Fig. 2, main text), we can PA-correct the citation rates by using the exponential regression:

$$ ce(y_{k} ) = {\frac{{y_{k} }}{{E(y_{k} )}}} = {\frac{{y_{k} }}{{\alpha e^{{\beta x_{k} }} }}}, $$

(1a)

where ce(y _k ) denotes the exponentially corrected citation score of author y with professional age k. The lower bound of all points ce(y _k ) is 0, and their GM is ${{\bar{y}_{\text{GM}} } \mathord{\left/ {\vphantom {{\bar{y}_{\text{GM}} } {\alpha e^{{\beta \bar{x}}} }}} \right. \kern-\nulldelimiterspace} {\alpha e^{{\beta \bar{x}}} }} = 1.$ The Cartesian point $\left( {\bar{x},\alpha e^{{\beta \bar{x}}} } \right) = (\bar{x},\bar{y}_{GM} )$ we call the geometric centre of gravity.

Alternatively, PA-correction can be based on the linear regression (cl standing for linear correction):

$$ cl(y_{k} ) = y_{k} - E(y_{k} ) = y_{k} - (\gamma + \delta x_{k} ). $$

(2a)

The arithmetic mean of all scores cl(y _k ) is $\bar{y} - (\bar{y} + \delta \bar{x}) = 0.$ The centre of gravity in the (x, y)-plane is the Cartesian point $(\bar{x},\gamma + \delta \bar{x}) = (\bar{x},\bar{y}).$

Since there are advantages in working with linear data, we may translate (1a) into linear form by taking logs. Because $\log \left[ {ce(y_{k} )} \right] = cl(\log \,y_{k} ),$ we thus apply the following log transformation of (1a):

$$ cl(\log \,y_{k} ) = \log \,y_{k} - (\log \,\alpha \, + \,\beta \,x_{k} ). $$

(1b)

The arithmetic mean of all cl(log y _k ) is $\overline{\log \,y} \, - \,(\log \,\alpha \, + \,\beta \bar{x}) = 0.$

So far we have two linearly corrected scores to work with, (1b) and (2a), which, if we take their origin into account, are fundamentally different in spite of their external similarity, since (1b) is indirectly based on exponential correction of the original counts, while (2a) is directly based on linear correction of the same counts. Hence, both (1a) and (1b) can be seen as representing a model based on exponential correction, while (2a) provides a model based on linear correction.

Finally we standardize scores (1b) and (2a), so that they not only have mean 0, but also standard deviation 1. This is done by applying the standardizing operation $z = (x - \bar{x})/s,$ where s is the standard deviation of all x. It should be reminded that a different type of standardizing procedure was applied above with regard to (1a). There we calculated the ratio $x/\bar{x}$ with mean 1 and lower bound 0, without standardizing the deviation.

Consequently, the standardized PA-corrected scores for the exponential and the linear model, corresponding with (1b) and (2a), are respectively:

$$ \log \,z_{k} = {\frac{{\log \,y_{k} - (\log \,\alpha \, + \,\beta x_{k} )}}{s}}, $$

(1c)

and

$$ z_{k} = {\frac{{y_{k} - (\gamma + \delta x_{k} )}}{s}}. $$

(2b)

We can add the following standardized scores without PA-correction:

$$ z = {\frac{{y - \bar{y}}}{s}}, $$

(3a)

and

$$ \log \,z = {\frac{{\log \,y\, - \,\overline{\log \,y} }}{s}}. $$

(3b)

Group means (g standing for group) $\bar{z}_{kg} ,\overline{\log \,z}_{kg} ,\,\bar{z}_{g} ,\overline{\log \,z}_{g}$ (in the main text denoted by:$\bar{z}_{x} ,\,\overline{\log \,z}_{x} ,\,\bar{z},\,\overline{\log \,z}$) are obtained by calculating the averages of the individual scores (2b), (1c), (3a) and (3b), respectively of all members of the group in question. It should be noted that the parameters α, β, δ, γ, the means $\bar{y},$ and $\,\overline{{{ \log }\,y}} ,$ and the standard deviation s are derived from the reference group. In our case as reference group we always have the union of the groups (samples) for which the group means are computed.

The sampling distributions of the aforementioned group means are normal distributions with μ = 0 (CLT). Should we use, instead, the aforementioned geometric scores of (1a), then the sampling distribution is a lognormal distribution (μ = 1).