Descriptive statistics, inferential statistics, rhetorical statistics

Peter van.den.Besselaar Peter.van.den.Besselaar at NIWI.KNAW.NL
Wed Aug 6 02:54:20 EDT 2003

In a contribution to this list, Loet Leydesdorff replied to my brief communication in JASIST (2003-1) "Empirical evidence for self-organization?". My reply - as letter to the editor - is now published in JASIST 2003-9:

"Descriptive statistics, inferential statistics, rhetorical statistics"

Loet Leydesdorff (2003) argues that my analysis (Van den Besselaar, 2003) is not correct and not relevant. In his argument, however, he mixes up samples and populations, and he incorrectly uses concepts such as 'significance' and 'eigenstructures'.

Leydesdorff's data are attributes of the papers in "a carefully selected set" of biotechnology journals. In other words, it is not a sample from a larger set of journals, and therefore he analyzes on the level of the population. Applying statistical techniques on a population is descriptive statistics. Of course statistical packages like SPSS calculate 'significance levels' but these belong to the realm of inferential statistics, that is generalizing from random samples to populations. In his claim that my "simulation results usually did not pass the significance tests provided by SPSS" and that  his "results using bibliometric data did pass these tests", he is confusing samples and populations. As there is no sample whatsoever, using the qualification 'significant' is irrelevant and misplaced. The same holds when he uses the results of the simulations to conclude that "the network of words does also not significantly correlate with the geographical division."

Samples come into play when testing the quality of the discriminant analysis. I have drawn random samples, and use the sample statistics (the discriminant functions) to predict the population parameters. As every random sample fails to do this, one has to conclude that using discriminant analysis for describing the relation between 'title words' and 'region of origin' is wrong. This can be explained by the large number of unique observations in the data, and this also explains the results of the simulations (Van den Besselaar, Heimeriks 1998, pp 98-100). Leydesdorff argues that this test of the DA is not relevant because "one cannot expect any significant correlation between the eigenstructures of highly specific samples." Of course one does not expect this in case of highly specific samples, but my test shows that the eigenstructures of random samples are completely different.

Leydesdorff states that I misread and selectively quote his paper, as he is not doing first order data analysis. He tries to develop a 'new methodology for second order theorizing' to answer 'what-if questions' about the interaction between the global knowledge production system and regional institutionalization. I do not have problems with type of questions, but the 'new methodology' needs clarification: what can we conclude from the 'significant' correlations between the 'regional word sets' with the word sets representing the 'intellectual space' (Leydesdorff & Heimeriks 2001, p.1268)? First, the mapping of the intellectual space is based on a very weak factor structure (Leydesdorff & Heimeriks 2001, 1266). Second, the regional word sets are highly questionable (Van den Besselaar 2003). Additionally, I showed that the positions of the three regions within the intellectual space change from year to year (E-mail communication, November 1998). This change is so implausible that one should seriously doubt about the adequacy of the methods used to measure these positions: the discriminant analysis. The conclusion is that, despite the 'significant' results, the 'new methodology' is not convincing. What remains is an example of rhetorical statistics.

More information about the SIGMETRICS mailing list