This title may sound like blasphemy to some. I would rather call it   
"the devil in the paradise of art history 
who promises new fruit from the tree of knowledge."  

This post is the first in a series with this title where some simple statistical techniques for art historical data will be demonstrated. (See March 5, 2013:  Statistics in Art History (II): The rise and decline of a myth)
They may be helpful and incentive to both 'digital natives and immigrants' who are not acquainted with statistics (1). The data are extracted from my Thematic Research Collection of 10671 artworks of 3880 identified artists born in four European regions who depicted the very popular 'Aphrodite - Venus from the Middle Ages to Modern Times'. All data have been published and are freely available. Hence, the results presented in these posts are verifiable and zealous readers could possibly explore alternative applications (2).

          Quantity versus quality

Author: Rjgodoy 2007 (Wikipedia)
There is a general consensus that 'quality' matters more than 'quantity'.
The French philosopher Michel Tournier quotes very well the antagonism between both qualifications (3):
 Sans doute la qualité vaut mieux que la quantité, mais sur la qualité, on peut discuter à l'infini, tandis que la quantité, elle, est indiscutable. (Edward Reinrot)
                   (Without doubt quality is better than quantity,  but quality can be discussed ad infinitum, while quantity is indisputable.)
There is endless discussion in art history about the quality of artworks and how to recognise a masterwork (4).  Unfortunately many monographs  focus only on works considered as the greatest masterpieces of art. Art history is shallow if lesser artists and their works are forgotten. This also implies that quantity in the arts cannot be dismissed: it is part of the historical complexity of art production.

          The quantitative approach in art history


Though art books and 'catalogues raisonnés' of artists discuss primarily the  qualitative evaluation of all facets of artworks, they do contain also quantitative data of many types. Obviously, historical dates of creation, of exhibitions, of ownership, loss or destruction - together with geographical data - are essential information. Also number of replicas, of dissemination by engravings and subsequent imitations by other artists are valuable data and are indisputable if known. The spreading and popularity of motifs and style can be analysed in quantitative terms. Equally, the economics and market related aspects of art production are relying on 'quantities'. The 'quantitative approach to art history' is a relatively new branch and its importance will steadily increase in the digital age of art history because more quantitative data become available and can be handled by new digital technologies (5).

Some preliminary remarks on statistics in art history

About sampling a thematic collection

The author of a 'catalogue raisonné' of a given artist may hope for an exhaustive list of artworks, including all extant and lost or destroyed works if all public and private information is available. On the contrary, a thematic collection can never be exhaustive. The number of artworks of the selected theme by an unknown number of artists is indefinite. This number is called in statistics the 'population' and information about the population can only be gathered through samples. Sampling is called 'at random' if all artworks have equal chance to be selected. The sampling, however, is often 'biased' for many reasons. Then it is called 'convenient sampling'. This is practically always the case in a thematic collection because many artworks, never recorded, were lost and anyhow the information sources are annoyingly limited to the collector. Hence, the representativeness of sampling and the size of the samples are issues. Comparing samples is one of the statistical techniques we will demonstrate in these posts.

About terminology

Observations are the artworks compiled and described in the Topical Catalogues (2).
Frequencies are the numbers of observations, which can be ordered in an interval scale (in this first application: the chosen time scales) and in a nominal scale (in this application: the regional categorization of the artists, i.e. the four regions discussed).
A table of ordered frequencies is called a contingency table. It can contain marginal totals and grand totals of frequencies.
Relative frequencies are frequencies divided by their marginal or grand totals. They are often expressed as frequency percentages.

About the types of statistics

Descriptive statistics is concerned with the ordering of observations, selection of scales, presentation in contingency tables and foremost with graphical visualization, i.e. simple-to-understand graphs, always the first and essential step in any statistical analysis of data. Descriptive statistics is also a set of brief descriptive measures, such as the mean and measures of variability.
Inferential statistics is concerned with how to draw conclusions about a 'population' on the basis of 'samples'.

First application: Descriptive Statistics

The contingency table of the time distribution of the frequencies of artworks in four regions and its graphical presentations in historical diagrams


In order to compare the frequencies in the four regions (Italy=IT, France=FR, Low Countries=LC, German, Switzerland & Central-European countries=GSCE), we established the contingency table for ten intervals, i.e. the time-periods of 50 years from 1500-1549 till 1950-1999. Thus the total of 10671 artworks, which includes works before 1500 and after 1999, is harmonized and reduced to a grand total of 10242.


Table I.1 (Click to enlarge)
A historical diagram is a bar chart with the frequencies (numbers of observations) on the vertical y-axis grouped into the adjacent, non-overlapping intervals (the time-periods of 50 years) defined on the horizontal x-axis.
Fig. I.1

Since the marginal totals of the four datasets are quite different, we prefer to use the relative frequencies (rf %) (5). Furthermore, a 3-D graph has the advantage of a better visual impression of the historical time distribution of the artworks in the four regions.
Fig. I.2

 Coping with uncertainty of dates of artworks

 The date of creation of an artwork is very often uncertain and frequently simply given as the time period of the active life of the artist. This means that the assignment of an artwork to a given interval of 50 year is highly questionable. A way to cope with this uncertainty in statistics is by calculating moving averages of overlapping intervals of 50 years. Thus, we calculate the arithmetic average of the frequencies of the intervals 1500-49 and 1550-99, and we assign this average frequency to the new interval 1500-99. We calculate then the average frequency of intervals 1550-99/1600-49 and assign it to interval 1550-1649. We shift forward till the last interval 1900-99 and this means that now only nine intervals can be distinguished with different totals. Furthermore, the arithmetic average is not necessarily an integer number. In other words, we created four different subsets of the original full datasets.
Table I.2 (Click to enlarge)
Transforming the original data in this manner is a regular statistical method in time series analysis to smooth out  fluctuations of uncertain observations. The result of the method is most striking in a historical diagram of the frequencies in the Low Countries where many artists, fond to depict Venus, were active in the periods 1550-99/1600-49. The time distribution of the 'moving average' frequencies is more reasonable.
Fig. I.3

The cumulative frequency percentages

Yet another way to present the data is by calculating the cumulative frequency percentages. The historical diagram of these percentages admits easily for a classification of the four datasets from Table I.1 into
* the group Italy (IT) and Low Countries (LC) with cumulative frequency of 50 % around 1600-50;
* the group France (FR) and Germany, Switzerland, Central-European countries (GSCE) with cumulative  frequency of 50 %  around 1750-99.
There is clearly a shift of popularity for the iconography of Venus of about 150 years between these two groups. The curve of the total dataset divides distinctly both groups.
Fig. I.4

A further conclusion of this purely descriptive exercise is that there is a strong decline of the frequencies in both  Italy and the Low Countries from 1750 onwards (percentages ranging between 8 and 2 %), while frequencies are still high in France and Germany, Switzerland and Central-Europe up to 1999 (percentages ranging between 15 and 8 %). It is indeed remarkable that the popularity of the Venus-iconography remained fairly constant in Germany, Switzerland and Central-European countries throughout the period 1500-1999.

This result is probably not a discovery for an art historian with expertise in the given thematic domain. But at least the quantitative approach is novel. The result enhances our understanding of the persistence of the Aphrodite-Venus myth in Modern Times and it could possibly underpin scholarly research in the domain (7). It would be interesting to compare this result with data extracted from related  thematic monographs (8).

The next post will explore how the differences among these datasets can be measured with statistical techniques.

Notes

(1) Evidently, these posts are not meant to be a course on statistics. Interested readers should consult scholarly textbooks on statistics, especially those written for the 'soft' sciences. A standard textbook is 'Nonparametric Statistics for the behavioral sciences' by Sidney Siegel, first published in 1956 by McGraw-Hill Book Co in its Series in Psychology (ISBN 07-057348-4) and revised in 2001.
(2) The Thematic Research Collection is fully described in my website 'Venus Iconography'



The data are compiled and published in Topical Catalogues of the Venus' iconography in different European regions. Presently catalogues of four regions (Italy, France, the Low Countries, Germany, Switzerland and Central-European Countries) were published. A fifth catalogue of Eastern-, Southern-, Western- and Northern-European Regions  is scheduled for 2013.  The methodology of the compilation is fully explained in the websection 'Topical Catalogues'. The catalogues are available as fully searchable pdf eBook or paperback book or as hardcover book. Read the Previews.
Readers interested in the quantitative approach in art history are kindly invited to contact the author directly.

(3) See chapter 'Quantité et qualité' in 'Le Miroir des idées - Traité'  Mercure de France, Paris, 1995, pp.205-208.

(4) For an example of a discussion 'in infinity' about quality in the arts, see  'What Distinguishes a Masterpiece?' in  the LinkedIn group 'Art Collecting Network' starting January 10, 2013 with numerous comments continuing for several days.

(5) See also my webpage 'Who's afraid of the quantitative approach ?' where one can read in attachment the Introduction of "L’ Art et la Mesure - Histoire de l’ art et méthodes quantitatives" edited by Béatrice Joyeux-Prunel, Editions Rue d’Ulm, Paris, 2010, 600 pages. A more recent article by the same author: 'Chiffres et cartes. Enjeux d’une « histoire totale » de l’art'. See also ARTLAS, a digital atlas of arts and literature history which combines spatial, social, cultural, and esthetic questionings, with a narrative/descriptive approach, and visualization techniques, including charts and maps created with GIS technologies (Geographic Information Service).
About 'Art versus Sciences' and, among many other topics, about 'Metric Iconography' (in 'Individual Artists - Leonardo Self-Portraiture'), see the fascinating website 'Art Investigations'  by Christopher W. Tyler,  Smith-Kettlewell Eye Research Institute, San Francisco.

(6) The first dataset ('The Italian Venus') with 1840 works, was compiled in 2006-07. The data sets of 'The French Venus' and 'The Venus of the Low Countries' with  2997 and 2636 artworks were compiled in 2008 and 2010, respectively. Meanwhile the database increased on this date, respectively with 2283, 2482 and 750 records, which will be compiled in revised catalogues. The assumption is made that the adjusted relative frequencies would have time distributions quite similar to the ones presented here.

(7) A recent example of scholarly investigation: "Venus as Muse – Figurations of the Creative. A conference addressing concrete cultural figurations of Aphrodite|Venus" January 18-19, 2012 Internationales Kolleg Morphomata, Center for Advanced Studies, University of Cologne.
(8) The largest related thematic monograph known is 'Faszination Venus. Bilder einer Göttin von Cranach bis Cabanel' or “Venus, vergeten mythe – Voorstellingen van een godin van Cranach tot Cézanne" edited by E. Mai. A catalogue including 17 topical contributions with 234 illustrations and 188 artworks (paintings, drawings, prints and sculptures) 527 pp  ISBN 90 534933 87 and published at the occasion of a series of exhibitions in 2000-01 in Cologne, Munich and Antwerp. See here.

  

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