Greek Doric Temples
Statistical Correlation/Regression: Results & Analysis
An explanation that contains predictions should at a minimum not only rule out most alternative theories, it should establish its theory as more credible than its negation. [Also, within]…models that generate data, the expectations are that the generated data will correspond with the real data corpus.
[Zubrow 1973:245-6]
The problem of formulating a system of proportion may now be dealt with from a perspective of ordered sets. One statistical technique designed to show relationships between proportional variables is the linear regression equation. This statistical method attempts to predict the exact value of one component as it relates to another by using a straight-line relationship between the two variables [Blalock 1960]. The coordinates for two sets of values are plotted on a graph and follows the path through the points that represent the average deviated value. This path “…minimizes the sum of the squared deviations of points from the line, that is, the least-square best fit” [Yates 1974:68]. Thus the sum of the squares of the distances of vertical lines from each data point to the least-square line will result in a number of less than a “…comparable sum of squares from any other straight line” [Blalock 1960:373].
“Once this ‘best fit’ line has been determined, it is characterized by parameter 'a' the intercept of the line with the 'Y' axis, and parameter 'b' the regression coefficient, which indicates the slope of the line. In the simplest terms, the calculated line shows that for every unit increase in one set of coordinates, a corresponding unit increase can be precisely determined in the value of the other set of coordinates. [Yates 1974:69]
The formula for calculating proportional means, which determines clustering along a straight line for two sets of variables, is Y=a+bx, where 'Y' is the independent variable; 'x' is the dependent variable; 'a' is the intercept with the 'Y' axis; and 'b' is the co-variation of 'x' and 'Y,' divided by the sum of the squares in 'x' and represents the slope of the line.
The formula for measuring the amount of change in 'y' with each unit change of 'x' is 'b' (regression):
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[Blalock 1972:373]
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The following is a list of the variables used for the statistical test:
Dependent Variable: the axial peristyle which defines the proportional rectangle (AXLL).
Independent Variables:
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width of temple using the sum of column interaxial measurements (AXLW).
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column base diameter (COLW)
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column height (COLH)
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triglyph & metope width (TRI-METW
The following is a list of the temples used for the sample where accurate values are available.
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≠ It should be noted that some structures are so poorly preserved that only the stylobate and/or portions of the crepis are preserved. In these cases, the excavators have attempted to form their reconstructions based on the best available information. When this occurs, the actual interaxial measurements are only estimates.
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The statistical results show the strongest linear relationship between temple interaxial width and length. More specifically, with every increase in temple width, there is an exact and corresponding increase in the length. It also shows the independent variables (temple width) have a remarkable predictive capacity (r), for the dependent variable temple length.
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The breakdown of the type temples under investigation indicate that type 6 12 temples have a noticeable break in the ratio continuity after Aegina Aphaia ca. 490 B.C., the usually accepted terminus between the Archaic and Classical periods. Those type 612 Archaic temples of Metapontum Hera (b=2.1769), Delphi Athena (b=2.1704), and Hermione Poseidon (b=2.1795) all have width/length ratios that are best expressed in a ratio of @13:6 or 2.175. Neither Tobin’s [1981:348] Archaic rule nor J.J. Coulton’s [1974:83] “Sicilian rule” adequately explain these deviant examples which clearly break from the rest of the temple group with a ratio of 2.2367. A similar phenomenon occurs in type 613 temples where a discrete break occurs between the Archaic and Classical periods (535 B.C. and 490 BC), when all temples begin to conform to a new and rigidly structured proportional rule.
The example of Athena at Assos (560 B.C.) for one, has a width/length ratio that is 8% deviated from the norm. The remaining Archaic temples within this class (Isthmia Poseidon 460 BC, W:L = 2.4054; Delos Apollo 475 BC, W:L = 2.3999; and Paestum Athena 530 BC, W:L = 2.3972), appear to follow the Tobin rule of Archaic temple proportions (12:5 = 2.40), all other type 6 13 temples follow a proportional mean that adheres to a value of 2.4456. At the surface, then, one could make the assumption that E.F Winter [1978:153] makes: “…at least during the Archaic period, there was no consistent and orderly development of temple plans….”
If one agrees with Winter, Archaic period buildings could be removed from the data set and the numbers recalculated.
The results of the Classical Period temple statistical correlations show an exceptionally high confidence of predictability for each Type 6 sub-type group. These results, however, contradict the view that Classical architects did not use “…specific rules of proportion [or] have a theoretical basis [in their design,” [Coulton, 1975:67-68].
What can be determined from the results is that temple peripteral dimensions, as defined by the axial peristyle at least, seemed to have formed the initial step in temple construction. Colton’s [1974:66] idea “…that once the stylobate dimensions had been defined, they were regarded as fixed dimensions to which the rest of the design must be adjusted” seems to be accurate. Although even with the aesthetic modifications of end column contractions, there appears to be no variation in the proportional rule for Classical period temple design. This applies to all Classical period type temples throughout the Mediterranean with no distinction between geographic regions.
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With regard to column heights for Archaic period temples, J-P Adams (Temple de Hera, a Paestum, Rev. Arch. 2[1973:219-236]) had a diagram of the temple of Hera II (Poseidon) at Paestum. A portion of that diagram employed an interesting geometric calculations showing a connection between column spacing to that of the column heights. In order to test his calculation, I used temple D at Selinunte, especially since that temple showed a significantly short stature to its columns. According to Adams’ diagram, the column height might have been determined by drawing an arc between three columns; column one being the interaxial starting point and column two separating the others, with the third column being the terminus of the arc at the interaxial height of the column abacus. The significance of the diagram is that the formula seems to work.
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In the case of temple D at Selinunte, the column height is measured at 8.94 meters. If we recreate the diagram used by Adams, we see that the column height comes out exactly as it is predicted. This seems to be a useful tool for determining column heights for archaic temples, although more research is needed to make it the rule.
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