Measurements

Each plan (seen as a spatial system linked by indoor accesses only) was translated into a set of dots and lines representing the spaces and their connections. As previously discussed, one dot was assigned for each room regardless of its geometrical form and for each lump of space connecting those rooms, according to bends and recesses. General procedures and restrictions

adopted in the process were described in the item 1.4 of chapter 1.

The graphs resulting from the system of dots and lines — herein referred to as access or permeability graph — were translated into numerical measurements by the software application developed for the purpose at the UAS-Bartlett. Figure 3 displays a plan dissected into a minimal living complex of interior spaces (as shown in figure 1), its resulting access graph, and the measure of asymmetry (RRA) of each space. RRA values are arrayed in ascendant order, (from more integrated to more segregated - less to more asymmetry) alongside the label of the space each value represents (or purpose, if label is not shown in the plan), and the number that identifies the space in the access graph.

The syntactic analysis in the present study deals chiefly with RRA (Real Relative Asymmetry) values. This measure enables comparison across

systems which differ in number of spaces by eliminating the effect that size can have on the level of relative asymmetry values.’'® As already stated, the higher the asymmetry (or RRA value) the more segregated a space is in relation to all others within a network of connected spaces, the lower the RRA value, the more integrated that space is.

The measure of integration, by revealing the exact bearing of a joint in a spatial structure, a relation not easily perceivable from the plan itself, shows how accessible that space is meant to be, in other words, how desirable whatever goes on and whoever enacts it in a certain space is to come into contact with what goes on in the others or, how welcome the people likely to occupy one room are by the occupants of other rooms. The integration values of the cells within a system of domestic spaces are then accurate clues for the norms underpinning the ways in which the network of walls and doorways is

constructed to halt, hinder or facilitate interaction among inhabitants, as well as between these and outsiders, and, therefore, for disclosing sociocultural content crystallised in space.

A high mean RRA value in a complex signifies high levels of asymmetry within the spatial network thus indicating that many spaces are segregated and, therefore, the access to them is highly controlled by other spaces which may, or

not, also be segregated from all others.

On the other hand, a wide range of differentiation in RRA values in a same system indicates that some spaces have easy access to and strong control over a number of segregated areas. The more structured a spatial network is the higher differentiation in integration values is expected to be found among its spaces. A measurement called BDF’'* (base difference factor), which compares a set of any three different values, can assess differentiation in

integration within a complex by comparing the mean integration (mean RRA) of the system, the RRA value of its most integrated space (minimum RRA) and the RRA value of its most segregated space (maximum RRA). A system with no differentiation will equal 1. Lower values translate more differentiation.

The assumptions behind the articulation of the two syntactic measurements, RRA and BDF, can be summarised as follows:

1) High mean RRA and high BDF values characterise segregated and non­ differentiated systems, here believed to translate networks in which most spaces are segregated from all others, in other words, where the mixing of people and activities is generally inhibited by the layout.

2) High mean RRA and low BDF values spell segregated but differentiated complexes and suggest that in these systems most spaces are segregated but with a few islands of well connected cells, a fact that may indicate privileged access and control of some spaces over the rest of the domestic complex.

3) Low mean RRA and low BDF values reverse the picture to one of a generally integrated system enclosing a few spots of highly segregated spaces. This configuration may translate discrimination against certain activities which are outcast from the general pattern of encouraged interaction.

4) Low mean RRA and high BDF values outline a network where integration is indiscriminately shared among most spaces. This mode of articulation

suggests a pattern of little hierarchy and greater informality in which the interplay of actions and people is generally promoted.

^^®The base difference factor Is an entropy-based measure adapted from Shannon’s H- measure for transition probabilities. See Millier, Hanson and Grahan, 1987, op.cit.p.365.

Table 3 arrays the cases in the sample Identified by their numbers and displays: year of publication; presumed association with a certain social layer, as identified in the previous chapter; minimum, maximum and average RRA values within the complex of interior spaces; BDF value; RRA value for each of the main day functions and the order (more integrated to more segregated) in which they rank.

Figure 3.1 compares mean RRA and BDF values for the whole sample. The R-squared of 0.191 and a significant probability value (p.=0.0001) indicate that the systems which present a large number of very integrated spaces (low mean RRA) tend to be more differentiated (low BDF) and those with a high average segregation (high mean RRA), less differentiated (high BDF).

Mean RRA values are correlated with the time (year of publication) and with a series of variables concerning the size of complexes in the sample in figure 3.2. Although statistically significant (p.= 0.0001 ), the week correlation between mean RRA and number of spaces (R-squared = 0.029) suggests that a large house does not necessarily have to be a complex of segregated spaces. Average RRA values correlate slightly better with time (R-squared 0.03, p.= 0.0001) showing a tendency for more integration in later houses. There seems to be no relation between integration levels and the number of function cells but that between the mean integration and the number of transition spaces is quite significant (R-squared = 0.09, p.=0.0001), showing that complexes presenting a more segmented circulation network tend to be more segregated. This seems to reflect directly in the relation between integration and number of storeys (R-squared = 0.174, p.=0.0001) since in higher houses there is an obvious need for extra transition routes — staircases and landings — for negotiating multiple floors. But the strongest correlation was found to be that regarding mean integration and the ratio between function and transition spaces (R-squared 0.248,jp.=0.0001). it indicates that complexes in which the proportion of transition spaces is lower tend to be more integrated.

Figure 3.3 shows the correlation between the same set of variables examined above and the differentiation in levels of integration in the

transition spaces (R-squared 0.012, p.=0.0133), the number of storeys (R- squared = 0.016, p. =0.0047), both correlations being weak, and the proportion of transition to function spaces (R-squared 0.076, p.=0.0001), which is quite significant. Two outliers were disregarded in the observations involving the ratio of function to transition spaces. These are bungalows (houses 396 and 397) with a single transition space and six and seven function spaces,

respectively.

The procedures developed above suggest that a highly segmented circulation network contributes to keep spaces well apart, as often stressed in the

reviewed literature. Observations in the previous chapter have shown that the proportion of transition to function cells tend to reduce with time. This may relate with the inclination for more integrated complexes in later buildings and point towards lesser demands of privacy in British homes.

3.2.1.1. Of social groups and structurin g

The next step was to compare the levels of average integration/differentiation in the complex of interior spaces among plans supposedly designed to house distinct social groups, as found in the previous chapter (table 3.1).

Plans expected to have been designed for the lower middle class (203 cases), present the highest average level of segregation (1.527 av. mean RRA) and the weakest differentiation (av. 0.836 BDF). Middle-of-the-social-road ones (170 cases) are the most integrated (1.475) and the most differentiated (0.826) and at the top of the social ladder (127 cases), houses supposedly inhabited from the well-to-do middle class upwards, feature in-between, being just a little more integrated (1.52) than those of the lower group and slightly more differentiated (0.833).

T-tests (one group, two-tail) indicate that the variation between the average mean RRA for the whole sample (1.508) and that for each social cluster is statistically relevant in the bottom group (p.= 0.0264), and specially in the middle one (p.= 0.0002), the former thus comprising complexes which are more segregating, on average, and the latter assembling more integrating ones. The variation between the average mean integration of the whole

sample and the upper cluster was shown to be insignificant (p.= 0.1542).

Unpaired T-tests (x-y, two-tail) for variation among the average mean RRA values of upper, middle and lower middle class groups (1.52, 1.475 and 1.527 aV.mean RRA, respectively) show that between the upper and the middle groups as well as between the former and the lower population (p. = 0.0785 and 0.772, respectively) the variation is neglectable whereas that between the middle middle class and the lower middle class cluster is quite significant (p.= 0.0027). The approximate levels of mean integration between the top and the bottom clusters look all the more striking because in the latter the proportion of transition spaces (1.6) is significantly (p.= 0.0126) less than in the former (1.4).

As far as differentiation in integration within the complexes go, middling plans were shown to be significantly (p.= 0.0005) more differentiated (0.826 BDF) than the average for the whole sample (0.832 BDF), and smaller ones (0.836 BDF) significantly less so (p.= 0.0204), whereas at the top end, (0.833 BDF) that difference is not significant (p.= 0.5606). The variation in mean BDF between the upper and both the middle and the lower populations is also irrelevant (p.0.1194 and 0.3683, resp.) whereas that between middle middle class and lower middle class complexes is, again, significant (p.= 0.0063).

It looks as if nineteenth and early twentieth century middle middle class houses, as represented in the sample, define a profile that sets them into a configuration niche of their own by assembling complexes which are more integrating and more differentiated than those of other social clusters, particularly the ones below their status boundaries.

The data is viewed for successive periods in table 3.2. Average values show a consistent shift towards more integrated complexes in time, a tendency

already indicated by the negative correlation between mean RRA and year of publication (fig 3.2a). A slight move towards less differentiation is also

suggested, however, tests indicate, this is statistically insignificant. Neither tendencies appear to follow a simultaneous move across distinct social clusters, though.

(1.568 av. mean RRA) and as differentiated as medium-sized ones (0.828 BDF) which present an average mean RRA value equal to that of small houses

(1.541), these being slightly less differentiated (0.833) than those in the middle bracket.

The ratio between function and transition spaces is very low (1.2) among upper complexes, corroborating the idea that transitional segmentation goes along with segregation. However, the smaller proportion of transition spaces among lower middle class plans, as compared to middle middle class ones, does not appear to have contributed much to Increase integration in their systems. Both groups show an equal average mean RRA value but quite diverse

functionAransition ratios, on average (1.5 and 1.3, respectively), although this variation is not statistically significant (p.= 0.922).

Figure 3.4 shows the correlation between mean RRA and BDF values across class and time. Perpendicular lines representing the average mean RRA (1.508) and the average BDF (0.832) values for the whole sample were drawn on the scattergrams to help visualise how complexes relate individually to the broad configuration tendency of the sample.

Most upper complexes tend to be either generally or discriminately segregated, that is, dots cluster mainly in the high mean RRAAiigh BDF and in the low mean RRA/low BDF quarters of the diagram. Among middling cases most dots

cluster around the intersection of the average lines, suggesting a fairer balance between integrated and segregated spaces within these complexes, a situation rùuÿl liy biiriiiai lO lhal ai II le bottom of the social scale, except that here highly differentiated complexes are not found.

After 1893 upper dwellings (tab.3.2b) show no alteration in average mean RRA but less average differentiation (1.568 RRA, 0.835 BDF) and middle middle class ones tend to become more integrated and more differentiated (1.487 RRA, 0.826 BDF). At the lower rank, an increase in integration goes with a reduction in differentiation (1.535 RRA, 0.838 BDF), tbese complexes remaining thus as the least differentiated.

Size and shrink in height. Among larger plans, a less fragmented circulation system, as compared to the previous period, does not appear to help pull complexes more closely together, a fact that, although not statistically significant, casts again, a doubt on the notion that more transitional segmentation equals more segregation.

If the scattergrams in figure 3.4a and b are compared, it can be seen that the distribution of upper plan dots is not very different from that of the previous period, apart from the fact that they are now more numerous. On the other hand the integrating half of the middle middle class diagram looks a lot denser than the segregation half as well as than it did in the previous period. Small plan dots cluster more tightly around the intersection of the average lines.

During and immediately after the war upper middle and middle middle class cases are too few to stand comparison. Small houses continue to grow in size, do not alter in height, reduces the proportion of transition to function

spaces, present the same average mean integration of the previous period and become slightly more differentiated (0.836 BDF).

After the war, however, the relationship integration/differentiation alters

radically. All groups become more integrated but whereas the change in the lower middle class houses is weak (1.5 RRA), the push towards more

integrated complexes is much stronger In middle-sized houses (1.433 RRA) and even more dramatically so at the top rank which shifts from the averagely

most segregated complexes in earlier times, to the most integrated ones (1.424 RRA). T-tests (unpaired two-tail) indicate that the gain in integration is quite significant between upper prewar and postwar plans (p.=0.0073) and, specially, between middling plans published from 1843 to 1893 and their postwar counterparts (p.=0.0007) whereas the gain in integration in the lower cluster is irrelevant throughout the period.

The general move towards higher integration, however, does not necessarily correspond to more differentiation as might be expected. Smaller plans alter little in terms of both average integration and differentiation, fy/ledium

dwellings although gaining more integration maintain a level of differentiation practically unaltered (0.827 BDF) from what was found before the war (0.828

and 0.826 BDF). Upper complexes, however, become less differentiated (from 0.828 before 1894 to 0.841 after 1923). Thus, the strongest push towards less integration hierarchy in upper middle class houses goes along the strongest move towards average integration, an inverted tendency in most systems.

Upper and middle middle class houses shrink in size and height whereas at the bottom band, plans still present a slight growth in size. The

function/transition-space ratio shows a reduction in the proportion of transition spaces in postwar larger dwellings as compared to turn-of-century ones and similar to that observed between these and earlier cases. As this later shift does seem to contribute towards more integrated complexes whereas the previous one does not, it is suggested, again, that the relationship between a less complex circulation network and higher levels of integration may be a relative one. This is incidentally emphasised by the fact that postwar larger houses are significantly (p.= 0.0329) more integrated than small ones but their variation in function/transition space ratio is not (p.= 0.4585).

Scattergrams show (fig.3.4c) that the dots representing upper middle class plans migrate from the segregating to the integrating and from the differentiated to the nondifferentiated halves of the graph quite radically. They also show that a highly integrated and highly differentiated model prevails among middling complexes and reveal a tendency for smaller plans to spread along the low mean RRA/BDF and high mean RRA/BDF quarters, similarly to what was found for prewar upper plans. This emphasises the existence of

configurational similarities, among upper and lower middle class houses, as previously suggested.

If findings are to be trusted it looks as if whereas in postwar middling and smaller households a significant number of spaces will remain away from the mainstream of movement, among upper houses, segregated spaces may have become very few.

In order to assess the effects of geometrical restrictions imposed by the plot on the internal structuring of spaces, some of the procedures above were

houses (table 3.3).

Figures suggest that the type of ground occupation does tend to encourage general segregation. Terraced houses show the highest average RRA as well as BDF values and detached ones the lowest for cases published until 1922 (tab. 3.3a/b/c). However, this is mainly due to the larger town houses which, not surprisingly, define the most segregated (1.884) and least differentiated networks (0.862). On the other hand, a terraced occupation does not imply a

necessary increase ini segregation levels since postwar lower middle class terraced (tab. 3.3d) complexes are significantly more integrated (1.491 RRA) than their semi-detached counterparts (1.547).

The question of the importance of the circulation network for defining

integration looks a little clearer. It seems that the highly fragmented transition routes in upper town houses greatly affected the average integration values of prewar upper middle class cases. The relation between a small proportion of transition spaces and more integration appears stronger now but exceptions to the rule still suggest that less extreme levels of high transition segmentation than the ones found in large terraced houses may have little influence on enhancing segregation.

Nineteenth century upper and middling semi-detached cases, for instance, have very different average mean integration, yet the the same proportion of transition spaces (tab .3 .3a); the same can be said about postwar small

terraced houses, which are more integrated than semi-detached ones although these present a much smaller proportion of transition to function spaces

(tab.3.3d).

The reduced number of postwar large and medium semi-detached (table 3.3d) and terraced houses do not allow comparison between these and prewar cases. The move towards more integrated systems that was verified for the sample as a whole, also holds when detached houses only are

considered, except that now it can be seen that upper middle class plans, too, become more integrated already in the decades around the turning of the century although T-tests (unpaired, two-tail) indicate that the increase in integration is more significant between plans published before 1893 and

postwar ones (p.= 0.0406 as opposed to p.= 0.0527 between nineteenth century and turn-of-century cases).

The almost disappearance of large terraced and semi-detached plans from the pages of the researched journals in later times is being taken as an indication