SPACIOUSNESS AND BOUNDARY ROUGHNESS

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Spaciousness and Boundary Roughness Arthur E. Stamps, III and V. V. Krishnan Environment and Behavior 2006; 38; 841 DOI: 10.1177/0013916506288052 The online version of this article can be found at: http://eab.sagepub.com/cgi/content/abstract/38/6/841

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On behalf of: Environmental Design Research Association

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SPACIOUSNESS AND BOUNDARY ROUGHNESS

ARTHUR E. STAMPS III extracted his PhD from UC Berkeley in 1980. The work focused on statistics (done in the psychology department), philosophy (in the Graduate School of Business), and futures research (Department of City Planning). He has published more than 80 articles and is an associate editor for psychology journals. Current research focuses on cognition and affect. He plays at the Institute of Environmental Quality in San Francisco. V. V. KRISHNAN received his PhD in mechanical engineering in 1972. He currently teaches control systems, systems modeling, instrumentation, computer methods, and applied statistics in the Engineering Department at San Francisco State University.

ABSTRACT: This article reports how strongly boundary roughness predicts impressions of spaciousness. In one experiment, 16 rooms with fractal walls were created in CAD simulations and 49 respondents rated the rooms in terms of spaciousness. In a second experiment, 16 respondents rated spaciousness for an additional 12 rooms with different wall systems. Fractal rooms with rough walls were judged as being more spacious than rooms with smooth walls, and opening bookshelves also made rooms seem more spacious. Thus, results from both studies indicate that boundary roughness makes rooms seem more spacious. Quantitative guidance is provided to assist future research. Keywords:

enclosure; fractal dimension; area; light

This article addresses the question of whether roughness of a room’s boundary influences impressions of spaciousness. Theory can help us understand why spaciousness is worth inquiry. Although there are many alternative theories that might apply, such as Hediger’s safety theory (Hediger, 1950/1964, 1955/1968); prospect and behavior theory (Appleton, 1975/1996, AUTHORS’ NOTE: Arthur E Stamps III, 290 Rutledge Street, San Francisco, CA 94110 USA, or at [email protected]. ENVIRONMENT AND BEHAVIOR, Vol. 38 No. 6, November 2006 841-872 DOI: 10.1177/0013916506288052 © 2006 Sage Publications

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842 ENVIRONMENT AND BEHAVIOR / November 2006

1990); ecological psychology (Gibson, 1979/1986); isovist theory (Davis & Benedikt, 1979); and the coherence, legibility, complexity, and mystery (R. Kaplan & S. Kaplan, 1989; S. Kaplan & R. Kaplan, 1982); space limitations preclude full discussion of each of these theories. For the connections to prospect and refuge theory, see Stamps (in preparation); for ecological psychology, see Stamps (2005a); for isovist theory, see Stamps (2005b); for a discussion of the coherence, legibility, complexity, and mystery theory, see Stamps (2004b); for an application of Hediger’s work to prospect, refuge, and escape as predictors of fear of crime, see Fisher and Nasar (1992). Accordingly, this article will concentrate on ideas related to Hediger’s (1950/1964, 1955/1968) observations regarding effects of spatial components on behavior. According to Hediger (1955/1968), safety is the most important function an environment can provide. Consequently, it is important to maintain constant watchfulness and constant awareness of locations of regions relative to oneself from which one can be attacked or to which one can move to safety. Thus, two abilities with obvious effects on safety are the ability to move and the ability to perceive. If movement is restricted, then escape is prevented and the animal is trapped. Movement is restricted by regions that block motion, such as walls. Enclosure is thus directly related to restriction of movement and hence to the critical biological purpose of safety. Because in most environments, long distance perception by humans is accomplished through vision, range of vision has a similar relationship to safety: The more one can see of potential enemies and the less they can see of you enhances your chances of survival. Thus, where prospect and refuge theory emphasizes range of vision, Hediger emphasized the evolutionary importance of ranges of both movement and vision. Flight distance is a crucial concept in Hediger’s theory. It is a specific distance to which, if intruded within, an organism will react by moving until the intruder is again beyond the flight distance. One consequence is that if an animal is confined to a region the horizontal dimensions of which are less than its flight distance, the animal will be unable to move away if intruded on. This limitation will cause stress and impair the health of the animal. Thus, anything that may make a spatial region seem more spacious could result in a decrease of environmental stress—hence, a theoretical motivation for trying to make regions appear as spacious as possible. Before embarking on the empirical literature, it may be useful to differentiate two related concepts: enclosure and spaciousness. In verbal terms, to enclose is “to surround (with walls, or other barriers) so as to prevent free ingress or egress,” whereas spaciousness is “of vast, large, or indefinite superficial extent or area, widely extended, extensive” (The Compact Edition of Downloaded from http://eab.sagepub.com at PENNSYLVANIA STATE UNIV on April 17, 2008 © 2006 SAGE Publications. All rights reserved. Not for commercial use or unauthorized distribution.

Stamps, Krishnan / BOUNDARY ROUGHNESS 843

the Oxford English Dictionary, 1971). A covered sports arena will be quite spacious but fully enclosed, whereas a zoo cage or a prison cell will be quite cramped but very open. Logically, both spaciousness and enclosure presuppose an observation point and blocking region (the boundary). Enclosure is a function of how strong that blocking is: A boundary made of a brick wall will seem more enclosing than a boundary of the same size and at the same distance but made of chicken wire. Because the strength of blocking movement through something is permeability, the concept of enclosure logically presupposes permeability. Spaciousness then becomes the apparent size of the region within the boundary. The connection between spaciousness and permeability is empirical. The relevant data are summarized in the next section.

PREVIOUS FINDINGS ON SPACIOUSNESS

Martylink, Flynn, Spencer, and Hendrick (1973), in a study of lighting in an office, reported that lighting levels ranging from 100 cd/m2 to 1000 cd/m2 correlated at r = .27 with judged spaciousness. Kirschbaum and Tonello (1997) also had people rate an office in terms of spaciousness under different amounts of light (280 to 1235 cd/m2). It was reported that 13% of the variance in judgments of spaciousness could be attributed to amount of light. Imamoglu (1973) had participants rate spaciousness for a room with three different amounts of furniture. Judged spaciousness and percentage of floor covered by furniture correlated at r = –.54. Benedikt and Burnham (1985) studied floor area and four other spatial measurements of rooms that looked similar to hotel lobbies. A strong effect of visible floor area on judged spaciousness was reported. Coeterier (1994) reported a study of boundary height, boundary variation, soil texture, isolated elements in space, light, and coming from small or large spaces for landscapes. Munakata and Oi (personal communication, January 4, 2004) constructed rooms with or without a window, of four ceiling heights (2100mm, 2400mm, 2600mm, and 3000mm) and, for the room with the window, seven views with depths ranging from 3.6 to 18.3m. Participants sat in the rooms and provided ratings of spaciousness. Correlations of impressions of spaciousness with ceiling heights were r = .21 for the room without a window and r = .25 for the room with a window. Moreover, for the room with a window, the correlation between depth of view out the window and impression of spaciousness for the room correlated at r = .94. Franz, von der Heyde, and Bülthoff (2003) collected spaciousness data for museum rooms. Sixteen respondents rated 16 rooms shown in virtual reality for several scales, including spaciousness. Physical factors that influenced impressions of spaciousness Downloaded from http://eab.sagepub.com at PENNSYLVANIA STATE UNIV on April 17, 2008 © 2006 SAGE Publications. All rights reserved. Not for commercial use or unauthorized distribution.

844 ENVIRONMENT AND BEHAVIOR / November 2006

included floor area (r = .84) and proportion of boundary covered by windows (r = .12). Another study was done on 12 octagonal rooms that looked similar to either greenhouses or libraries, depending on the wall treatment. There were two areas: 77.25 m2 and 309 m2. The walls were panels that could be either clear glass or windows, thus permitting the creation of rooms with different amounts of visual permeability. Spaciousness was again related to floor area (r = .71) and percentage of walls that were windows (r = .56). In addition, because these effects were obtained in spaces with diverse functions (hotel lobby, museum, conservatory, library), the results tend to suggest that judgments of physical properties of environments were not confounded with judgments regarding projections of possible activities within those spaces.

SUMMARY OF FINDINGS ON SPACIOUSNESS TO DATE

Several physical variables have already been repeatedly found to influence impressions of spaciousness: floor area, light, and percentage of the walls that were windows (boundary permeability). In addition, single studies reported effects on impressions of spaciousness for amount of floor covered by furniture and depth of view out a window. Another possible variable — boundary roughness — was suggested by Wise (1988). Based on “the interior designer’s heuristic of increased spaciousness accruing from ‘the eye’s ability to move easily over a room’” (p. 75), it was hypothesized that the roughness of the boundary might influence spaciousness, with smoother boundaries creating an impression of larger spaces. I could not locate any empirical studies on how boundary roughness might or might not influence impressions of spaciousness, so the following hypothesis seemed to be ripe for inquiry: H1: Impressions of spaciousness ∝ smoothness of boundary.

EXPERIMENT 1: FRACTAL GROTTOS METHOD

Selection of Independent Variables

As explained in the appendix, the logistics of experimental design required some selection of independent variables. I chose four: room size, lighting,

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and two measures of roughness (fractal dimension and fractal recursion depth). Room size was chosen because strong effects had already been found and so it seemed time to find out if those effects could be replicated in a different venue. Lighting was chosen because it has direct relevance to the design of environments: If one wants to make a space seem larger, which is more cost-effective: actually making it larger or changing the lighting? The empirical data on lighting and spaciousness were less solid than the data on floor area and spaciousness, so there seemed to be a need for more data on lighting. There remained the issue of how to measure the main variable of interest: roughness. Roughness, as defined in The American Collegiate Dictionary, is “uneven from projections, irregularities, or breaks of surface; not smooth” (Barnhard, 1966, p. 1057). For scientific purposes, a more precise definition is required. One way to measure roughness objectively is to use the properties of fractal dimension and fractal recursion depth. These mathematical constructs were chosen because previous empirical research has shown that those variables are related to human judgments of roughness. In a pair of studies, fractal dimension was strongly related (.59 < r < .98) to judgments of roughness (Marchak, 1987; Pentland, 1984). Cutting and Garvin (1987) found that fractal recursion depth was more strongly related to human perception of surface complexity than was fractal dimension. Gilden, Schmuckler, and Clayton (1993) suggested that the human discrimination responses could be better predicted with the range of the fractal values rather than fractal dimension, so range of fractal values is a variable that needed to be controlled. These findings suggest that if fractal properties are used to create rough surfaces, three properties should be either designed in or controlled out: range of fractals, fractal recursion depth, and fractal dimension. Having decided on measures for roughness, there still remained the issue of how to design environments with intended fractal dimensions and recursion depths. Fractals tend to be highly photogenic and have attracted a large amount of attention. Excellent introductions to fractals include Mandelbrot (1977/1983) and Barnsley (1988/1993). For an introduction to the engineering references on fractals, see Russ (1995, pp. 262–270); for the architectural references, see Stamps (2002a). There are many ways to create fractals. Peitgen, Jürgens, and Saupe (1992) list computer routines for creating simple fractals. However, a different approach is needed to control for the three fractal variables that influence impressions of roughness (dimension, recursion depth, and range). Mandelbrot- Weirerstrass fractals allow that control. The equations needed to create Mandelbrot-Weirerstrass fractals are given in Hastings and Sugihara (1995). Figure 1 shows how the walls were created for this experiment.

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846 ENVIRONMENT AND BEHAVIOR / November 2006

Figure 1: Creation of Walls With Known Fractal Dimensions NOTE: Step A: Use the math given in Hastings and Sugihara (1995) to create a line with known values of fractal dimension and recursion depth. Import that line into a computer-aided drafting program (I use Microstation). Step B: Create a blank slab for the wall. The slab used in the figure measured 7m × 1m × 2.75m high. Think of it as a piece of clay. Step C: Use the line to slice the wall in a vertical direction. Think hot wire and plasticine. Steps D, E, F: Repeat steps A, B, and C, but this time slice the slab in the vertical direction. Move both Slabs C and F to the same location. The result is a surface (G) with the intended properties.

Selection of simulation media. Both experiments in this article used static color simulations to represent environments. This medium was chosen because a review of previous research of environmental simulation validity indicated that responses to static color images correlate at r = .83 (n = 185 scenes, .05 confidence interval [CI] = [.79, .87]) with responses obtained on-site (Stamps, 2000, pp. 101-113). Palmer and Hoffman (2001) extended the analysis to include 470 scenes. The revised estimated effect size was r = .78 (.05 CI = [.73, .82]). Gärling (1969a, 1969b, 1970a, 1970b) extended the work on simulation validity to judgments of enclosure. Findings indicated very high correlations between judgments obtained on-site and with static simulations. Gärling conducted a series of studies on the validity of measuring environmental enclosure. The stimuli were scenes of streets in a small town. Dependent variables included rated openness or closedness, actual depth

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(range: 20m to 140m), and actual area (range: 40m2 to 900m2). In one experiment, subjects rated openness and closedness on site in two ways: an overall impression and four impressions taken from four different directions. Correlations between the two methods were r = .65 for openness and r = .73 for closedness. Other findings included inter-rater reliability (.93 < r < .99) comparing actual size with ratings or magnitude estimation (.83 < r < .90), judgments obtained on site or from color photographs (.67 < r < .84), and judgments versus actual depth and area for four different media: on site (.79 < r < .91), color photographs (.90 < r < .91), detailed line drawings (.94 < r < .95), and undetailed line drawings (.61 < r < .89). STIMULI

Size and light. The stimuli were computer renderings of 16 rooms. The rooms were designed to test for four factors. For the factor of size, the levels were 3 × 3 m, 4 × 4, 5 × 5, and 6 × 6. Measurements were made from the outsides of the walls. Height was constant at 2.75m because of Nasar’s (1981) finding that height of rooms (range: 2.44 m and 6.10 m) correlated at r = .36 with impressions of security. Light was provided by a single bulb in the horizontal center of the room and 20 cm below the ceiling. Light levels were created at four levels: 10 cd/m2, 37 cd/m2, 136 cd/m2, and 500 cd/m2. These levels provided equal log changes in light level from really dim to really bright. The walls were created with lines with fractal dimensions of 1.1 (nearly flat), 1.37, 1.63, and 1.90 (very kinky). Because the fractal dimension of a surface is 1.00 plus the fractal dimension of its cross-section (Russ, 1995, p. 310), the fractal dimensions of the walls (boundaries) were 2.10, 2.37, 2.63, and 2.90. Recursion depths were 2 (coarse grain), 4, 6, and 8 (fine grain). Walls and ceilings were all made from the same material (red granite, reflectance = .65), and the camera location was constant (view angle: 1.29 radians × .86 radians; location: 1.7 m. above the floor). To give a sense of scale, a door was inserted into the back wall and a person was shown .75 m. in front of the back wall. Range of the fractal values was normalized to .75 m. The experimental design was a Graeco-Latin Square. Figure 2 shows black and white versions of the 16 stimuli. RESPONDENTS

Respondents were undergraduate engineering students. There were 49 respondents, of whom 37 were male. Average age was 21.5 years (SD = 5.5).

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Figure 2: Black and White Copies of the Fractal Rooms 848 Downloaded from http://eab.sagepub.com at PENNSYLVANIA STATE UNIV on April 17, 2008 © 2006 SAGE Publications. All rights reserved. Not for commercial use or unauthorized distribution.

Stamps, Krishnan / BOUNDARY ROUGHNESS 849

TABLE 1 Analysis of Variance, Experiment 1

Source Respondents Size Light Recursion depth Fractal dimension Residual Total

SS

df

MS

F

α

ωˆ 2

781.07 1377.36 9.88 6.59 0.00 1120.23 3295.13

48 1 1 1 1 731 783

1377.36 9.88 6.59 0.00 1.53

898.79 6.48 4.30 0.0

2e-129 .01 .04 1.00

41.7% 0.2% 0.1% 0.0%

NOTE: Dependent variable is rated spaciousness.

Task. Stimuli were presented in a class. The experiment was not announced ahead of time, so possible self-selection was controlled. Stimuli were shown in a PowerPoint Show. Two warm-up images were shown to help respondents calibrate their responses; then each stimulus was shown. Stimuli were shown until all respondents finished their responses. Average presentation time was about 20 seconds. Presentation order was randomized with respect to the independent variables. Respondents rated each stimulus on a scale of not spacious (1) to spacious (8). Sample size. The minimum required sample size was calculated using power analysis Cohen (1988). Because large correlations were previously found between roughness and fractal properties, we used Cohen’s criterion for a large effect size (f 2 = .35, R 2 = .26). For a repeated-measures experimental design with 16 stimuli, α = .01, power = .80, and effect size = .35, only three subjects would suffice. Because our budget allowed for more participants, sample size was not a controlling aspect of this study. RESULTS

Table 1 shows the repeated measures regression analysis. Actual room size had the largest effect on impressions of room size. The relevant effect size is the variance component, the estimate of which is Hay’s omega hat squared (ωˆ 2 ). The amount of variance in impressions of room size attributable to actual rooms was 41%, as compared to .2% for light, .1% to recursion depth, and 0% to fractal dimension. More detailed results can be obtained from the contrasts between levels for each factor. These results are shown in Table 2. The important datum

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850 ENVIRONMENT AND BEHAVIOR / November 2006

TABLE 2 Standardized Mean Differences Between Levels of Factors for Experiment 1

Levels

Stimuli

µ

× 3m × 4m × 4m × 5m × 5m × 6m

NDME IAKJ IAKJ POFG POFG BHLC

2.68 4.23 4.23 5.44 5.44 6.23

10cd/m 37cd/m2 37cd/m2 136cd/m2 136cd/m2 500cd/m2

PHMJ IDLG IDLG BOKE BOKE NAFC

4.67 4.71 4.71 4.78 4.78 4.43

2 4 4 6 6 8

PDKC IHFE IHFE BAMG BAMG NOLJ

4.39 4.72 4.72 4.81 4.81 4.65

2.10 2.37 2.37 2.63 2.63 2.90

DHAO CEGJ CEGJ PIBN PIBN KFML

4.62 4.68 4.68 4.57 4.57 4.72

Factor Size

3 4 4 5 5 6

2

Light

Fractal depth

Fractal d

F1,720

α

1.27

157.2

1e-32

0.96

97.0

1e-21

0.64

40.61

4e-10

.03

0.11

0.74

.05 .28

0.26 7.68

0.61 .005

.27

7.23

.007

–.07 .12

0.49 1.54

0.48 0.21

.04

0.14

0.71

.08

0.68

0.41

.12

1.54

0.21

d

NOTE: mse for respondents × stimuli anova = 1.49. To see which letter goes with which stimulus, please look at the figures. Letters in Stimuli column indicate individual stimuli: Thus “BHLC” means stimuli B, H, L, and C expressed the 6 × 6m level of the size factor.

is the effect size, which, for contrasts, is a standardized mean difference d. Contrasts between levels of each factor are shown in Figure 3. The contrasts between sizes were all large. The contrast between the smallest and —–– largest size, for example, was d = (6.23 – 2.68)/ 1.49 = 2.90. There were also large effects between each level of size (d’s of 1.2, .96, and .64). Parenthetically, these contrasts correlated highly (r = .99) with the ratio’s of the relevant sizes (3:4, 4:5, 5:6). Coincidence? Or were the subjects implicitly judging spaciousness on a log scale? For light, contrasts were

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Figure 3: Plots of Means of Levels of Factors for Fractal Rooms NOTE: Solid lines indicate contrasts that were significant at p < .05; dotted lines indicate contrasts that were not significant at p < .05.

small except for the contrast between 137cd/m2 and 500cd/m2, where there was a decrease in impressions of spaciousness for the higher amount of light. For fractal depth, there was a nontrivial effect between depths of 2 and 4. Because 22 = 4 and 24 = 16, this means that dividing the surface into 16ths instead of 4ths made the rooms seem more spacious. Further divisions into 64ths (26) and 256ths (28) had little effect on perceived spaciousness. Changing the fractal dimension from 2.1 (nearly flat) to 2.9 (nearly solid) had very small effects on perceived spaciousness. The interpretation seems to be that rougher boundaries (higher recursion depth) increased impressions of spaciousness, but the effect was small. Light had a similar effect on perceived spaciousness: d = –.19 for dark vs. bright. Darker seemed bigger, although quite modestly. Fractal dimension was a no-show.

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852 ENVIRONMENT AND BEHAVIOR / November 2006

DISCUSSION

Implications

We were able to obtain partial replication of previous work. The factor with the largest effect on impressions of room size was just that: actual size of the room. The results for roughness (H1) did not support the hypothesis. There were two measures of roughness: fractal dimension and fractal recursion depth. Fractal dimension had no detectable variance in impressions of spaciousness, and the response contrast between the highest and lowest fractal dimensions (1.9 vs. 1.1) was only d = –.08, which is about molehill size. The minus sign indicates that the results were opposite to the claim, so for this factor, replication was not obtained. Fractal recursion depth had a larger effect on subjective impressions, replicating findings from the psychology literature, but the walls with greater recursion depths produced rooms that appeared larger, not smaller, than rooms produced with smaller recursion depths. The interpretation is that for these stimuli, rougher seemed larger. Smoother was not more spacious. In addition, the effect of floor area on impressions of spaciousness was replicated within yet another venue.

EXPERIMENT 2: WALL SYSTEMS AND SPACIOUSNESS

The environments in Experiment 1 were designed using scientific protocols of randomization and balanced experimental design. This controlled for familiarity and confounding of inferences. Because the environments were intentionally designed to be unfamiliar, they necessarily look pretty strange. It is also pretty hard to imagine how the relevant principles apply to actual design decisions. For the environments to be applied in design, the features of the environments should be something familiar. This makes the design relevance easier to understand but requires some adjustment of the intellectual purity obtainable with randomized environments. Because one reason for research in environment and behavior is to produce knowledge that is useful for design, this article has two parts. The first part was intended for science. Priority was given to randomization and experimental design with familiarity controlled. This second part is intended more for designers. The priorities and environments are different. Architectural design typically begins with a program statement. In this case, the statement was as follows: given specified floor areas and storage requirements and given that the areas are to appear as spacious as possible, how much do

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the following options change the impression of spaciousness: solid doors, partially filled book cases, or empty book cases? The nod to science is inclusion of the books so that there can be three levels of roughness. Consideration was given to controlling the actual volume of each room, which would mean calculating the volumes of doors, shelves, and books and scaling each room to make the volumes absolutely identical. However, this would produce weirdly sized rooms that are no longer relevant to the program statement. Because the weirding had already been done in the first experiment, Experiment 2 was based on the designers’ needs rather than the scientists’. More specifically, in this study, the design problem is to design a wall system that will maximize impressions of spaciousness under the following constraints: floor areas: 5 × 5m and 6 × 6m, height: 2.75m, and bookshelves on all walls. Figure 4 shows two floor plans. Materials were wood for the walls and bookcases (45% reflectance), a carpet for the floor (reflectance of 20%), books (reflectance 40%), and a luminous ceiling. The units for area and lighting were the same as those used in the first experiment (square meters and cd/m2 of floor area), but boundary roughness was expressed differently. In the first experiment, boundary roughness was expressed as fractal measures and primarily by recursion depth. In less abstract terms, the recursion depth indicates the grain of a pattern: more recursion depth, smaller grain. Grain size can also be changed by using design elements of smaller and smaller scales. The design elements used in this experiment were bookcases. At the largest scale, the bookcases were shown with solid, flat doors. At the smallest scale, the bookcases were shown as open shelves with books. An intermediate scale showed the open shelves but no books. Thus, the abstract example used in the previous experiment could be converted into another experiment in a more familiar setting. HYPOTHESES

Conflicting claims for the effect of spaciousness have been proposed: namely, that smoother is more spacious and that rougher is more spaciousness. In this experiment, the main effect of roughness is measured as the contrast between stimuli with or without flat doors. Thus, the claim that smoother seems more spacious becomes H1: µ (flat doors) > µ (shelves, shelves with books).

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854 ENVIRONMENT AND BEHAVIOR / November 2006

Figure 4: Floor Plans for Wall Systems NOTE: The smaller room is shown with open shelves; the larger room is shown with flat cabinet doors.

Likewise, for lighting, the claim that brighter seems more spacious becomes H2: µ (600 cd/m2 > µ (300 cd/m2).

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Stamps, Krishnan / BOUNDARY ROUGHNESS 855

For area, the claim that larger seems more spacious becomes the contrast H3: µ (6 × 6m) > µ (5 × 5m).

The experimental design was a full factorial, so main effects of boundary roughness could be distinguished from the main effects of floor area. However, some researchers may prefer to inspect pairs of stimuli rather than rely on the experimental design. For those readers, the relevant contrast is between the larger rooms with flat doors and the smaller rooms without doors. In this contrast, the distance from solid wall to solid wall is the same for all stimuli. Accordingly, the hypothesis for the effect of boundary roughness for rooms with equal visible area can be tested with the following contrast: H4: µ (6 × 6, doors) > µ (5 × 5, open shelves, 5 × 5, books). METHOD

Stimuli

The design parameters were boundary roughness (solid doors, empty shelves, and shelves with books), area (5 × 5m, 6 × 6m), and lighting levels (300 and 600cd/m2 of floor). The experimental design was a full factorial of boundary roughness (3) × area (2) × lighting (2), for a total of 12 stimuli. Black and white versions of the stimuli are shown in Figure 5. Sample Size

Minimum sample size was calculated for repeated measures data (Cohen & Cohen, 1993). Based on the results given earlier, we anticipated one large effect (for area) and two small effects (for boundary roughness and lighting). We split the difference and designed the study for a medium effect size (13% of variance; Cohen, 1988). With three tests, we adjusted the overall alpha level for each hypothesis to .05/2 = .016 and calculated the dfe required for power = .80. For an experiment with 12 stimuli, only 8 respondents were required. Respondents

Respondents were recruited by a professional survey research firm from the adult population of a city in the United States. There were 16 respondents,

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Figure 5: Stimuli for Wall Systems 856 Downloaded from http://eab.sagepub.com at PENNSYLVANIA STATE UNIV on April 17, 2008 © 2006 SAGE Publications. All rights reserved. Not for commercial use or unauthorized distribution.

Stamps, Krishnan / BOUNDARY ROUGHNESS 857

of whom 8 were female and 8 were male. The mean age was 44.37 years (SD = 9.38). Dependent Variable

The dependent variable was a semantic differential scale ranging from not spacious (1) to spacious (8). Task

Images were shown on a laptop computer. First, three trial images were presented to give the respondents practice at using the program. Then an introduction screen was displayed (Figure 6, top). This screen had two images to help respondents calibrate their answers. Finally, each stimulus was shown with a row of buttons and verbal labels (Figure 6, bottom). When a button was pressed, the OK button came on; when the OK button was pressed, the answer was recorded and the next image was shown. At the end, another screen collected the demographic data. RESULTS

Table 3 shows the analysis of variance; Table 4 shows the contrasts. Figure 7 shows the contrasts between the levels of the factors. The most influential spatial feature on spaciousness was boundary roughness, with rougher boundaries (open shelves, shelves with books) making a space seem larger than if the wall were smooth (flat doors)(d = .60). The effect of area was d = .26, with 6 × 6m rooms seeming more spacious than 5 × 5m rooms. This was smaller than the effect found in Experiment 1 for the difference between the same sized rooms (d = .64), possibly because a 5 × 5 m room with open shelves would show solid walls at the same distance as would a 6 × 6m room with flat doors on the shelves. This possibility is supported by the contrast between rooms with small areas but open shelves (Stimuli BCIA) and larger rooms with flat doors (Stimuli EK). The contrast between these two design options was d = .37, with the smaller but rougher rooms appearing more spacious than the larger but smoother rooms. Because this effect does not achieve the criterion of p < .05, we can, at this point, only claim that there was no detectable difference in spaciousness between 5 × 5m rough rooms and 6 × 6m smooth rooms. Finally, the effect of light was that brighter rooms (600cd/m2) appear more spacious than dimmer rooms (300cd/m2), d = .26.

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858 ENVIRONMENT AND BEHAVIOR / November 2006

Figure 6: Instruction Screens for Laptop Data Collection NOTE: Top: The first screen in the data set gave the title, the basic response question, the number of scenes in the set, and two examples to help the respondents calibrate their answers. Bottom: Then each scene was shown with the scale anchors, a row of response buttons numbered from 1 to 8, and a running count of how far along one was. When a response button was pressed, the OK button came on. When the OK button was pressed, the response was recorded and the next scene was shown.

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Stamps, Krishnan / BOUNDARY ROUGHNESS 859

TABLE 3 Analysis of Variance, Experiment 2

Source Respondents Area Boundary roughness Light Residual Total

SS

df

MS

F

α

ωˆ 2

336.03 6.76 33.05 27.79 352.49 756.12

15 1 2 1 172 191

22.40 6.76 16.52 27.79 2.05

3.29 8.06 13.56

.07 4e-4 3e-4

0.6% 3.8% 3.4%

NOTE: Dependent variable is rated spaciousness.

TABLE 4 Standardized Mean Contrasts for Not Spacious/Spacious, Experiment 2

µ

d

r

F1,165

α

JDEK IBLFACHG JDEK IBLF JDEK ACHG IBLF ACHG EKLFHG JDIBAC DKBFCG JEILAH

3.86 4.72 3.86 4.83 3.86 4.61 4.83 4.61 4.62 4.24 4.81 4.05

–.60

.28

15.27

1e-4

–.67

.32

14.56

2e-4

–.52

.25

8.75

.003

–.15

.07

0.74

.78

.20

.10

1.58

.21

.53

.25

13.45

3e-4

EK BCIA

3.92 4.69

–.37

.18

2.91

.09

Factor

Levels

Stimuli

Roughness

Smooth Rough Doors Shelves Doors Books Shelves Books 6 × 6m 5 × 5m 600cd/m2 300 cd/m2 Flat walls Rough walls

Area Light H4: Constant visible floor area

NOTE: mse for respondents × stimuli anova = 2.06. To see which letter goes with which stimulus, please look at the figures. Letters in Stimuli column indicate individual stimuli. Thus “JDEK” means stimuli J, D, E, and K expressed the smooth level of the roughness factor.

Thus, in terms of the hypotheses, we have the following. H1: Contrary to the hypothesis, roughness increased perceived spaciousness. H2: The hypothesis that brighter seems more spacious was supported. H3: The hypothesis that more area seems more spacious was also supported but with an interesting addendum: The effect of area on perceived spaciousness can be strongly modified by boundary roughness.

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860 ENVIRONMENT AND BEHAVIOR / November 2006

Figure 7: Plots of Means of Levels of Factors for Wall Systems NOTE: Solid lines indicate contrasts that were significant at p < .05; dotted lines indicate contrasts that were not significant at p < .05.

DISCUSSION

Possible Limitations

Possible limitations include lack of control for size of presentation room, viewing distance, ambient light levels, time of day, time stimuli were displayed, alternate presentation orders, or other conditions in which the stimuli were shown. The reason is previous studies indicate that psychological responses to environments can be replicated without controlling for these conditions. In one pair of experiments, preferences were obtained for

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Stamps, Krishnan / BOUNDARY ROUGHNESS 861

the same 13 scenes but using different participants, different locations, different viewing conditions, different viewing orders, and different scaling methods (Stamps, 1992). The preferences between the two replications correlated at r = .90. In another experiment on preferences for 35 houses, two sets of responses were obtained from different groups of respondents, in different cities, under different viewing conditions (Stamps & Nasar, 1997). The results again correlated at r = .90. Feimer (1984) reported findings from a large (1,148 participants) study of effects of experimental conditions on evaluations of environments. One of the tests compared evaluation scores obtained from two different rooms (a room in a church and another room, at a different location, in a school). The effect of interview site was very small—r = 0.006, t(103) = 0.07, p = .94. Similar results were obtained in a literature review of demographic effects on environmental preferences (Stamps, 1999). The review covered data from more than 19,000 participants and more than 3,200 environmental scenes. Of particular relevance was the contrast between results generated from the protocols used in the present article with results obtained in other laboratories. The size of the contrast was quite small—eta = .03, F(1,36) = .048, p = .83—indicating that the protocols used in this article are quite reproducible. Accordingly, the present experiments did not control for viewing conditions. In addition, Experiment 2 did not address the issue of whether meanings associated with have affected the responses. It may, for example, be possible that some people were thinking of some images as empty storage rooms, whereas others may have thought of an empty room for storing boxes (H5). An alternate hypothesis is that when asked to identify physical properties such as color, material, or geometric relations such as size, people can do so without recourse to meanings (H6). This is not say that meanings do not always mediate judgments about physical things. For example, Jacobsen (2002) tested the hypothesis that certain colors naturally belong with certain shapes: triangles were associated with yellow, circles with blue, and squares with red. The experiment consisted of asking 200 members of one social group in one country to assign the colors to the shapes and also to provide rationales for their choices. About half of the respondents chose one scheme; the other choices were spread out across the possible answers. About a quarter of the respondents said they associated yellow with the sun and so the circles were yellow, and they associated the red triangles with their country’s road signs, so red went with the triangles. The authors suggested that the assignment of colors to shapes was a result of world knowledge, education, historical change, societal, group-specific and individual leitmotifs. Here, meaning mediated judgment, thus supporting H5.

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862 ENVIRONMENT AND BEHAVIOR / November 2006

Another relevant study was one Nasar, Stamps, and Hanyu (in press) did on the question of whether functions of public buildings were communicated by the forms of those buildings. In plainer language: did form convey function? The answer was a sound no. Even with a very limited set of possible answers (city hall, library, museum, theater), identification of the correct function was only 7 % off pure random guessing. Like color to shape, inferring function from form had a very small effect size. So, it might be the case that physical properties such as color, material, or size are pretty much determined by the object rather than the observer and so there isn’t much wiggle room in trying to explain responses. However, for things with no necessary physical connections, inferences will be based on subjective factors such as social conventions. When dealing with convention, one could reasonably expect a wide range of possible responses, just as Jacobsen (2002) and Nasar, Stamps, and Haynu (in press) found. To see if meanings made a difference in judging spaciousness in the bookcase rooms, I did a screening experiment. (The reasons for doing this type of experiment are given in the Appendix.) The stimuli were the six brightly lit rooms from Experiment 2 (Stimuli B, C, D, G, K). The response form showed the six rooms. Respondents were a convenience sample. Half of the respondents were asked to rank order the storage rooms in terms of spaciousness. The other half were asked to rank order the storage rooms for boxes in terms of spaciousness. There were 14 respondents. The effect size was the point biserial correlation between question (storage room or storage room for boxes) and ranks (the validity of using parametric analyses on ranks was established by Zimmerman and Zumbo, 1993). The correlation was r = –.02. This effect is 5 to 10 times smaller than effects due to light, boundary roughness, or floor area (r = of .25, .18, and .10). The size of a future experiment that is designed to test for r = –.02 would be huge. Even with 10,000 participants, the chance of finding such a small effect (the power of the experiment) would be only 40%. More generally, if one is concentrating on physical properties, it seems unlikely to suppose that judgments about those properties will be changed if an imaginary use for the properties changes. The reasoning is that the geometric properties are logically independent of the purposes, just as materials are logically independent of both geometry and purpose. A wood room does not become a concrete room when the furniture is changed from a sofa to a bed. A horizontal stick does not automatically seem vertical if one thinks of it as a hockey stick instead of wood log. For identifying physical properties (Is it red? Blue? Wood? Glass?) or their geometrical relations (Is it vertical?

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Stamps, Krishnan / BOUNDARY ROUGHNESS 863

Horizontal? Above me? Around me? Spacious?) reference to possible mediation by presumption of function is probably not needed. The situation is different, of course, if the question is about the use of an environment for some purpose. A well-lit space is good for reading; a dim space is good for sleeping, so if one wants to inquire as to whether a specific amount of light is good for reading or sleeping, then clearly projected possible usage matters. The question “How spacious is this room?” is different from the question “Is this room large enough for ballroom dancing?” Experiments can be done that do cross the physical and functional factors. For example, planners may be interested in whether better physical design can compensate for unsavory uses. An applicable experiment would be to create some buildings, put different signs on them, and find out if, say, a well-appointed pawn shop makes a given street look better than a ratty coffee boutique. But, for the focus of this article (finding out what physical factors influence spaciousness), the factor of mediation by function seems unnecessary.

GENERAL SUMMARY STUDY GOALS

The main goal of this study is to find out how strongly boundary roughness influences peoples’ impressions of spaciousness. If a room has smooth boundaries, will it appear to be more spacious? Secondary goals included testing for effects of floor area and amount of light on impressions of spaciousness. KEY VARIABLES

The variable for floor area was simply the floor area in square meters. The variable for light was candelas per square meter of floor area. In one experiment, boundary roughness was measured with two abstract mathematical constructs: fractal dimension and fractal recursion depth. Roughly writing, fractal dimension is how flat or kinky a surface is, and fractal recursion depth indicates the smallest grain size in the surface. Roughness was measured using these mathematical constructs rather than using ordinary language because ordinary language does not provide the precision necessary to conduct valid experiments on roughness. In a follow-up experiment, boundary roughness was indicated by three different wall systems: flat doors, shelves half filled with books, and empty shelves.

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864 ENVIRONMENT AND BEHAVIOR / November 2006

METHODS

This article used the experimental method, in which environments are created with or without various properties, and respondents evaluate those environments using some subjective criterion. The criterion used in this article is a rating of spaciousness. Experiment 1 had 16 rooms and Experiment 2 had another 12 rooms. FINDINGS

Findings for both experiments were consistent with the hypothesis that smoothing the boundaries did not make the rooms appear more spacious. Floor area was a very strong predictor of impressions of spaciousness. In Experiment 1, amount of light had a very small effect on impressions of spaciousness at levels below 136cd/m2 and a nontrivial effect from 136m2 to 500cd/m2, with the darker rooms appearing to be more spacious. This finding contradicted previously published findings and so replication was attempted in Experiment 2 with light levels of 300cd/m2 and 600cd/m2. This time light had a strong effect on impressions of spaciousness: the more light, the more spacious the room seemed.

SUMMARY OF FINDINGS

This article began with the hypothesis that smoother walls would make rooms appear more spacious. Neither set of data supported that hypothesis. In one experiment, increased boundary roughness produced a small increase in apparent size; in the other experiment, increased boundary roughness produced a moderate increase in apparent size. Rougher was more spacious. In addition to the main hypothesis, the experiments were designed to test for effects of the room’s actual horizontal area and for lighting. Area had such a huge effect on apparent spaciousness in the first experiment that it dominated the judgments. When the range of area was reduced in the second experiment, the more subtle effect of boundary roughness became stronger. The findings for area replicated findings from previous research and generalized the finding to another venue. Mixed results were obtained for lighting. Increasing the light from 300cd/m2 to 600cd/m2 increased the impression of spaciousness in Experiment 2, thus replicating previous work. In Experiment 1, effects on spaciousness for light levels of 10cd/m2 to 136cd/m2 had trivial effects on

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Stamps, Krishnan / BOUNDARY ROUGHNESS 865

apparent spaciousness; and raising the light from 136cd/m2 to 500cd/m2 made the grottos look less spacious. Finally, in terms of the specific application in the second experiment, it would seem that if spaciousness is a design criterion, then open shelves will increase apparent size without increasing the total size of the room. CONNECTIONS TO THEORY

The theory used here is that safety is the primary function an environment can provide; that safety is related to range of perception and locomotion; and therefore environmental properties that constrain or enhance either perception or locomotion will be important. The findings regarding roughness can be interpreted under that theory as follows: From a geometric viewpoint, a region of three-dimensional space is not enclosed unless it has a boundary. That boundary is itself a three-dimensional region. Thus, we think of the union of both enclosed space and boundary space. (For the bookcases, that would be the wall-to-wall dimension, including both the floor and the shelves). If partial vision is possible through that boundary (e.g., open bookshelves), then the range of vision will be larger than if vision cannot penetrate the boundary (smooth walls) even if the range of locomotion (e.g., the area of the floor) is the same. Hence, rougher boundaries should make enclosures feel more spacious. Another possible theoretical connection might be made with Gibson’s (1979/1986) theory of ecological psychology. The closest connections I could find were that texture is one of the nine ecological laws of surfaces, that texture is the structure of a surface rather than the structure of the underlying substance, that texture is seldom homogeneous, that there are pigment and layout textures, that when the units are small the texture is fine and when the units are large the texture is coarse (Gibson, 1979/1986, pp. 24-28). Because the fractal recursion depth also generates units of different sizes, there may be a connection here. There is also a construct called “optical texture” (Gibson, 1979/1986, pp. 161-164), which is how the texture appears in a spherical coordinate system with the observer at the center. Simple trigonometry indicates that the visual angle of something will decrease with distance; so will the spherical projections of areas (steradians). Thus, the size or grain of the texture, when projected onto spherical coordinates, will subtend fewer and fewer steradians as the location of the texture increases. This gives rise to a texture gradient that could be used to estimate distances. There may be a connection to the grottos because there are apparent differences in texture from the front of the side walls to the

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866 ENVIRONMENT AND BEHAVIOR / November 2006

back of the room and that gradient may be one of the cues that respondents used to judge space. However, a person and a door were included in each scene to provide the depth cue of size constancy, so it was not possible to distinguish between response variance due to size constancy from the effect variance due to optical texture. Overall, I could not think of a really tight connection between Gibson’s texture and the present work. That shouldn’t be too surprising because I am not a Gibson expert. Perhaps another researcher who is an expert on Gibson could write another article that makes the desired connection more firmly. FUTURE WORK

Because the current findings for light were contradictory, an obvious point in need of future work is the effect of light on apparent spaciousness. Because actual area has such a large effect on apparent spaciousness, it should be controlled or randomized in future experiments. More detailed guidance on the design of future experiments can be obtained from the contrasts. These contrasts provide the effect sizes needed to perform power analysis and hence provide the information needed to calculate how large an experiment will be needed. For example, attempts to detect the effect of fractal dimension on apparent spaciousness will be looking for d = .08. A quick flip through Cohen (1988, p. 39) indicates that for d = .10, two samples of n = 1000 would have a power of 72%. For the usual criterion (80% power) and a smaller effect size (d = .08 vs. d = .10), an even larger experiment would be needed to test for the effect of fractal dimension on apparent spaciousness. Conversely, replicating the finding for roughness in the bookcases (H4) would use a target effect size of d = .60, for which the power analysis calls for two groups of only 80 (Cohen, 1988). The variables one chooses to investigate will clearly depend on the researchers’ interests and resources. General pointers on how to select variables for future work are given in the appendix.

APPENDIX: ON SELECTING VARIABLES FOR INQUIRY

It is often the case that there are too many possible variables to include in any particular experiment. What then, is one to do? The approach used in this article was to implement a quality control program for basic research. First, by basic research I mean to suggest that the purpose of the experiment is to generate knowledge, and reliable and generalizable knowledge

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Stamps, Krishnan / BOUNDARY ROUGHNESS 867

at that, rather than to make decisions about practical applications. This is not to denigrate applied research but merely to state that the scope of this appendix is limited to basic research. The theory of quality control dates back more than 60 years (Shewhart, 1939). Quality control requires something called a measure of performance. This is just some way to tell how well something is working. For business, it often is profit; for governmental institutions, it often is number of people helped or average time to help people. Descriptions of quality control are widely available in the literature (Deming, 1986, 1994; Juran, 1992, 1995). A couple of decades ago it occurred to me that (a) my resources, both temporal and financial, were limited; and (b) I wanted to create as much knowledge as I could as fast as I could. To do this required creating of a quality control program for basic research. Because my research work usually requires scientific experiments, the place to begin was clearly Francis Bacon (1605/1952). Prior to Bacon, of course, the professional standard of care in research was scholastic disputation, in which truth was generated through rhetorical discourse on speculative topics and was validated by opinions of authorities with high status (Kenny & Pinborg, 1982). With Bacon, the situation changed. Speculation was replaced by positive facts, which is to say, observable facts rather than speculations about possibilities, deliberation was replaced by trying things out and authority was replaced by replication of empirical findings at other times or in other venues. Thus Baconian science is inherently a collective tradition. Bacon actually wrote another, less well-known book, describing such a collective. He called it the “New Atlantis” (Bacon, 1980). The implication is this: The bottom line for any individual experiment is not to produce a one-off decision (as would be desirable for a practical application) but rather something that will hold up as strongly and as reliably across as great a range as possible. The past 400 years has seen considerable refinement of Bacon’s ideals. In 1976, it became possible to implement a new Atlantis using statistics. The new statistical trick was called meta-analysis (Glass, 1976). In general, the way meta-analysis works is this. Each experiment produces an estimate of how strong a relationship is. For example, if two things correlate at r = .50, the strength of that relationship is the correlation of .50. Because effect sizes are quantitatively comparable (an r of .01 is smaller than an r of .40, for example), effect sizes can be used as measures of performance in basic research. Thus, a factor that accounts for, say, 50% of preference, works better than a factor that accounts for 5% of preference. The strength of the relationship is called an effect size. If the experiment also reports the sample size, then the CI can be calculated. A small CI

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868 ENVIRONMENT AND BEHAVIOR / November 2006

TABLE 5 Qualitative Summary of Implications of Effect Sizes and Confidence Intervals (CIs) on the Selection of Future Research

CI Effect size

Large

Small

Large

Large effect size indicates importance; large CI indicates ripeness for inquiry. Time to plan next study on this topic.

Large effect size indicates importance; small CI indicates that future work won’t make much difference. Time to move on to another idea.

Small

Not sufficient data to establish any claim. Future research will require considerable resources, so more work may or may not be worthwhile, depending on what else could be accomplished with the same amount of time and money.

Unimportant effect, solidly supported. Write it off as a dead end.

indicates higher precision than does a large CI. It also means that the collective effect size will be harder to change with future research. If the literature already contains effect sizes and their samples, it becomes possible to estimate not only how well various factors work but also how strong or flimsy the current empirical support is. A wide CI means the empirical support is currently weak and a new experience is likely to make a substantial difference in the collective finding. A tight CI means the current empirical support is strong and new work is likely to make a minor or trivial change in the collective findings. Table 5 shows the consequences in qualitative format. Thus, if one can afford to do an experiment and the choice is between studying Hypothesis 1 for which the collective r = .03 or Hypothesis 2 for which r = .50 but the CI is wide, crunching the numbers will probably recommend working on Hypothesis 2. If the CI for Hypothesis 2 is already tight, then it would probably be more rewarding to segue to another hypothesis. More precise recommendations can be obtained by doing the math. The math behind this use of meta-analysis is in the literature (Stamps, 2002b), as are applications to topics of interest to environmental researcher

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Stamps, Krishnan / BOUNDARY ROUGHNESS 869

(simulation validity [Stamps, 1993], demographic effects [Stamps, 1999], and the mystery theory of environmental preference [Stamps, 2004a]). Accessible presentations of the underlying math and how one can use these methods to plan an entire scientific career are also available (Stamps, 1997, 2003). Implementation details can be found in Rosenthal and Rosnow (1991), Cohen (1988), and Hedges and Olkin (1985). It may be the case — particularly with new ideas — that prior effect sizes are not already in the record. What then? If a decision needs to be made before data can be collected, then logic, plausibility, and the need for the decision will have to be balanced with judgment or experience. If there is time for data collection, then one can implement what Montgomery (1997) calls a strategy of experimentation. In effect, this means that when faced with possibilities with unknown effect sizes, one starts with small studies and one of the various incomplete experimental designs to establish some estimates of effect sizes before committing major resources to something that may be a wild goose chase. These studies are called screening experiments. If there is a there there, larger follow-up experiments can reveal the details. Thus, if one is interested in four factors with four levels each, using a Greaco-Latin square with 16 cells is probably a better course of action than trying a full factorial with 256 cells. The screening experiments will generate collective effect sizes, and we then are back to the use of meta-analysis for guiding research. Screening experiments are not, of course, determinate. They do not provide final answers. What they do is to allow us to move beyond the unsupported assertions of medieval scholasticism to the evidence on the record that is characteristic of empirical science. Some empirical evidence trumps no empirical evidence whatsoever. To sum up: In empirical science, emphasis is on reliable, collective knowledge, based on facts in the record rather than on speculations about possibilities. This maps onto the statistics of meta-analysis, thus implementing Bacon’s New Atlantis in virtual form. The creation of collective effect sizes and CIs become the goals, and the refinement of the effect sizes and cis become the measures of performance required for implementation of a quality control program for basic research.

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Stamps, Krishnan / BOUNDARY ROUGHNESS 871

Hedges, L. V., & Olkin, I. (1985). Statistical methods for meta-analysis. Orlando, FL: Academic. Hediger, H. (1964). Wild animals in captivity: An outline of the biology of zoological gardens (G. Sircom, Trans.). New York: Dover. (Original work published in1950) Hediger, H. (1968). The psychology and behaviour of animals in zoos and circuses (G. Sircom, Trans.). New York: Dover. (Original work published 1955) Imamoglu, V. (1973). The effect of furniture on the subjective evaluation of spaciousness and estimation of size of rooms. In R. Küller (Ed.), Architectural psychology (pp. 314-352). Stroudsburg, PE: Dowden, Hutchinson & Ross. Jacobsen, T. (2002). Kandinsky’s questionnaire revisited: Fundamental correspondence of basic colors and forms. Perceptual and Motor Skills, 95, 903-913. Juran, J. M. (1992). Juran on quality by design: The new steps for planning quality into goods and services. New York: Free Press. Juran, J. M. (1995). A history of managing for quality in the United States of America. In J. M. Juran (Ed.), A history of managing for quality: The evolution, trends, and future directions of managing for quality (pp. 553-601). Milwaukee, WI: American Society of Quality Control. Kaplan, R., & Kaplan, S. (1989). The experience of nature: A psychological perspective. Cambridge, UK: Cambridge University Press. Kaplan, S., & Kaplan, R. (1982). Cognition and Environment. New York: Praeger. Kenny, A., & Pinborg, J. (1982). Medieval philosophical literature. In N. Kretzmann & A. Kenny & J. Pinborg (Eds.), The Cambridge history of later Medieval philosophy (pp. 9-42). Cambridge, UK: Cambridge University Press. Kirschbaum, C. F., & Tonello, G. (1997). Visual appearance of office lighting. Right Light, 1, 143-148. Mandelbrot, B. B. (1983). The fractal geometry of nature. New York: W. H. Freeman. (Original work published 1977) Marchak, F. M. (1987). Fractal models in the visual perception of textures and surfaces in nature. Hanover, NH: Dartmouth. Martyniuk, O., Flynn, J. E., Spencer, T. J., & Hendrick, C. (1973). Effect of environmental lighting on impression and behavior. In R. Küller (Ed.), Architectural psychology (pp. 51-63). Stroudsburg, PE: Dowden, Hutchinson & Ross. Montgomery, D. C. (1997). Design and analysis of experiments. New York: Wiley. Nasar, J. L. (1981). Responses to different spatial configurations. Human Factors, 23, 439-446. Nasar, J. L., Stamps, A. E., & Hanyu, K. (in press). Form and function in public buildings. Journal of Environmental Psychology. Palmer, J. F., & Hoffman, R. E. (2001). Rating reliability and representation validity in scenic landscape assessments. Landscape and Urban Planning, 54, 149-161. Peitgen, H.-O., Jurens, H., & Saupe, D. (1992). Fractals for the classroom. New York: Springer-Verlag. Pentland, A. P. (1984). Fractal-based description of natural scenes. Transactions on Pattern Analysis and Machine Intelligence, PAMI-6(6), 661-674. Rosenthal, R., & Rosnow, R. L. (1991). Essentials of behavioral research: Methods and data analysis. New York: McGraw-Hill. Russ, J. C. (1995). The image processing handbook. Boca Raton, FL: CRC. Shewhart, W. A. (1986). Statistical method from the viewpoint of quality control. New York: Dover. (Original work published 1939) Stamps, A. E. (1992). Bootstrap investigation of respondent sample size for environmental preference. Perceptual and Motor Skills, 75, 220-222.

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872 ENVIRONMENT AND BEHAVIOR / November 2006

Stamps, A. E. (1993). Simulation effects on environmental preference. Journal of Environmental Management, 38, 115-132. Stamps, A. E. (1997). Managing a scientific career: An autobiography. Institute of Environmental Quality. Retrieved on December 10, 2005, from http://ieq.att.home.net Stamps, A. E. (1999). Demographic effects in environmental preferences: A meta-analysis. Journal of Planning Literature, 14(2), 155-175. Stamps, A. E. (2000). Psychology and the aesthetics of the built environment. Norwell, MA: Kluwer Academic. Stamps, A. E. (2002a). Fractals, skylines, nature and beauty. Landscape and Urban Planning, 60, 163-184. Stamps, A. E. (2002b). Meta analysis. In R. Bechtel & A. Churchman (Eds.), The handbook of environmental psychology (pp. 222-232). New York: Wiley. Stamps, A. E. (2003). Summa contra Pisces: How to fully utilize contemporary statistical methods. Institute of Environmental Quality. Retrieved on December 10, 2005, from http:// ieq.home.att.net Stamps, A. E. (2004a). Environmental preference, coherence, legibility, complexity, and mystery: A meta-analysis. Journal of Environmental Psychology, 24, 1-16. Stamps, A. E. (2004b). Mystery, complexity, legibility, and coherence: A meta-analysis. Journal of Environmental Psychology, 24, 1-16. Stamps, A. E. (2005a). Enclosure and safety in urbanscapes. Environment & Behavior, 37(1), 102-133. Stamps, A. E. (2005b). Isovists, enclosure, and permeability theory. Environment and Planning B: Planning and Design, 32, 735-762. Stamps, A. E., & Nasar, J. L. (1997). Design review and public preferences: Effects of geographical location, public consensus, sensation seeking, and architectural styles. Journal of Environmental Psychology, 17, 11-32. Wise, J. A. (1988). The quantitative modeling of human spatial habitability (NASA-CR-177501 NAS1.26:177501). National Aeronautics and Space Administration, Science & Technology Information. Moffitt Field, CA: Ames Research Center. Zimmerman, D. W., & Zumbo, B. D. (1993). The relative power of parametric and nonparametric statistical methods. In G. Keren & C. Lewis (Eds.), A handbook for data analysis in the behavioral sciences: Methodological issues (pp. 481-517). Hillsdale, NJ: Lawrence Erlbaum.

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