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Environment and Behavior
http://eab.sagepub.com/content/43/2/252
The online version of this article can be found at:
DOI: 10.1177/0013916509354696
2011 43: 252 originally published online 8 April 2010Environment and Behavior
Arthur E. Stamps III
Spaciousness
Effects of Area, Height, Elongation, and Color on Perceived
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Article
Environment and Behavior
43(2) 252 –273
© 2011 SAGE Publications
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DOI: 10.1177/0013916509354696
http://eab.sagepub.com
Effects of Area, Height,
Elongation, and Color on
Perceived Spaciousness
Arthur E. Stamps III
1
Abstract
This article reports findings from three experiments, covering 46 environments
and 66 participants, on how strongly four properties of the physical environment
influence perceived spaciousness. The properties were horizontal area, boundary
height, elongation, and color. Ten original findings were reported. Overall,
horizontal area had the strongest effect on perceived spaciousness (r = .60; more
floor area increases perceived spaciousness), followed by height (r = –.22; lower
boundaries increase perceived spaciousness). The effect of color on perceived
spaciousness, when amount of light is controlled, was much smaller (r = .14).
Findings for elongation were different for concave and convex spaces (r’s of –.22
and +.26). Quantitative syntheses of the current work with previous work are
presented, as is numerical guidance for cost-effective future work.
Keywords
spaciousness, smart growth, sustainable design
Space! the formal frontier. These are some studies from the research enter-
prise. Its five part mission: to create new worlds, to seek out new views and
new spatial relations, to boldly write what no one has writ before, to report
new findings on the question of what makes a space seem . . . well . . . er. . .
more spacious? There are both theoretical and practical reasons for consider-
ing this question. The theoretical reason was described in previous articles
1
Institute of Environmental Quality, San Francisco, CA
Corresponding Author:
Arthur E. Stamps III, Institute of Environmental Quality, 290 Rutledge Street,
San Francisco, CA 94110
Email: artstamps@att.net
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Stamps 253
(Stamps, 2007, 2010): animals, including people, feel threatened if they do
not have sufficient space. Environments that do not provide sufficient space
are ambient stressors and thus should be avoided if possible or, if unavoid-
able, mitigated as much as possible. The practical reason for discovering
what properties of the environment influence perceptions of spaciousness is
that the creation of resource-conserving cities requires increases in density.
The importance of high density was noted by, among others, the visionary
city planner R.L. Meier in the 1970’s (Meier, 1975), and has since become a
major design goal for policies such as sustainable design, countering global
warming, and transit villages (Calthorpe & Fulton, 2001; International City
Management Association, 2003, pp. 11-20; Talen, 2003; Williams, Burton, &
Jenks, 2000). The combination of the need at the global level for increased
density and the need at the individual level for adequate space thus generates
the question of how, within a given volume of space, can it be made to appear
larger than it really is? Hence the studies reported in this article.
Previous Findings
There is a substantial amount of research on how strongly various environmental
properties influence impressions of spaciousness. Emphasis in this article is
placed on research that reports the strength of relationships—for example,
efficacy—in terms of correlations or standardized mean differences. The reasons
for this criterion are given in the section on statistical protocols below. The rele-
vant literature on spaciousness, covering 11 studies, 214 scenes, and 337
participants was recently reviewed (Stamps, 2007). The following environmental
properties were investigated: (a) Effects of horizontal area on perceived spa-
ciousness were reported by Gärling (1970a, 1970b), Benedikt and Burnham
(1985), Inui and Miyata (1973), Franz, von der Heyde, and Bülthoff (2003), and
Franz and Wiener (2005), with the overall finding being that the larger the hori-
zontal area within a boundary, the more spacious the space seemed to be. (b)
Effects on perceived spaciousness due to amount of light were reported by
Martyniuk, Flynn, Spencer, and Hendrick (1973), Kirschbaum and Tonello
(1997), and Inui and Miyata (1973),with the overall finding that brighter spaces
seemed more spacious. (c) Relationships between shape and perceived
spaciousness were reported in two studies. Sadalla and Oxley (1984) constructed
rooms of with walls of gray plywood panels and had different degrees of elonga-
tion ranging from a square room (1:1 ratio of width to length) up to a corridor
(1:9 ratio). The shapes of these rooms were convex. The correlation between
estimated size of the room and elongation, based on data reported in Tables 1 and
2 in the referenced article, was r = –.27 (on n = 7 rooms for which data were
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254 Environment and Behavior 43(2)
given), indicating that long, narrow convex spaces would appear to be less spa-
cious than fat, short spaces of the same area. Ishikawa, Okabe, Sadahiro, and
Kakumoto (1998) investigated design alternatives to a Japanese street. The alter-
natives were inclusion of setbacks that varied in proportions. Some were long
and shallow; others were short but deep. In this case, the shapes of the streets
were concave. The concept was intriguing, but since there was not sufficient data
to calculate an effect size, any conclusions regarding this particular point would
have to be withheld pending replication that did report effect sizes. (d) There was
one study for the effect of occlusion on perceived spaciousness, done by
Imamoglu (1973), on the amount of furniture in rooms. The effect on spacious-
ness was r = –.54 (n = 3): the more furniture, the less spacious the room
appeared. (e) There was one study on the permeability of the boundary. Franz
et al. (2003) reported data indicating that perceived spaciousness and percentage
of walls in 16 museum rooms correlated at r = .12. (f) The effect of
boundary roughness on perceived spaciousness was reported in a pair of
studies by Stamps and Krishnan (2006), with the finding that rougher boundaries
made spaces seem larger (r’s of .10 on n = 16 rooms and r = .28 on another
12 rooms).
Seven additional studies, covering 106 scenes and 217 participants, have
been done subsequent to that review. Two of the studies, reported in Stamps
(2007), reported effect sizes of floor area, occlusion (expressed as interior
partitions), and light (expressed in cd/m
2
), for art galleries shown as 24 static
images and as 8 virtual reality models. Results indicated that floor area
correlated with spaciousness at r = .26 in the static medium and r = .42 in the
dynamic medium; occlusion (the presence or absence of interior partitions)
correlated with perceived spaciousness at r = .23 in the static medium and
r = .56 in the static medium; amount of light correlated at r = .20 in the static
medium and r = .17 in the dynamic, and, overall, responses obtained from
static simulations correlated at r = .79 with responses obtained with the
dynamic medium. The same hypotheses were statistically tenable with both
media. Another pair of studies, reported in Stamps (2009) patched the work
reported in Ishikawa et al. (1998) by reporting effect sizes for effects of
recesses in streets with concave shapes. The venue was the deliciously pho-
togenic traditional Japanese machinami style as expressed in the Gion district
of Kyoto (Durston & Mizuno, 2002; Plutschow, 1979). Factors were area of
setbacks and elongation of setbacks. Media were static color images and vir-
tual reality models. In the static media, area of setback correlated at r = .45
and elongation of setback correlated with perceived area at r = .28. In the
dynamic medium, the respective correlations were r = .56 and .17. The cor-
relation of perceived spaciousness between the six virtual reality models and
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Stamps 255
Table 1. Quantitative Summary of a priori Database on Perceived Spaciousness
Factor Venue n r Source
Horizontal area Streets 12 .96 Gärling (1970a)
Streets 12 .78 Gärling (1970b)
Rooms 15 .63 Inui and Miyata (1973)
Art galleries 16 .84 Franz, von der Heyde,
and Bülthoff (2003)
Art galleries static 24 .26 Stamps (2007)
Art galleries dynamic 8 .42 Stamps (2007)
Streets static 18 .45 Stamps (2009)
Streets dynamic 12 .56 Stamps (2009)
Rooms 12 .56 Stamps (2010)
Synthesis 129 .65 .05 ci = [.54, .73]
Light Rooms 6 .27 Martyniuk, Flynn, Spencer,
and Hendrick (1973)
Rooms 13 .94 Inui and Miyata (1973)
Rooms 12 .66 Stamps (2010)
Landscapes 18 .18 Stamps (2010)
Synthesis 49 .64 .05 ci = [.45, .77]
Elongation—Convex Rooms 7 -.27 Sadalla and Oxley (1984)
Synthesis 7 -.27 .05 ci = [-.80, .49]
Elongation— Street recesses static 18 .28 Stamps (2009)
Concave
Street recesses dynamic 12 .17 Stamps (2009)
Synthesis 30 .24 .05 ci = [-.09, .52]
Occlusion Art galleries static 24 .23 Stamps (2007)
Art galleries dynamic 8 .56 Stamps (2007)
Synthesis 32 .30 .05 ci = [-.01, .56]
Boundary Rooms 16 .12 Franz et al. (2003)
permeability
Rooms 12 .55 Stamps (2010)
Landscapes 8 .62 Stamps (2010)n
Landscapes 18 .70 Stamps (2010)
Synthesis 54 .51 .05 ci = [.03, .67]
Boundary Rooms 16 .10 Stamps and Krishnan (2006)
roughness
Rooms 12 .28 Stamps and Krishnan (2006)
Synthesis 28 .17 .05 ci = [-.17, .48]
Boundary depth Landscapes 8 .03 Stamps (2010)
Landscapes 18 .10 Stamps (2010)
Synthesis 26 .08 .05 ci = [-.27, .42]
Static/dynamic Art galleries 11
a
.79 Stamps (2007)
media
Streets 9
a
.87 Stamps (2009)
Synthesis 20 .82 .05 ci = [.63, .92]
a. Harmonic means from two different numbers of stimuli.
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256 Environment and Behavior 43(2)
Table 2. Repeated Measures Analysis of Variance, Experiment 1
Source SS df MS F p % Variance
Participants 316.78 24 13.19
(Within) (250.92) (11) 22.81
Area 64.93 1 64.93 37.75 4e-09 6.2%
Height 90.02 1 90.02 52.33 5e-12 8.7%
Setback ratio 68.69 1 68.69 39.93 1e-9 6.6%
Residual 467.68 272 1.72
Total 1008.10 299
the 28 corresponding static images was .87 (on n = 6). Again, the same
hypotheses were statistically tenable in both media, replicating the finding
obtained for the art galleries regarding the equivalence of results over static
and dynamic media. The next three studies are reported in Stamps (2010).
A study of 12 rooms indicated that perceived spaciousness correlated at
r = .56 with floor area, r = .55 with percentage of walls and roof that are
glass, and r = .66 with luminosity. Another study, this time of 8 landscapes,
indicated that perceived spaciousness correlated at r = .03 with depth of
boundary and r = .62 with the percentage of view not covered by solid objects.
These findings were replicated in another study of 18 landscapes, for which the
correlations with perceived spaciousness were r = .70 for percentage of view not
covered with solid objects, .18 for light, and .10 for boundary depth.
Thus, the a priori empirical database on how the environment influences
perceived spaciousness covered 18 studies, 320 scenes, 554 participants, and
8 environmental properties. Estimates of the efficacies of the eight environ-
mental properties with respect to perceived spaciousness are listed in Table 1.
Overall, the property with the largest effect on perceived spaciousness was
horizontal area (r = .65, .05 ci = [.54, .73]), followed by light (.64, [.45, .77),
boundary permeability (.51, [.03, .67), interior occlusion (.30, [–.01, .56]),
elongation for convex shapes (–.27, [–.80, .49]), elongation for concave
shapes (r = .24, [–.09, .52]), boundary roughness (.17. [–.17, .48), and bound-
ary depth (.08, [–.27, .42]). Also, responses of spaciousness were highly
correlated between the static and dynamic media (r = .82. .05 ci = [.63, .92]).
Selection of Variables
Based on the data described above, four environmental properties were selected
for inquiry. The first variable was horizontal area. This was chosen to increase the
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Stamps 257
diversity of environments for the area/spaciousness relationship. The second was
height, because we were unable to locate prior reports of effect sizes for the influ-
ence of height on spaciousness. The third factor was elongation, because
the relevant studies generated conflicting findings. It seemed possible that the
discrepancy due to elongation in one experiment was a function of recesses in a
concave environment (streets with alcoves), whereas the others consisted of
elongation of a convex space (rectangular rooms). Accordingly, it was decided to
attempt replication with both convex and concave shapes. The last variable was
color. The amount of light (luminosity) had already been shown to have an effect
on spaciousness, so the next step seemed to be variation in colors with equal
luminosity. The effects of occlusion, boundary permeability, boundary rough-
ness, and boundary depth could be controlled by holding them constant for all
environments within an experiment. Both static and dynamic media
produced the same results, so either would be adequate for the present work.
We chose to use the dynamic virtual reality medium.
Presuppositions
This article is based on extensive previous work for topics of (a) simulation
validity, (b) equivalence of different scaling models, and (c) presentation proto-
col options such as stimulus order and viewing conditions. The following
assumptions are made: (a) estimates of affective responses obtained on-site
correlate highly with affective responses obtained from static color images,
(b) different scaling models produce virtually identical results, and (c) results are
highly reproducible over different presentation orders and venues. The claim for
simulation validity is based on 40 years of research, covering 4,200 participants
and 1,215 environments, indicating that (1) responses to static color images cor-
relate highly and reproducibly with responses obtained in the field, (2) choice of
medium (sketch, black and white photograph, computer simulation, etc.) has an
effect on responses but this effect can be controlled by using the same medium
for all stimuli in an experiment, and (3) it is probably prudent to validate each
simulation medium before using it (Stamps, 2000, pp. 100-113). The claim for
validity of static color images versus on-site evaluations was based on 185 envi-
ronments (Stamps, 2000, p. 103) and was subsequently replicated with 470
environments (Palmer & Hoffman, 2001, p. 155). The claim for the equivalence
of different scaling protocols is based on a review of eight articles with 1,150
stimuli indicating that the choice of scaling protocol made very little difference
in the obtained results (Stamps, 2000, pp. 100-101). The claim that presentation
protocols have had very minor effects on findings is supported by studies repli-
cating findings obtained within the present laboratory (Stamps, 1992), between
the present and another laboratory (Stamps & Nasar, 1997), independent
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258 Environment and Behavior 43(2)
replication with 1,148 participants (Feimer, 1984), and between the present labo-
ratory and results obtained from a review covering 19,000 participants from 23
countries and more than 3,200 environments (Stamps, 1999).
Statistical Protocols
Analyses of variance, covariance, or regression for repeated measures data were
done following Cohen and Cohen (1993, Chapter 11). Emphasis on contrasts and
reporting results in terms of effect sizes such as standardized mean differences
(d) or correlations (r) was done following Rosenthal and Rosnow (1991).
Mathematically, d and r are equivalent and can readily calculated from each other
(see Rosenthal & Rosnow (1991) for the equations) but sometimes the results are
easier to understand in one of the measures. Sample sizes were calculated using
power analysis following Cohen (1988). Summarizing findings over multiple
studies was done with meta-analyses following Hedges and Olkin (1985). A free
plug-in for doing meta-analysis in Excel is given in Bax, Yu, Ikeda, Tsuruta, and
Moons (2006, 2008). These considerations constitute what has been called the
effect size paradigm for statistical quality control in basic research. Descriptions
of how to execute this paradigm and examples taken from the environment and
behavior literature are given in Stamps (2002).
Experiment 1: Height, Area, and Elongation
Stimuli and Experimental Design
The venue for this experiment was the traditional Japanese street used in the
previous study of recess setbacks but with the added dimension of height of
buildings. Buildings were created with heights of 1, 2, or 3 stories, or, in terms of
meters to eaves, 3, 6.7, and 10 m. Twelve sites were selected from the previous
study using the criteria that (a) the full range of variables would be replicated, and
(b) the number of scenes would be kept low because of the costs of using dynamic
simulations. Twelve streets were created, using a factorial experimental design of
setback area (2) by elongation of setback (2) by height (3), for a total of 12 streets.
The site plans and screen shots of four scenes are shown in Figure 1.
Participants and Sample Size
The required number of participants was calculated with power analysis.
Relevant previous findings were that horizontal area and perceived spacious-
ness correlated at r = .73 and elongation correlated with perceived
spaciousness at r = –.27. The smaller value was used in this study. A
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Stamps 259
Figure 1. Site plans, screen shots, and plots of mean spaciousness for experiment 1
correlation of –.27 translates into about 7% of variance. For a = .05, three
intended tests (area, elongation, height), a target effect size of 13%, power =
.80, and a repeated measures experimental design with 12 stimuli, the mini-
mum number of participants was 15. In the event, 25 participants were
recruited by a professional survey research firm from the adult population of
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260 Environment and Behavior 43(2)
a major city in the United States. There were 12 males and 13 females.
Politically there were 8 liberals, 9 moderates, and 8 conservatives. The mean
and standard deviation of age were 44.7 and 16.3 years. Occupations ranged
from hair stylist to college professor.
Task
Virtual reality models were shown on a laptop computer using a custom com-
puter program. The screen measured 337 mm by 208 mm. Luminosity was
150 lux. Participants sat approximately 400 mm from the screen in a room
with an ambient light level of 150 lux. The computer program had two parts.
The first part was a demonstration that showed the participants how to use
the controls. After completing the demonstration, participants viewed the
main part. In this part, the first screen stated what judgment was requested
(“Please rate the following pictures on the criterion of how not spacious
(1) or spacious (8) they appear.”), along with two images showing the extreme
conditions in the experimental design. Then each stimulus was shown with a
row of buttons on the bottom. The buttons were numbered from 1 to 8. When
a button was pressed, an “OK” button appeared. When the “OK” button was
pressed, the next stimulus was shown. Participants could change their minds
and press other numbered buttons until they pressed the “OK” button.
Participants were allowed to take as much time as they needed.
Results and Discussion
The analysis of variance is listed in Table 2. All three environmental proper-
ties had substantial effects on impressions of spaciousness. Height had the
strongest effect (8.7% of variance, p = 5e-12), followed by horizontal area
(6.2%, p = 4e-9), and setback ratio (6.6%, p = 1e-9). More detailed findings
are shown in Table 3. Table 3 lists the means for each level of each factor, the
standardized mean contrasts (d) and correlations (r) between levels of fac-
tors. The values of d and r are listed because they are necessary to synthesize
the findings of this study with the other studies in the literature. Thus, the
efficacy of area of street, over the range of 194 to 258 m
2
, was r = .31, with
larger areas appearing more spacious (finding #1, or F1). The efficacy of
height of building, over the range of 3 to 10 m, on impressions of spacious-
ness was r = .49, with lower buildings making the street seem more spacious
(F2). For elongation, indicated by the elongation of the setback, the efficacy
was r = –.32 (F3), with long, shallow setbacks making the street seem more
spacious. For quick comparisons, plots of the contrasts are also shown at the
bottom of Figure 1.
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Stamps 261
Experiment 2: Height, Area, and Elongation
Stimuli and Experimental Design
In this study, the venue was changed from outdoor to indoor. The environments
were very simple, plain, convex spaces with a wood floor, gray walls with verti-
cal joints 1.22 m on center, and a white ceiling. Three properties of the
environment were created: horizontal area, elongation, and height. The levels of
area were 12, 16, and 20 m
2
. The levels of elongation were width-to-length ratios
of 1:1, 1:2, and 1:9, or, in verbal terms, a square, a rectangle, and a corridor.
Heights were 2.44 and 3.66 m. These sizes were chosen because, in local units,
they could be made with 4 × 8 foot or 4 × 12 foot plywood panels. The experi-
mental design was a factorial of area (3) by elongation (3) by height (2), for a
total of 18 rooms. Figure 2 shows the floor plans and screen shots of four rooms.
Participants and Sample Size
The same target effect size was used in studies 1 and 2, but, with more stim-
uli, fewer participants were needed. For a = .05, three tests, power at .80, and
18 stimuli, the minimum number of participants fell to 6. Twenty-four par-
ticipants were recruited by the professional survey research firm. The
participant sample was balanced for sex and political affiliation. Ages ranged
from 22 to 72 years with a mean of 45.1 and standard deviation of 13.5 years.
Occupations ranged from unemployed to business owner.
Task
The same task was used in studies 1 and 2.
Table 3. Contrasts for Perceived Spaciousness, Experiment 1
Factor Level Stimuli M d r F
(1,264)
p
Area (m
2
) 258 DEFJKL 4.56 .65 .31 37.72 3e-9
194 ABCGHI 3.72
Height (m) 3.0 GADJ 5.04 .95 .43 45.34 1e-10
6.7 HBEK 3.81
6.7 HBEK 3.81 .18 .09 1.72 0.19
10.0 ICFL 3.53
3.0 GADJ 5.04 1.13 .49 64.76 3e-14
10.0 ICFL 3.57
Setback ratio 1:4 GHIDEF 4.57 .67 .32 33.76 2e-8
1:1 ABCJKL 3.71
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262 Environment and Behavior 43(2)
Figure 2. Site plans, screen shots, and plots of mean spaciousness for experiment 2.
Note: Rooms A, B, C, D, E, F, G, H, and I were 3.04 m high. Rooms J, K, L, M, N, O, P, Q, and R
were 2.43 m high.
Results and Discussion
The analysis of variance is listed in Table 4. The factor with the largest effect
on perceived spaciousness was elongation (10.3% of variance, p = 3e-17).
The effect of area was less (4.3%, p = 6e-9), and the effect of height was
undetectable (0% of variance, p = .39). In terms of efficacies (Table 5), the
correlation of elongation with perceived spaciousness was r = .40, with all
the effect being attributable to the long, narrow corridors. Long, narrow
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Stamps 263
Table 5. Contrasts for Perceived Spaciousness, Experiment 2
Factor Level Stimuli M d r F
(1, 391)
p
Area (m
2
) 12 ABCJKL 3.06
16 DEFMNO 3.52 .33 .16 7.77 .005
16 DEFMNO 3.52
20 GHIPQR 4.03 .37 .18 9.77 .002
12 ABCJKL 3.06
20 GHIPQR 4.03 .70 .33 34.98 7e-9
Elongation 1:1 ADGJMP 3.92
1:2 BEHKNQ 3.95 0.0 0.0 0.0 1.0
1:2 BEHKNQ 3.95 .90 .41 58.48 1e-13
1:9 CFILOR 2.69
1:1 ADGJMP 3.92 .88 .40 55.92 5e-13
1:9 CFILOR 2.69
Height (m) 2.44 ABCDEFGHI 3.48
3.66 JKLMNOPQR 3.60 .08 .04 0.74 .39
Table 4. Repeated Measures Analysis of Variance, Experiment 2
Source SS df MS F p % Variance
Participants 431.05 23
(Within) (1004.30) 408
Area (m
2
) 68.05 1 68.05 35.26 6e-9 4.6%
Height (m) 1.44 1 1.44 0.75 .39 0.0%
Elongation 150.33 1 150.33 77.89 3e-17 10.3%
Residual 784.46 405 1.93
Total 1435.39 431
spaces were perceived as being much less spacious than square or rectangular
spaces of the same area. There was no detectable difference in spaciousness
between the square and rectangular rooms (r = .0, p = 1.0).
Experiment 3: Height, Area, Elongation, and Color
Stimuli and Experimental Design
This study also used rooms as stimuli. Three criteria were used to design these
rooms. First, the volume was held constant at 125 m
3
. Thus, this experiment could
address the question of how, given a program calling for high density housing,
could that building’s volume be subdivided to make each unit seem as spacious as
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264 Environment and Behavior 43(2)
possible? Should the floor area be increased and the ceiling lowered, or vice
versa? Should the rooms be compact or elongated? Would changing the wall color
compensate for a lack of square footage or ceiling height? A second criterion was
that the ratio among levels of factors should be such that the largest level would be
twice the size of the lowest. With four levels for each factor, the required ratio
between levels was
2
3
, which might explain some of the otherwise incomprehen-
sible dimensions. Third, the overall sizes of both the smallest and largest rooms
had to be reasonable. The result consisted of the floor plans shown in Figure 3.
Levels of horizontal area were 49, 38.9, 30.9, and 24.5 m
2
. Heights were 2.5, 3.15,
3.96, and 5.0 m. Elongation ratio’s were 1:1, 1:1.26, 1:1.57, and 1:2. Because
luminosity has been shown to influence perceived spaciousness, it had to be con-
trolled. This was done using colors created under the CIELAB color space with
constant luminosity, with constant reflectivity of the walls, and a constant level of
source lighting (200 cd/m
2
of floor area). For details on color spaces, see Wyszecki
and Styles (2000) or Pascale (2003). Essentially, this implies that the overall
amount of light (e.g., the luminosity) was controlled, so the factor of color in this
experiment was variation in hue and saturation. CIELAB coordinates for each
color, as given in Photoshop, were 90, 0, –40 for blue, 90, –40, 0 for green, 90,0,
40 for yellow, and 90, 40, 0 for pink. A person was rendered in each room to help
participants evaluate scale, and each room contained pictures done by the author.
The content of the pictures varied widely so descriptions of them would be diffi-
cult, but, considering who the painter was, they are, of course, all works of Art.
The experimental design was a Graeco-Latin square (Cochran & Cox, 1957,
p. 146) of horizontal area (4), elongation (4), height (4), and color (4), with a total
of 16 rooms. Screen shots of four rooms are also shown in Figure 3.
Participants and Sample Size
Since experiments 1 and 2 were done before experiment 3, the estimate of the
target effect size could be based on the data listed in Table 1 plus the findings
for experiment 1. For horizontal area, the overall correlation with perceived
spaciousness was r = .63 (≈39% of variance). For height, the correlation was
r = –.49 (24% of variance). For elongation in convex spaces, the correlation
was r = –.27 (7%). No prior effect size was available for color, so we used a
default value of Cohen’s medium (13% of variance). The minimum of these
effect sizes was 7% of variance, so, with a target of 7%, a = .05, power = .89,
four tests, and 16 stimuli, the minimum number of participants was 14.
Seventeen participants were recruited by the professional survey research
firm. There were nine males and eight females. The mean age was 39 years
with a standard deviation of 14 years. There were 6 political liberals, 5 mod-
erates, 5 conservatives, and one person who did not state political affiliation.
Occupations ranged from writer to commercial real estate.
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Stamps 265
Figure 3. Site plans and screen shots for experiment 3
Task
The same task was used in all three studies.
Results and Discussion
The analysis of variance is listed in Table 6. Horizontal area again had the
strongest effect on perceived spaciousness (12% of variance, p = 2e-4).
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266 Environment and Behavior 43(2)
Effects of elongation and height were an order of magnitude less (2% and 1%
of variance, p’s = .002 and .04). Color had an effect two orders of magnitude
less than area (0.1% of variance, p = .61). Contrasts are listed in Table 7 and
are shown in Figure 4. Thus, the effect of horizontal area, over the range of
24.5 to 49 m
2
, was F7: r = .54, with larger horizontal area leading to an
increase in perceived spaciousness. For height, over the range of 2.5 to 5 m,
was F8: r = –.26, with the rooms with lower ceilings being judged as more
spacious than the rooms with higher ceilings. For elongation, over the range
of 1:1 to 1:2, the effect was F9: r = .14, with no detectable difference between
these levels of elongation. Finally, for color, no detectable differences were
found for effects of color on impressions of spaciousness. The largest con-
trast was between yellow and pink, with F10: r = .11.
Discussion
Overall, the data reported in this article increased the literature on how the
environment influences perceived spaciousness to 21 experiments, 366 envi-
ronments, and 620 participants. The database for effects of horizontal area,
height, elongation, and color are listed in Table 8. Data for each factor will be
Figure 4. Plots of mean spaciousness for experiment 3
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Stamps 267
Table 6. Repeated Measures Analysis of Variance, Experiment 3
Source SS df MS F p % Variance
Participants 263.00 16
(Within) 586.75 255
Area 104.51 1 104.51 57.74 8e-14 12%
Elongation 18.76 1 18.76 10.36 .002 2%
Height 7.92 1 7.92 4.37 .04 1%
Color 3.30 3 1.10 0.60 .61 0.1%
Residual 492.26 249 1.81
Total 849.75 271
discussed in turn. Inferences regarding the identification of new contribu-
tions to the literature, the effects of the new data on the previously existing
data, and estimating the amount of work needed for future work are based on
the effect size paradigm for statistical quality control in basic research as
described in Stamps (1996, 1997a, 1997b, 2002).
Horizontal Area
New findings for the effect of horizontal area on perceived spaciousness
were reported as F1, F4, and F7. In addition to the three new effect sizes, the
current work also contributed to the collective body of knowledge by expand-
ing the relevant sample size (n = 129 before the work and n = 175 after the
work) and the range of venues over which the effect size was reported (new
venues of streets with buildings of different heights; new proportions of
rooms). Prior to the work reported in this article, the .05 ci for this effect was
[.54, .73]. After the current work, this ci shrank to [.51, .68]. Clearly, this was
not much of a change. The reason is that the effect of horizontal area on per-
ceived spaciousness was already pretty firmly established in previous work,
so additional work is most unlikely to make a contribution on this particular
point. An estimate of how much additional work would make a change in the
collective body of knowledge is provided in the last column of Table 8. This
column is labeled “n
over
”. We use n
over
as an index of how solid the collective
evidence is on a particular point. High positive values of n
over
indicate very
solid evidence that would be hard to change with future work. More techni-
cally, n
over
is the amount of additional data that would be required to change
the significance of the collective finding. If n
over
is positive, it would be the
amount of work, reporting a finding of r = 0, that would make the collective
estimate indistinguishable from random noise (e.g., p > .05). Higher values
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268 Environment and Behavior 43(2)
Table 7. Contrasts for Perceived Spaciousness, Experiment 3
Factor Level Stimuli M d r F
(1, 240)
p
Area (m
2
) 49.0 AEIM 4.57 .63 .30 13.77 2e-4
38.9 BFJN 3.73
38.9 BFJN 3.73 .33 .16 3.81 .05
30.9 CGKO 3.29
30.9 CGKO 3.29 .30 .15 3.09 .08
24.5 DHLP 2.90
49.0 AEIM 4.57 1.27 .54 55.07 2e-12
24.5 DHLP 2.90
Height (m) 2.50 AFKP 4.03 .23 .12 1.87 .17
3.15 BELO 3.72
3.15 BELO 5.72 .22 .11 1.70 .20
3.96 CHIN 3.42
3.96 CHIN 3.42 .08 .04 0.21 .64
5.00 DGJM 3.32
2.50 AFKP 4.03 .53 .26 9.76 .002
5.00 DGJM 3.32
Elongation ratio 1:100 ABCD 4.09 .31 .15 3.32 .07
1:1.26 EFGH 3.68
1:1.26 EFGH 3.68 .49 .24 8.20 .004
1:1.587 IJKL 3.03
1:1.587 IJKL 3.03 .51 .24 8.20 .003
1:2.00 MNOP 3.70
1:1.00 ABCD 3.03 .29 .14 2.86 .09
1:2.00 MNOP 3.70
Color Blue AHJO 3.59 .06 .03 0.10 .75
Yellow BGIP 3.51
Yellow BFIP 3.51
Pink CFLM 3.81 .22 .11 1.70 .20
Pink CFLM 3.81 .17 .08 0.95 .32
Green DEKN 3.59
Blue AHJO 3.59 .00 .00 1.00 .32
Green DEKN 3.58
mean the effect is already established and further work may not be the best
use of one’s research resources. The effect of horizontal area on perceived
spaciousness would appear to fall into this category, joining claims such as
the validity of static color simulations, the interchangeability of alternate
scaling methods, and the effect of experimental viewing venues for evaluat-
ing affective responses to environments.
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Stamps 269
Table 8. Relationships Among Past, Present, and Future Work on Spaciousness
Factor Source n r Sn
rˆ
.05 ci n
over
Horizontal Previous work
a
129 .65 .54, .73
area F1 Experiment 1 12 .31
F4 Experiment 2 18 .35
F7 Experiment 3 16 .54
Summary 175 .60 .51, .68 5,203
Height Previous work 0 0 -1.00, 1.00
F2 Experiment 1 12 -.49
F5 Experiment 2 18 .04
F8 Experiment 3 16 -.26
Summary 46 -.22 -.46, .04 -14
Elongation— Previous work 30 .24 -.09, .52
Concave F3 Experiment 1 12 .32
Summary 42 .26 -.001, .49 -2
Elongation— Previous work 7 -.27 -.78, .28
Convex F6 Experiment 2 18 -.40
F9 Experiment 3 16 .14
Summary 41 -.18 -.44, .11 -.52
Color Previous work 0 0 -1.00, 1.00
F10 Experiment 3 16 .14 16 14 -.30, .53 -126
a. Please see Table 1 for details on previous work.
Height
For height, we were unable to find previously reported effect sizes, so the .05
ci before the current work was [–1.0, 1.0]. After the three new findings (F2,
F5, F8), the sample size was increased from 0 to 46 environments and the .05
ci was upgraded to [–.46, .04]. For the effect of boundary height on perceived
spaciousness, the ci does not currently include zero, or, in terms of p levels,
p > .05. In this case, n
over
will be negative, and, technically, is the amount of
data, reporting the current estimated effect size, that would make the collec-
tive finding significant (p < .05). A negative n
over
that is close to 0 means that
only a small amount of work would be needed to establish a relationship
beyond random chance. For the effect of height on perceived spaciousness,
n
over
is –14, indicating that an experiment with n
stim
= 14 could make a useful
contribution to the literature. The relationship of n
over
to future research can
be seen by comparing how much work and how much benefit would be
involved in choosing whether to work next on horizontal area or on boundary
height. For horizontal area, a study of 5,203 stimuli would be needed; for
boundary height, that number drops to 12 stimuli. If one’s resources are
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270 Environment and Behavior 43(2)
limited, it would seem that future work on boundary height would be more
rewarding than future work on horizontal area.
Elongation
The relationship of elongation to perceived spaciousness was split into two
variations because, although the same measurement was made (length
divided by width), the prior findings were divergent. For the street scenes,
elongation was measured for one part of a concave space. For rooms, elonga-
tion was measured for the whole, concave shape. New findings (F3 for the
streets; F6 and F9 for rooms) supported the previous work with streets with
long, shallow alcoves would be more spacious than streets with short, deep
alcoves and rooms with compact shapes would be more spacious than long,
narrow spaces such as corridors. However, with both n
over’s
being negative, it
would be premature to make the call on these points. Establishing the alcove
effect would require less work than establishing the room effect (n
over’s
= –2
and –52 respectively, for anyone contemplating such future work.
Color
For color, the range of stimuli was extended to go beyond the effect of amount of
light. The relevant a priori finding was that amount of light has nearly the same
effect on perceived spaciousness as does horizontal floor area (r’s of .65 and .64).
But color, at least as perceived by people, also has two other properties. Readers
may be accustomed to thinking of color in terms of hue, value, and saturation; for
analytical work, the CIELAB system is generally more useful. The work reported
in this article (F10) used rigorous controls in both the technical specification of
color and in the creation of the environments so that the effect of overall amount
of light was eliminated. The result: sans amount of light, the effect of color on
perceived spaciousness was small (r = .16) and will take a study with an addi-
tional 126 environments to distinguish this effect from chance.
In conclusion, therefore, we suggest that since sustainable design often
implies higher densities and insufficient space can be a strong ambient
stressor, there are good reasons to refine our understanding of how perceived
spaciousness can be mitigated through environmental design. To paraphrase
numerous previous authors, more work is needed. Engage!
Summary
This article reports findings from 3 experiments, covering 46 environments and
66 participants, on how strongly four properties of the physical environment
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Stamps 271
influence perceived enclosure. The properties were horizontal area, boundary
height, elongation, and color. Ten original findings were reported. Overall, hori-
zontal area had the strongest effect on perceived spaciousness (r = .60; more floor
area increases perceived spaciousness), followed by height (r = –.22; lower
boundaries increase perceived spaciousness). The effect of color on perceived
spaciousness, when amount of light is controlled was much smaller (r = .14).
Findings for elongation were different for concave and convex spaces (r’s of –.22
and +.26). Quantitative syntheses of the current work with previous work are
presented, as is numerical guidance for cost-effective future work.
Declaration of Conflicting Interests
The author(s) declared no potential conflicts of interests with respect to the authorship
and/or publication of this article.
Funding
The author(s) received no financial support for the research and/or authorship of this
article.
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Bio
Arthur E. Stamps III extracted his PhD from U.C. 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 90 articles, does a substantial amount of peer review on submis-
sions relating to environment and behavior, and serves on the editorial boards of
several major journals. Current research focuses on cognition and affect. He works at
the Institute of Environmental Quality in San Francisco.
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