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Examination of relationships between buildingform and function, and the cost of mechanicaland electrical servicesL. M. SWAFFIELD & C. L. PASQUIREPublished online: 21 Oct 2010.

To cite this article: L. M. SWAFFIELD & C. L. PASQUIRE (1999) Examination of relationships between buildingform and function, and the cost of mechanical and electrical services, Construction Management and Economics,17:4, 483-492, DOI: 10.1080/014461999371402

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Introduction

Under traditional methods of budget estimating andpre-contract cost planning, cost estimates for mechan-ical and electrical (M&E) services generally were basedsolely on the gross ¯ oor area of a building. Swaf® eldand Pasquire (1995) argued that it was inappropriateto use gross ¯ oor area as the sole descriptor for deter-mining M&E services cost. Swaf® eld and Pasquire(1996) attempted to predict M&E services costs usinggross ¯ oor area as one of several independent variables(using data published by the Building Cost InformationService (BCIS) on detailed cost analyses), and foundthat there was not a strong relationship between M&Eservices cost and the building form descriptors used bythe BCIS.

Swaf® eld and Pasquire (1996) also argued thatbuilding form descriptors other than those publishedin the BCIS detailed cost analyses, may be useful forestimating M&E services cost. This paper describes theselection of building form descriptors appropriate forthe research (including the development of new

descriptors), the collection of data for the buildingdescriptors, the transformation work and analysisundertaken, and the results, taking building functioninto consideration.

Figure 1 summarizes the analysis work undertakenand demonstrates how M&E services cost was relatedto building form, building function, M&E servicesperformance (numerical expression of designed provi-sion, such as boiler rating in kilowatts, speed andweight capacity of lifts, or illumination level in lux)and M&E services quality (material speci® cationsdetermined by aesthetic considerations, such as lift car® nishes, types of luminaire or heat emitter).

Building function

Brown (1987) identi® ed a relationship betweenbuilding function and M&E services cost. From asample containing factories, of® ces, housing, generalhospitals, health centres, sports halls, primary schoolsand sheltered housing, Brown (1987) established that

Construction Management and Economics (1999) 17, 483± 492

Examination of relationships between building formand function, and the cost of mechanical and electrical services

L.M. SWAFFIELD and C.L. PASQUIRE

Department of Civil and Building Engineering, Loughborough University, Leicestershire LE11 3TU, UK

Received 22 September 1997; accepted 22 January 1998

This paper describes analysis work undertaken to examine relationships between building function, buildingform and mechanical and electrical services cost, including the collection of raw data, and the transforma-tion work undertaken to enable analysis. Relationships are identi® ed between building form parameters, e.g.perimeter of external walls, gross ¯ oor area, storey heights, percentage of glazing, and the mechanical andelectrical services costs for buildings of different functions (commercial, industrial and residential). Thereare relationships between the costs of the mechanical and electrical services installations and some buildingform descriptors, but the particular descriptors and the strength of the relationships vary according to thefunction of the building.

Keywords: Mechanical and electrical services, tender cost, cost planning, building function, building form

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the `cost of building services’ to `cost of scheme’ ratioscame from different populations, and therefore thepercentage cost of M&E services varied betweenbuilding functions. Brown (1987) found also that theallocation of the total services cost among the variousservices elements could not be predicted accuratelyfrom knowledge of building function. Therefore, thisresearch used the total M&E services cost for theanalysis, rather than more detailed breakdowns of theM&E services cost among the elements. It was arguedthat the function of the building affected M&E servicescost because building function determined M&Eservices performance and quality, and could affect thedesign of the systems. For example, McLellan (1995)described how the horizontal distribution of M&Eservices varied between the different laboratory facili-ties in Glaxo’ s medical research centre, because of themaintenance requirements that arose from the opera-tions carried out in each type of laboratory.

Leivers (1995) believed that the function of thebuilding affected the relationship between source plantcapacity and cost, because certain buildings (such ashospitals) required back-up plant in case of break-downs or routine servicing/maintenance. Statutoryregulations played a large part in determining thequality of terminal outlets for particular types of build-ings, which also affected cost (Leivers, 1995).

Building form parameters

Kouskoulas and Koehn (1974) argued that the cost ofa building was a function of many variables, and a setof independent variables should be selected thatdescribed a project and de® ned its cost. Such variablesmust be measurable for each new building project.Kouskoulas and Koehn identi® ed the following inde-pendent variables that de® ned the cost of a building:building locality, price index, building type, buildingheight, building quality, and building technology.Their cost estimation function involved assessingvalues for each of the identi® ed variables, and wastherefore rather subjective.

Fletcher (1968) believed that the identi® cation andproving of useful cost parameters for M&E serviceswas hindered by the prevalence of contracts based ondrawings and speci® cation, and the associated absenceof detailed analyses of the M&E services cost.

In order to test the hypothesis that building formwas related to M&E services cost, it was necessary toidentify variables that described building form accu-rately. Brandon (1978) identi® ed the following as suit-able descriptors of building form: plan shape index,number of storeys, boundary coef® cient, average storeyheight, percentage of glazed area, and plan compact-

ness. Swaf® eld and Pasquire (1996) identi® edpercentage of glazed wall area, perimeter length, totalbuilding height, volume of plant rooms and servicescores, and volume of air handled by HVAC systems,as descriptors that may be useful for determining M&Eservices cost.

Identi® cation of data required

The information published by the BCIS had been inad-equate for forecasting M&E services cost because ofthe parameters used for collecting information and thelack of detail in the information submitted bysubscribers (Swaf® eld and Pasquire, 1996). Thereforefurther information had to be collected that was suit-able for the necessary analysis work. Raw project costinformation from previous projects was required,together with building form and function details, andspeci® cation data concerning the M&E servicescontained in the buildings.

Development of building form descriptors

Swaf® eld and Pasquire (1996) did not establishwhether the poor relationships observed between M&Eservices cost and the information published by theBCIS, were due to the descriptors used or the way thatsubscribers analysed the costs of previous projects.Therefore it was decided that the BCIS descriptorswould be included in this analysis, to identify theirsuitability for determining M&E services costs whenall the ® gures were analysed in a consistent manner.

Some new building form descriptors were developedfor the analysis (Table 1) after M&E services designliterature had been studied to identify factors that wererelevant to the design of various M&E systems. Thesefactors were then examined in relation to project draw-ings, and building form parameters already in use. Thenew descriptors represented building form parametersthat were relevant to M&E systems design, and could

484 Swaf® eld and Pasquire

Figure 1 Diagram of relationship analysed

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be measured from tender drawings, but were not usedcurrently for analysing costs. The building formdescriptors as de® ned by the BCIS also were usedwhere applicable, except ancillary area and storeyheight (see below).

Previously published building descriptors also wereidenti® ed and tested. These were:

plan shape index (Banks, 1974),plan compactness parameter or POP ratio

(Strathclyde University, cited by Ferry andBrandon, 1991),

square index (RICS, 1982), andperimeter index (J. Cooke cited by Ferry and

Brandon, 1991).Figure 2 shows some of the building form descrip-

tors used for the analysis.

Relationships between building formdescriptors

It was proposed that the M&E service requirements ofa building had implications on the size of ceiling voids,storey heights, and usable to gross ¯ oor area ratios,because of space required for plant rooms and risers(Chelmick, 1995). To enable more detailed analysis,

ratios were calculated that represented relation-ships between some of the building form descriptors(Table 2). These derived variables emphasized rela-tionships with plant room space, and the amount ofglazing. The space required for plant rooms was anindication of the intensity of the M&E services provi-sion in the building (Figure 2). For example, a highlyserviced building such as a laboratory or a hospital,would require more space for plant rooms than abuilding with less complex M&E services installations,such as a primary school. The extent of glazing in abuilding was believed to be signi® cant when consid-ering the M&E services cost because glazed areasaffected heat loss, solar gain, lighting and ventilation(if opening windows) requirements (Crane, 1995).

Mechanical and electrical services 485

Table 1 Building form descriptors developed for theresearch

Descriptor De® nition

Floor to Height measured from top of ¯ oor height structural ¯ oor to underside of structural

¯ oorTotal height Sum of all ¯ oor to ¯ oor heightsUsable height Sum of usable heights at each storeyUsable volume Sum of plan areas of each ¯ oor multiplied

by the usable heights at each storey(Note: usable volume = internal cube± horizontal distribution volume)

Plant room area Floor area used for lift, tank and plantrooms, measured on internal structuralface of enclosing walls

Plant room Plant room area multiplied by usable volume height of plant rooms

Horizontal (Total height ± usable height) ´ average distribution plan ¯ oor areavolume

Vertical Usable height ´ plan area of vertical distribution distribution space (such as service volume cores)

Glazed area Area of windows, glazed doors, andpanels

Internal Perimeter of building measured on perimeter internal structural face of enclosing length walls Figure 2 Building form descriptors : area, height, volume

and enclosure

Table 2 Ratios calculated from building form descriptors

Average storey heightWall:¯ oor ratioPercentage glazed wall area (for each elevation and total)Glazing:¯ oor ratioPlant room area as a percentage of gross ¯ oor areaPlant room area:usable area ratioPlant room volume:usable volume ratioPlant room volume as a percentage of internal cube

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Data collection

Information containing the building form descriptorsidenti® ed as worthy of further analysis was not availablein a published form. Therefore a method of collectingthe required information had to be devised. It was estab-lished that information for many of the building formdescriptors could be taken from tender drawings.Therefore it was necessary to collect priced tender doc-uments and analyse the M&E services costs against thequantities calculated for the building form descriptors.Due to dif® culties in obtaining data considered com-mercially sensitive, usable information was obtained foronly ® fteen projects. However, the volume of workinvolved in measuring quantities for the building formdescriptors from the tender drawings, and the detailedanalysis subsequently required, meant that large samplesizes were not practical anyway. The data collection dif-® culty also meant that there was no control over thebuilding functions of the tender information collected.In addition, the sample contained refurbishment andextension projects, which were deemed to be inappro-priate to analyse (at this stage) with respect to the build-ing form descriptors.

These limitations resulted in the detailed analysis oftwelve new build projects: ® ve of® ce buildings, ® veuniversity student accommodation projects, one docu-ment store, and one factory with integral of® ceaccommodation. The projects were grouped underbroader building functions of commercial (of® ces),residential (student accommodation), and industrial(document warehouse and factory).

Re-de® nition of some descriptors

While analysing the tender documents collected itbecame apparent that some of the descriptors were notentirely appropriate to the data set. It was thereforenecessary to re-de® ne some of the descriptors, andothers had to be omitted from the analysis (see below).

The BCIS de® nition of storey height was the `heightmeasured from ¯ oor ® nish to ¯ oor ® nish’ (BCIS,1969). Ceiling void depths were affected by the M&Eservices requirements of the building (Chelmick, 1995),and therefore were an indication of the intensity of theM&E services provision in the building (Figure 2).

This research deviated from the BCIS de® nition ofstorey height, and measured height from ¯ oor ® nish tounderside of ceiling ® nish, thus considering only usableheight (Figure 3). This enabled the introduction of a new parameter, the `̄ oor to ¯ oor height’ (Table 1).The depth of the service voids (whether suspended ceil-ings, raised ¯ oors or both) could then be calculated, asthe total height minus the usable height, and includedin the analysis.

BCIS (1969) de® ned ancillary area as the t̀otal areaof all enclosed spaces for lavatories, cloakrooms,kitchens, cleaners’ rooms, lift, plant and tank roomsand the like, supplementary to the main function ofthe building’ . This research was particularly interestedin the space required for plant rooms, as an approxi-mation of the intensity of the M&E services provision,(as discussed above). Therefore it was deemed inap-propriate to include plant rooms in the ancillary area.Many of the residential building projects analysed haden-suite toilets and shower rooms to each bedroom,and kitchens to share between a group of bedrooms.Therefore it was seen as more appropriate to includethese toilets and kitchens with usable area. Thisresulted in the re-de® nition of the usable areadescriptor (to include the BCIS ancillary area itemswith the exception of lift, plant and tank rooms), thedevelopment of a new descriptor for plant room area(Table 1), and the re-measurement of some quantitiesfrom the tender drawings, in line with the revised de® -nitions of the building form descriptors.

Examination of the tender documents obtained forthe research revealed that only two of the projects hadbasements, therefore it was deemed inappropriate toinclude basement area in the analysis. Two of theprojects were largely single storey, and therefore upper

486 Swaf® eld and Pasquire

Figure 3 Building height descriptors

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¯ oor area, and average storey height above ground ̄ oorwere inappropriate for the analysis of the available data,and were discounted. To simplify the analysis work,ground ¯ oor area and average storey height at ground¯ oor also were discounted from the analysis, and storeyheights were averaged over all ¯ oors whether above orat ground level.

Vertical distribution volume had to be omitted fromthe research because it was not possible to identify thelocation (and therefore calculate the total plan area)of the service cores/ducts for all the projects. The draw-ings for the highly serviced multi-storey of® ce projectsshowed the locations of cores, dry risers, stair andlobby pressurization, car park and WC extract ducts,etc.; however, the drawings for the residential projectswere far less detailed. The student accommodationprojects typically showed furniture arrangements ineach bedroom (desk, bed, etc.) but contained very littleinformation about vertical services distribution.

Data transformation

Due to physical differences between the buildingprojects, and the economic conditions at the tenderdates of the various projects (the projects analysed weretendered between December 1991 and June 1996),several adjustments were required to minimize tenderprice differentials. The tender price of a project wasaffected by many factors. Smith (1995) found thatM&E services tender costs were in¯ uenced by loca-tion, programme, terms and conditions of contract,nature of the site and the state of the market.

Adjustments were made to the actual tender ® guresusing published indices and factors (BCIS, 1997a,b)intended speci® cally for use when comparing costs ofdifferent projects. The factors used for the researchminimized variations in M&E tender costs due to thedifferent locations, contract sums, procurement routes,building heights, types of work and building functionsof the projects analysed. Brief descriptions of the BCISindices and factors are given in Table 3. BCIS (1977a)described how project factors could be used to showthe effect of certain variables on contractors’ pricing.In this research, the range of building forms and func-tions, locations, time periods, contract sizes and typesof building work required meant that many variablescould have explained the variation in tender pricesbetween the projects. The published individual adjust-ment factors for the various physical and economicdifferences (such as number of storeys, geographicallocation, etc.) were multiplied together, as describedby BCIS (1997a), to produce project factors speci® -cally for this analysis.

In this study, the main focus was the cost of theM&E services element of the tender, so factors for thesize of the M&E services element of the contract wereincluded in the way described by BCIS (1997a) forthe size of contract (Table 3).

The market conditions index was included in the pro-ject factors developed for this analysis as the competi-tiveness of the tendering climate was believed to besigni® cant in determining the tender prices. Table 3shows that the BCIS calculations for the market condi-tions index excluded costs of mechanical, electrical andlift installation works from the general building costindex used to de¯ ate the TPI. Therefore any peculiar-ities in the competitiveness of the M&E sector wouldnot be accounted for when considering the adjustmentsto M&E tender costs. The project factors developed forthis analysis were as follows.

Mechanical and electrical services 487

Table 3 BCIS adjustments made to actual tender ® gures

Tender price Measured the trend of indices contractors’ pricing levels in accepted

tenders (BCIS, 1997b). The all-in tenderprice index was selected for the analysiswork

Market Based on the tender price index de¯ ated conditions by the general building cost (excluding index M&E) index. It was therefore an indica-

tion of the competitiveness of thetendering climate

Location The BCIS location factors (BCIS, 1997a)attempt to identify some general buildingcost differences due to localized variablessuch as demand and supply of labour andmaterials, workload, taxation and grants,the physical characteristics of a particularsite, its size, accessibility and topography

Size of contract A factor representing the general relation-ship between price levels, as measured bythe tender price index and contract size at1985 prices (BCIS, 1997a)

Procurement Adjustment factors relating to the route variation in price levels between competi-

tive, negotiated and serial contracts(BCIS, 1997a)

Type of work Adjustment factors for new build,horizontal extension, vertical extension,shell only or rehabilitation/conversionprojects (BCIS, 1997a)

Building form The only BCIS adjustment for buildingform was for the height element, whichwas represented by the number of storeysfactor (BCIS, 1997a)

Building Adjustment factors relating to the function variation in tender price levels between

buildings of different functions (arrangedin broad CI/SfB Table 0 (RIBA, 1969)categories) were published (BCIS, 1997a)

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Factor 1 T ´ L ´ N ´ C ´ P ´ W ´ B

Factor 2 T ´ L ´ N ´ S ´ P ´ W ´ B

Factor 3 M ´ L ´ N ´ C ´ P ´ W ´ B

Factor 4 M ´ L ´ N ´ S ´ P ´ W ´ B

Here, T is the tender price index, M is the marketconditions index, L is the location factor, N is thenumber of storeys factor, C is the size of contract factorbased on total contract sum, S is the size of contractfactor based on M&E services element of the contractsum, P is the procurement route factor, W is the typeof work factor, and B is the building type factor.

The market conditions index was derived from thetender price index (Table 3), so these two adjustmentswere not included in the same project factor. Theproject factors above included either C or S, but it mayhave been useful to develop further factors that incor-porated both of these variables in the same factor.However, this was not done because it was believedthat four project factors would be suf® cient for theanalysis at this stage.

Analysis of data

The analysis was undertaken in three stages: ® rst, the® gures were analysed by inspection; then sample meansand standard deviations were calculated and examined;® nally, the data were analysed for correlations betweenthe data sets for the variables used. At each stage thedata were analysed as a sample of twelve projects, andthen re-grouped by building function.

Inspection

When the data were inspected as one sample, the vari-ation in scale and cost of the projects was apparent:the projects ranged in contract value from £871 415to £25 799 701; in gross ¯ oor area from 1 231 m2 to24 315 m2; and in M&E services cost from £311 390to £6 032 706. These variations in cost and size,together with the range of building functions and M&E

services provision, made it unlikely that any signi® cantrelationships would be observed between building formand function and M&E services cost for this sample.

The residential projects ranged in size from 3 757 m2

to 11 376 m2 gross ¯ oor area, and actual M&E servicestender cost ranged from £456 546 to £1 534 008. Thesmallest project in terms of gross ¯ oor area did nothave the lowest M&E services cost, but did have thelowest total contract value. This indicated that theremay not be a relationship between gross ¯ oor area andM&E services cost for residential projects.

Inspection of the ® gures for residential projectsrevealed that relationships between M&E services costand the building form descriptors and ratios appearedto be reasonably signi® cant for four of the projects.The other project (residential 3) was considerablylarger than the rest, and appeared to be outside therange of the relationships observed for many of thevariables. For example, percentage of glazed wall areashowed an interesting relationship with M&E servicescost for residential buildings (Table 4). The actualM&E services cost per percentage of glazed wall areawas around £50 000 for four of the projects, but over£120 000 for residential 3, even though the percentageof glazing was within the range of the sample. Therange was narrowed by the adjustments applied to theM&E services cost data set, with factor 2 producingthe smallest spread of values. Table 4 shows that thereduction in M&E services cost per percentage ofglazed wall area was greatest for residential 3, againindicating that this project appeared to show differentrelationships to the others in the sample.

All the residential projects comprised several indi-vidual blocks of accommodation. Values of the planshape index, plan compactness parameter, squareindex, and perimeter index were calculated for eachblock, and an average value for the project was thencalculated for each descriptor. When analysing the datafor the residential projects it became apparent that theproject averages for the above building form descrip-tors were misleading. All the above descriptors werebased on the relationship between the area andperimeter of a building, but a ¯ oor area divided into,for example, four blocks, would require a different

488 Swaf® eld and Pasquire

Table 4 M&E services cost per percentage of glazed wall area, for residential buildings

Project Percentage of Services cost per % glazed wall areaglazed wall area Actual Adjusted (factor 2)

Residential 1 10.18 £45 363 £43 844Residential 2 10.37 £44 019 £43 766Residential 3 12.60 £121 791 £85 938Residential 4 15.42 £56 615 £56 108Residential 5 19.42 £50 211 £49 160

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amount of enclosing walls from the same area in asingle building. Therefore it was decided to discountthese building form descriptors from the analysis of theresidential projects.

Coincidentally the largest, most expensive andsmallest, least expensive projects were both commer-cial buildings. Indeed it could be concluded that therewas a vague relationship between M&E services costand gross ¯ oor area for commercial buildings, as theproject with the largest ¯ oor area also had the highestM&E services cost.

The two industrial projects were not comparable insize nor in M&E services cost. The projects had gross¯ oor areas of 1 540 m2 and 18 517 m2, and the actualM&E services cost tender ® gures were £425 897 and£1 798 059, respectively.

The data indicated that percentage of glazed wallarea was the building form descriptor with the strongestrelationship with M&E services cost, for the industrialsample. When the M&E services cost was adjusted forproject location, the maximum and minimum ® gureswere £203 681 and £203 646, respectively, a differ-ence of only £35 for each percentage of glazed area.In this sample the glazing ranged from 2.3% to 9.2%of external wall area.

The relationships observed by inspection indicatedthat the actual M&E services cost per unit of thebuilding form descriptors and ratios generally varied agreat deal. The ranges were considered too wide forus to conclude with con® dence that particular rela-tionships existed for each sample. Some of the adjust-ments applied for the factors affecting tender pricelevels did reduce the ranges for some variables.However, the variations in the relative successes of thedifferent adjustments for each building form descriptorand ratio led to the conclusion that more accuratemeasures of the relationships were required to explainthe apparent inconsistencies observed.

It was considered useful to examine the averagevalues of M&E services cost per unit of each variable,and the location of these values around the centraltendency, for each of the samples. It was believed thatthis would allow relationships between the variables tobe identi® ed with greater certainty than by inspectionalone, and that the suitability of the various M&Eservices cost adjustments could be examined.

Sample means and standard deviations

The sample mean is the most common measure of loca-tion, and is the ordinary arithmetic average of a data set.One of the most important measures of variability was the sample standard deviation (Montgomery andRunger, 1994). The purpose of the adjustments appliedto the M&E services cost tender ® gures was to facilitate

comparisons between different types of project, ten-dered for under different market conditions. So far, thesuitability of the various adjustments has not been dis-cussed. It may be that some adjustments were usefulonly for certain building form descriptors or ratios, orfor particular samples. For the purposes of this analysis,any adjustment that reduced the standard deviation ofthe actual M&E services cost data set was deemed to beuseful as it reduced the variability in the relationshipsobserved for the sample.

In the sample containing all twelve projects, thesample standard deviation of the M&E services costper m2 gross ¯ oor area was £80, with a sample meanof £192. The adjustments that resulted in smallersample standard deviations were TPI (with S = 59),number of storeys (S = 79), and factor 2 (S = 63). Thisanalysis was carried out for all building form descrip-tors and ratios, in all four samples. Table 5 shows theadjustments that reduced the standard deviations ineach of the four samples.

The residential sample had the smallest sample meanfor actual M&E services cost per m2 gross ¯ oor area,which indicated that the residential projects were lesshighly serviced than the other building functionsamples. As the residential projects were not veryhighly serviced, they did not require a great deal ofplant room space (the sample mean for percentageplant room ¯ oor area was 1.61% for residentialprojects, compared with 8.69% for commercialprojects, 4.15% for industrial projects, and 4.98% ofgross ¯ oor area for the total sample). The commercialsample had the lowest sample mean for actual M&Eservices cost per m2 plant room area, percentage plantroom ¯ oor area, and m3 plant room volume. This wasdue to the relatively large spaces allocated to plantrooms, compared with the other samples. In the indus-trial sample, the standard deviations were generallylarge relative to the sample means, indicating a highdegree of variability in the relationships observed inthe sample. Exceptions, where sample standard devi-ations were small in relation to the sample means were

Mechanical and electrical services 489

Table 5 Adjustments to M&E services cost that reducedthe sample standard deviations for all variables

Total Residential Commercial Industrialsample sample sample sample

TPI TPI TPI TPIFactor 2 Number of Number of Factor 2

storeys storeysType of Type of

building buildingFactor 1Factor 2

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actual M&E services cost per m2 external wall area,actual M&E services cost per percentage glazed wallarea, and actual M&E services cost per metre internalperimeter. These variables may prove useful for indus-trial buildings.

Examination of the sample means and sample stan-dard deviations for the building form descriptors andratios, and the adjusted and actual M&E services costvalues, revealed that there were differences in the rela-tionships observed among the samples. This indicatedthat M&E services costs varied according to buildingfunction.

The suitability of the various tender price factoradjustments was also examined. It was found thatadjusting the actual M&E services cost tender ® guresfor the tender price index was appropriate for all foursamples; factor 2 was appropriate for all samples exceptresidential; the number of storeys and type of buildingfactor adjustments were suitable for use with residen-tial and commercial projects, and factor 1 was suitableonly for commercial buildings.

Correlations

Correlation is a dimensionless quantity that can beused to compare the linear relationships between pairsof variables in different units (Montgomery andRunger, 1994). Calculations of the strengths of therelationships between different sets of data, in this casetender costs of M&E services and various building formdescriptors, were done mathematically with the corre-lation coef® cient.

The correlation coef® cient r represents the strengthof a relationship, ± 1 < r < + 1. If two sets of data havea perfect positive correlation, then as data set 1 isincreased, data set 2 also would increase. Conversely,if a perfect negative correlation exists, then as data set1 increased, data set 2 would decrease. If a correla-tion coef® cient were close to zero, there would be noapparent relationship between the data sets.

Correlation analysis could identify only whether alinear relationship existed between two sets of data.There was no implication that a change in one vari-able caused a change in the other, both variables mayhave responded to a change in some other unobservedvariable, or the observed relationship could be purelycoincidental. Correlation analysis could not identifywhether a nonlinear relationship existed between thevariables, or whether the data fell into more than onepattern on a graph. The relationships identi® edthrough correlation analysis were speci® c to the sampleanalysed. Correlational signi® cance indicated thepercentage probability that the relationships observedwere due to chance ¯ uctuations. The linear correla-tion coef® cients calculated were compared with crit-

ical values from statistical tables, to identify whetherthe observed correlation was signi® cant.

The total data set had a sample size of twelve, andtherefore ten degrees of freedom. The 95% con® dencelevel was selected as adequate for the analysis. Withten degrees of freedom and p < 0.05, the critical valueof the correlation coef® cient was 0.576. Thereforethere was less than 5% chance of observing absolutevalues of correlation coef® cients greater than 0.576 bychance, and the relationship observed was consideredsigni® cant.

For the total sample, correlation coef® cients werecalculated for M&E services cost (the actual ® gure andthe ® gures adjusted for the thirteen indices and factorsdescribed above and in Table 3) and twenty-twobuilding form descriptors and ratios. A strong positivecorrelation was observed between gross ¯ oor area andM&E services cost, ranging from 0.9584 for the actualtender ® gure, to 0.8726 for the tender ® gure adjustedfor the size of services contract factor. A signi® cantpositive correlation for all M&E services cost adjusteddata sets was observed also with usable area, circula-tion area, internal divisions, plant room area, plantroom volume, usable height, total height, external wallarea, glazed area, usable volume, and plant room area:

usable area ratio.The strong positive correlations observed between

M&E services cost and many of the building formdescriptors indicated that as buildings increased in size(either in ¯ oor area, volume enclosed or height) thecost of the M&E services increased. This showed onlythat larger buildings had more expensive M&Eservices. It was decided that this relationship was notvery useful in terms of identifying determinants ofservices cost, and that further analysis was required.

Correlation coef® cients were calculated for M&Eservices cost per unit of each building form descriptorand ratio, such as per percentage of glazed wall area,or per metre of internal perimeter. This was done forthe actual M&E services cost, and each of the adjustedtender ® gures, for the total sample, the residentialsample, and the commercial sample. The industrialsample was too small for correlation analysis.

Comparison of correlations observed for the

three samples

Tables 6 and 7 show summaries of the more signi® -cant relationships observed from correlation analysis.Relationships between building form and function andM&E services cost appeared stronger for the commer-cial projects. However, none of the building formdescriptors or ratios had perfect correlations with anyof the M&E services cost per unit variable data sets,either actual or adjusted.

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Conclusions

The research established that the M&E services cost(the research considered cost to the client, and usedtender price as an approximation of cost) was indeedrelated to building function, because the relationshipsbetween M&E services cost and the building formdescriptors and ratios analysed varied between thebuilding function determined samples.

It was observed that M&E services cost did not haveprecise linear relationships with building form andbuilding function, and it was hypothesized that M&Eservices cost was not related solely to building formand function, and that the variations in cost relation-ships were due to the performance and quality of theM&E services.

The study indicates that the analysis of M&Eservices cost in terms of building form descriptors isvalid, but the commonly used building form descriptorgross ¯ oor area is not the most appropriate for M&Eservices cost estimates.

Horizontal distribution volume and internal cubewere the variables with the most signi® cant relation-ships with M&E services tender cost.

The sample sizes in the study were rather small, butthe research methods described in this paper can beapplied to larger samples in the future, to verify thepreliminary ® ndings. There is scope also for develop-ment and testing of further descriptors, ratios andtender price adjustments. However, this work repre-sents a contribution to knowledge in this importantarea.

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BCIS (1969) Standard Form Of Cost Analysis, Principles,

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Mechanical and electrical services 491

Table 6 Most useful M&E services cost per unit variable data sets

Total sample Residential sample Commercial sample

M&E services cost per metre M&E services cost per metre M&E services cost per wall:¯ oor ratioaverage storey height usable height

M&E services cost per M&E services cost per metre M&E services cost per metre usable heightwall:¯ oor ratio total height

M&E services cost per m2 M&E services cost per percentage M&E services cost per metre total heightexternal wall area glazed wall area

M&E services cost per glazing: M&E services cost per percentage ¯ oor ratio glazed wall area

M&E services cost per glazing:¯ oor ratioM&E services cost per m2 external

wall areaM&E services cost per plan compactness

indexM&E services cost per square index

Table 7 Most useful building form descriptors and ratios

Total sample Residential sample Commercial sample

Usable volume Horizontal distribution volume External wall areaUsable area Internal cube Internal perimeterInternal cube Usable volumeAverage storey height Internal cubeHorizontal distribution volume Plant room areaWall:¯ oor ratio Gross ¯ oor area

Circulation areaHorizontal distribution volume

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