Toward Statistics on Construction Engineering and Management Research

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1 1139 Toward Statistics on Construction Engineering and Management Research Dai TRAN 1, Henry LESTER 2, and Nathaniel SOBIN 3 1 Assistant Professor, Department of Civil, Environmental and Architectural Engineering, 2150 Learned Hall, 1530 W. 15 th Street, The University of Kansas, Lawrence, KS 66045; PH (785) ; daniel.tran@ku.edu 2 Ph.D. Candidate, Department of Civil, Construction, and Environmental Engineering, The University of Alabama, Box , Tuscaloosa, AL ; PH (205) ; leste019@crimson.ua.edu 3 Ph.D. Research Associate, Department of Civil, Environmental and Architectural Engineering, Campus Box 428, University of Colorado, Boulder, CO ; PH (303) ; FAX (303) ; nathaniel.sobin@colorado.edu ABSTRACT Surveys and other opinion-based data collection techniques are prevalent across various disciplines. However, a lengthy controversy over employing the traditional descriptive and inferential statistics for this type of data continues. In the field of construction engineering and management (CEM), conducting experimental research is a challenging task due to the dynamic and transient nature of the construction industry. As a result, CEM researchers studying topics that involve human behaviors in the construction process must commonly employ research methods that use categorical level measurements to collect data based on expert judgment and opinion. While the interval between ordinal values is not always equal, researchers often perform parametric descriptive and inferential statistics for their data. This analysis may lead to inappropriate results or indefensible conclusions. This paper reviews measurement scales to obtain expert opinion and associated appropriate statistical analyses. The paper analyzes 151 manuscripts published in the 12 issues of the Journal of Construction Engineering and Management (JCEM) from January to December 2012 to identify the typical statistical applications used in CEM research. The paper describes interconnection between scales of measurement and statistical applications and then provides recommendations for CEM researchers to select appropriate statistics tests corresponding to a given data set. In particular, the paper discusses when and how researchers can employ traditional descriptive and inferential statistics to analyze categorical and ordinal data to enhance validity and reliability of the given study. INTRODUCTION Construction engineering and management (CEM) research commonly works to advance the body of knowledge based on latent constructs and variables for regularly uncollected or unshared data. Construction projects often deal with multilingual work crews, dynamic and transient work environments, industry fragmentation, weather, and other factors. These characteristics lead to challenge in conducting research based on the experimental setting. As a result, CEM researchers often rely on non-experimental research methodologies. In fact, through examining 1,102 manuscripts published over the period from 1993 to 2007 in the Journal of

2 1140 Construction Engineering and Management (JCEM), Taylor and Jaselskis (2010) pointed out that the approximately 842 articles (73%) employed non-experimental research methodologies. Non-experimental research methodologies commonly employed in CEM research include non-randomly sampled surveys, interviews, content analysis, focus groups, nominal group techniques, and Delphi panels. While this group of methodological approaches constitutes valuable research tools, they address different types of research questions than their experimental counterparts. In addition, these research tools rely heavily on subjective scale human responses from program managers, project managers, designers, contractors, industry experts, and workers. These types of methodologies commonly collect and analyze nominal or ordinal data types (e.g., Likert scales) to provide the findings necessary to address the research question(s) at hand. As testament to the frequent employment of these methods, we analyzed 151 manuscripts published in the 12 issues of the JCEM from January to December The results showed that 49 papers directly employed questionnaire survey to collect data with a wide range of the CEM research areas including construction safety and health, productivity, risk management, project delivery methods and procurements. Out of these 49 papers, 32 papers (65%) explicitly used Likert scales. Although these types of methodologies and analyses are common, it is also common to find instances in which the wrong types of statistical analyses are applied to nominal or ordinal data types. In addition, nominal or ordinal data types are sometimes converted to continuous data. In this paper, we review some hypothetical examples of when and how these types of data are misidentified, misinterpreted, and misanalysed. While the premise may come across as negative, the purpose of this paper is not to point out errors or assign blame. The purpose of this paper is to help delineate common complications in CEM research and define a framework researchers can use to ensure that the data analysis is appropriate and defensible. In addition, the intent of this paper is not to be an exhaustive background or framework on statistical analysis. Rather, the objectives of this paper is to present a brief review on the levels of data measurement, how they pertain to scales commonly used in CEM research, and to provide a brief framework that can be used to select an appropriate statistical analysis for data types that are most common in CEM research. BACKGROUND The types of CEM research methodologies commonly used vary greatly in comparison to other more concise fields of research. Because of the project-based nature of the work, one-of-a-kind products, site-based productions in construction projects, it is commonly difficult to draw a random sample to minimize bias in the data and to obtain a strong inference and statistical conclusion as is common in traditional, experimental research methods. Instead, convenience samples (e.g., subgroups of interests, specific committees or organizations, relevant firms or individuals) are prevalent in CEM research. In fact, 32 papers that explicitly used Likert scales and published in the JCEM from January to December 2012 either utilized convenience samples or were silent on the topic of random sampling. While

3 1141 the use of convenience samples while can enhance response rates and provide useful information to answer research questions, this methodological approach commonly suffers from a weak external validity because of the inability to estimate sampling errors and confident intervals (Abowitz and Toole 2010; Fellows and Liu 2008). To address this, improvements in many non-experimental methodologies and employed in CEM research. As previously noted, the majority of CEM research relies on descriptive and non-experimental research. The subjective input relies on measurements subject to interpretation from experts or well-qualified respondents, gathered from interviews, surveys, questionnaires, and observations play an important role in the data collection process in the CEM research. Sillars and Hallowell (2009) pointed out four primary techniques that often use to collect subjective data in the CEM research: (1) surveys or interviews; (2) the Delphi method; (3) the Nominal Group technique, and (4) Focus group technique. In the following paragraphs, we summarize a few of these statistical comparisons techniques and applications of these methodological approaches. Classification of surveys and interviews into staticized group techniques include one round of gathering information from well-qualified participants with little or no communication among participants and between the facilitator and the participant (Dayananda et al 2002; Sillars and Hallowell 2009). Sillars and Hallowell (2009) indicated that staticized group techniques have a medium ability to reduce bias and require a medium timeline to collect data. Designing questionnaires and surveys (e.g., using appropriate scales, carefully constructed questions) is a key to success in using this technique. One recommendation is survey questionnaires include both closed questions to ensure the statistical comparison among the answers and openended questions to obtain useful insight into the problem (Sillars and Hallowell 2009). The Delphi method is a systematic and interactive research technique that includes more than one round (often two or three) to obtain consensus in judgment of independent experts on a specific topic (Hallowell and Gambatese 2010). Different from the traditional surveys and interviews, the Delphi method requires participants to expert certification before the survey process begins, and allows the expert panelist to interact anonymously to achieve consensus. The Delphi method has low communication level among participants but high communication level between facilitator and the participant. This technique has a high ability to reduce bias but requires a long timeline to collect data. The Nominal Group technique uses the same process as Delphi method except the anonymous interaction among expert panelist. The Nominal Group technique uses face-to-face meetings and discussions between rounds to obtain consensus in judgment. While this technique requires a low timeline to collect data, it often yields more biased results and is difficult to conduct because of challenging in gathering experts in one geographic location (Erffmeyer and Lane 1984; Hallowell and Gambatese 2010). The focus group technique is an opinion-based research tool that includes one round of collecting information from experts through face-to-face or virtual meetings in one physical location where experts can communicate with one another in real time (Hallowell and Gambatese 2010; Webb and Keven 2001). Similar to the Nominal

4 1142 Group technique, this technique requires a low timeline to collect data, but it is difficult to conduct and potentially yields more biased results because of the challenges in gathering experts in one physical location and non-anonymous interaction among expert panelists. The four techniques described previously are different tools to collect subjective data, but they share the same feature: nominal and ordinal level scales of measurement. To better explain how and when to apply the appropriate statistical approach, the authors re-visit the definition of scales of measurement described below section. SCALES OF MEASUREMENT AND STATISICAL APPLICATIONS Three prominent measurement theories that constitute permissible statistics are representational, operational, and classical. The representational measure theory suggests a relationship between measurement scales and statistics whereas the operational and classical measure theories do not (Mitchell 1986). Essentially, the representational measure theory is a process of assigning numbers to objects in such a way that interesting qualitative empirical relations among the objects in are reflected in the numbers themselves as well as is in important properties of the number system (Townsend and Ashby 1984) and serves as a foundation for Stevens scales of measurement (Stevens 1946). While Stevens idea of a measurement scale-statistical relationship is controversial among some statisticians, Stevens scales of measurement scale serves as a fundamental tenant of many statistical texts (Gaito 1980; Mitchell 1986; Mitchell 2002; Townsend and Ashby 1984). Since a full discussion of measure theory and measurement scale-statistical relationships is beyond the scope of this paper, this paper will only outline the fundamentals of Stevens scales of measurement. The fundamental concept of the scales of measurement is different data type s present distinct informative properties and mathematical operations. The noun nomenclature for these scales of measurement is nominal, ordinal, interval, and ratio (Stevens 1946). The common data classifications equate nominal and ordinal as qualitative and interval and ratio as quantitative. An important fact to note is each of these scales contains represents an empirical data set possessing intrinsic characteristics inherent to that particular scale of measurement. The intrinsic characteristics of the scales of measurement comprise identity, magnitude, equal interval, and absolute zero. Stevens (1946) referred these intrinsic characteristics as basic empirical operations where identity liken to determination of equality, magnitude liken to determination of greater or less, equal interval liken to determination of equality of intervals or differences, and absolute zero liken to determination of equality of ratio. It should be noted that each scale of measurement use different mathematical group structures and operations (Wadsworth Cengage Learning 2005). For example, the nominal scale uses a permutation group structure and the mathematical operation of count; the ordinal scale of measurement consists of an isotonic group structure and uses count and rank order as mathematical operation; the interval scale consists of a general linear group structure and uses the

5 1143 mathematical operations of count, rank order, addition, and subtraction; the ratio scale of measurement consists of a similarity group structure and permits the mathematical operations of count, rank order, addition, subtraction, multiplication, and division. Table 1 summarizes the properties and mathematical operations of different scales of measurement. Table 1: Scale of Measurement Properties and Mathematical Operations Properties Nominal Ordinal Interval Ratio Identity Identity Magnitude Identity Magnitude Equal Interval Identity Magnitude Equal Interval True Zero Mathematical Operations Count Rank Order Addition Subtraction Addition Subtraction Multiplication Division Adapted from Wadsworth Cengage Learning 2005 The different mathematical operations associated with each scale of measurement lead to a medley of descriptive and inferential statistical operations. Descriptive statistics summarize and describe important features of the data collection or sample. Such summaries often include mode, median, mean, range statistics, variance, and standard deviation. However, descriptive statistics provides little information pertaining to the data s particular population. Unlike the descriptive statistics, inferential statistics are used to draws a conclusion about a population from a sample. Inferential statistical operations typically include parametric, non-parametric, chisquare, Mann-Whitney U, Kruskal-Wallis H, Freidman ANOVA (Analysis of Variance), Spearman correlation, t-test, ANOVA, and Pearson correlation (Devore 2012; Wadsworth Cengage Learning 2005). Table 2 summarizes the suitable descriptive and inferential statistics for four different types of data: nominal, ordinal, interval, and ratio scales. Table 2: Appropriate Statistics for Different Scales of Measurement Nominal Ordinal Interval Ratio Typical Descriptive Statistics Mode Frequency Mode Median Range Statistics Mode Median Mean Range Statistics Variance Standard Deviation Mode Median Mean Range Statistics Variance Standard Deviation Typical Inferential Statistics Contingency coefficient Chi-Squared Non-Parametric Kendall W Mann-Whitney U Kruskal-Wallis H Friedman ANOVA Spearman Correlation Non-parametric t-test ANOVA Pearson Correlation Parametric t-test ANOVA Pearson Correlation Coefficient of variation Parametric Adapted from Wadsworth Cengage Learning 2005

6 1144 The suitable descriptive statistics for the nominal data are mode; for the ordinal data are mode, median, and range statistics; for the interval data are mode, median, mean, range statistics, variance, and standard deviation; and for the ratio scale of measurement are mode, median, mean, range statistics, variance, and standard deviation. Similarly, the suitable inferential statistics for the nominal data are non-parametric and chi-square; for the ordinal scale of measurement are nonparametric, Mann-Whitney U, Kruskal-Wallis H, Freidman ANOVA, and Spearman correlation; for the interval scale of measurement are parametric, t-test, ANOVA, and Pearson correlation; and for the ratio scale of measurement are parametric, t-test, ANOVA, and Pearson correlation. Selecting an appropriate statistical analysis is critical to obtain meaningful results regarding research questions or hypotheses. As was previously described, CEM research relies heavily on non-experimental data collection methods, such as non-randomized surveys and interviews resulting in the majority of data classified as categorical variables (i.e., ordinal scales of measurement). Researchers pointed out that construction is a social process in nature and effective CEM research requires the proper application of social science research methods (Abowitz and Toole 2010). Statistics is the science of collecting, organizing, summarizing, and interpreting data for drawing conclusions (Devore 2012). Organization and summarization of requires knowing the type data or scale of measurement that represent of represents the variables of interest. It is important to note that an appropriate relaxation of the equal interval assumption transforms ordinal scale of measurement to an approximate interval scale of measurement (Wadsworth Cengage Learning 2005). Additionally, under applicable assumptions transform to a ratio scale of measurement exists. Therefore, designing appropriate scale is critical to the success of the research project. The following section discusses the appropriate design of ordinal scales of measurement in CEM research areas. DESIGN OF APPROPRIATE SCALES The data collection process often involves defining specific observable indicators, specifying the procedures to access the attribute of measured research objectives, and explaining how to interpret the measurement. As was previously discussed, 32 out of the 49 papers (65%) published in the 12 issues of the JCEM in 2012 employed a survey questionnaire methodology and explicitly used Likert scales performing both parametric tests and non-parametric tests in the 32 papers:. Some papers utilize a one sample t-test was used to compare the sample mean with the population mean. Others utilized non-parametric Kruskall-Wallis test to rank-ordered measures rather than on the raw measures. There has been a lengthy controversy over employing the mean and the standard deviation as the measure of central tendency and it seems remain to date. On one side, researchers argue that the mean is inappropriate for ordinal data. For example, Marcus-Roberts and Roberts (1987) pointed out that it is always appropriate to calculate the means for ordinal-scale data, but it may be inappropriate to make certain statements about such means. The reason for this argument lies in the

7 1145 presumption of equal intervals between values. For example, the intensity of feeling between strongly disagree and disagree is not clearly equivalent to the intensity of feeling between strongly agree and agree on the Likert scale (Cohen et al. 2000). Some non-parametric tests, such as Kruskall-Wallis and Mann Whitney, are more appropriate with ordinal scale data. These tests function as an ANOVA by ranks and are extremely powerful tests for the ordinal scale data when interval analysis is not appropriate. For example, the Kruskall-Wallis technique tests the null hypothesis that the k-samples come from the identical population with respect to mean entailing replacement of each observation by a single rank. Rank one replaces the lowest score and the rank of the total number of independent observations replaces the largest score. On the other side, researchers show that there is nothing wrong with using means and parametric tests for ordinal data. For instance, through empirical analyses, Baker et al. (1966) and Labovitz (1967) showed that it matters little considering ordinal scale data as interval scale data. Similarly, Santina and Perez (2003) employed means and standard deviations and performed parametric analyses such as ANOVA to their Likert scale data. Thomas (1982) highlighted that if an ordinal scale shows a normal distribution, it is appropriate to use the sample mean to estimate the population mean or test hypotheses. Sisson and Stoker (1989) also pointed out that if the survey process produces order, normality, t-tests, and other parametric procedures apply for ordinal scale data. It is important to note that different from other engineering areas (e.g. structural engineering, biology, or chemistry), many construction management terms are ambiguous, and their meaning can vary depending on research context. For example, the concept of risk management may consider the project level, program level, or enterprise level. Likewise, project delivery methods and procurement procedures while they are two different terms, they share some similar characteristics. Further, the concept of project delivery methods and procurement procedure vary slightly between horizontal and vertical construction projects as well as sophistication of participants. Thus, researchers should define explicitly their theoretical concepts on the research problem to maintain uniform definition and input from participants in the data collection process. DISCUSSIONS AND RECOMMENDATIONS Prior to any statistical analysis determining the approximate scale of measurement and variable data distribution is paramount. Grouping and graphical display of data provides invaluable insight into the scales of measurement. Properties of importance include general shape, typical value, spread, and outliers. Typically, the grouping and graphical display represents a sample distribution. These sample distributions (probability functions) are the basis for drawing a conclusion about variable association with a given population distribution (cumulative distribution function) (Devore 2012; Wackerly et al. 2008; Weiss 2005). Evaluation of the qualitative variables obtained through the CEM research non-experimental necessitates an understanding of some important distributions the binomial distribution, the multinomial distribution, and the Poisson distribution (Agresti 2013). The binomial distribution is an appropriate model for a series of

8 1146 Bernoulli trails that adhere to the following four assumptions: (1) n trials, (2) two outcomes, (3) independent trails, and (4) constant probability for each trail. The multinomial distribution is an extension of the binomial distribution and is an appropriate model where some trials allow for more than two outcomes. The Poisson distribution is an appropriate model for events occurring is space, time, volume, etc. where represents the average. A binomial random variable with a large sample size and a constant parameter may follow a Poisson random variable (Agresti 2013; Wackerly et al. 2008). Most of the non-experimental techniques discussed for CEM research will generally follow one of these basic probability distributions or a variant such as hypergeometric, geometric or negative binominal distributions. An additional distribution of interest is the chi-squared distribution. The chisquared distribution is an appropriate model for many statistics of a sampling distribution. Since both binomial and Poisson distributions converge to a normal distribution, a normal distribution might be suitable to model CEM research data providing the data is approximately normal. Many engineering and scientific processes follow this common distribution (Agresti 2013; Wackerly et al. 2008). Determining appropriate distributions to model data requires a numerical analysis beyond a basic graphical display. Probability plots and goodness-of-fit techniques such as the Kolmogorov-Smirnov or Anderson-Darling tests help identify an appropriate model. Another important concept in statistical modeling is parameter estimation. Some common estimation techniques include maximum likelihood, Wald, and method of moments (Agresti 2013; Wackerly et al. 2008). In addition to the aforementioned distribution selection techniques, data transformations techniques permit changing one random variable to another random variable. Common transformation methods include method of transformations, moment generating functions, and Jacobians (Casella and Berger 2002; Wackerly et al. 2008). Two transformations to change a random variable to a normal random variable are the Box-Cox transformation and the Johnson transformation. Since transformations change the response variable, any interpretation requires caution to prevent erroneous conclusions. Another common tool for displaying categorical data distributions is the contingency table. A contingency table displays relationship between categorical data as raw data or a proportion. Of special note are the concepts of relative risk and odds ratios. Relative risk is the ratio of probabilities and the odds ratio is the probability of a given outcome with respect to a base unit. The odds ratio is critical for inferences regarding binary random variables (Agresti 2013; Myers et al. 2010). Furthermore, inferential methods presented above for the scales of measurement, random variables following an exponential family distribution can utilize general linear modeling procedures. Examples of random variables that follow an exponential family distribution include, binomial, multinomial, Poisson, geometric, negative binomial, exponential, and normal random variables. General linear modeling allows the analysis to fit the data into a regression model. These regression models include linear, non-linear, logistic, stepwise, Poisson, and mixed effects regression models (Agresti 2013; Casella and Berger 2002; Kutner et al. 2004; Myers et al. 2010). An alternate perspective to general linear modeling is factor analysis. Essentially, factor analysis is an expansion of principle components

9 1147 analysis. The objective is to describe the variance-covariance configuration among a set of random variables. Factor grouping of correlated variables allows for data reduction and interpretation (Johnson and Wichern, 2007). CONCLUSIONS Statistical analysis within the CEM research realm relies heavily on categorical (i.e. nominal and ordinal) data obtained via non-experimental approaches. Fields such as sociology, psychology, and education advocate these non-experimental approaches often providing implicit solutions. Data acquired through experimental design address research questions in an objective manner leading to results that are more explicit. Thus, experimental data secured through design is preferred over nonexperimental data. Irrespective of data collection procedure, inappropriate statistical analysis can lead to erroneous conclusions. Applicable identification of measurement scales and sample data distribution allows for selection of suitable statistical techniques. Often more than one statistical technique is suitable for data analysis. However, final selection should minimize the statistical error to answer the intended research questions based on the CEM researcher s judgment. REFERENCES Abowitz, D. A., & Toole, T. M. (2010). Mized Method Research: Fundamental Issues of Design, Validity, and Reliability in Construction Research. Journal of Construction Engineering and Management, 136(1), Agresti, A. (2013). Categorical Data Analysis (3rd ed.). Hoboken, NJ: John Wiley & Sons. Baker, B. O., Hardyck, C. D., & Petrinovich, L. F. (1966). Weak Measurements vs. Strong Statistics: An Empirical Critique of S. S. Stevens's Proscriptions on Statistics. Education and Psychological Measurement, 26(2), Casella, G., & Berger, R. L. (2002). Statistical Inference (2nd ed.). Pacific Grove, CA: Duxbury. Cohen, L., Mansion, L., & Morrison, K. (2000). Research Methods in Education (5th ed.). London, UK: Routledge Falmer. Dayananda, D., Irons, R., Harrison, S., Herbohn, J., & Rowland, P. (2002). Capital Budgeting-Financial Appraisal of Investment Projects. Cambridge: Cambridge University Press. Devore, J. L. (2012). Probability and Statistics for Engineering and the Sciences (8th ed.). Boston, MA: Brooks/Cole. Erffmeyer, R. C., & Lane, I. M. (1984). Quality and Acceptance of an Evaluative Task: The Effects of Four Group Decision-Making Formats. Group & Organization Management, 9(4), Fellows, R. F., & Liu, A. M. (2008). Research Methods for Construction (3rd ed.). West Sussex, United Kingdom: Wiley-Blackwell. Gaito, J. (1980). Measurement Scales and Statistics: Regurgernces of an Old Misconception. Psychlogical Bulletin, 87(3), Hallowell, M. R., & Gambatese, J. A. (2010). Oualitative Research: Application of the Dephi Method to CEM Research. Journal of Construction Engineering and Management, 136(1),

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