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The steel congestion ratio is presented by “the total quantity of reinforcement contained in the concrete volume” (Jarkas 2005) and is expressed in kg per cubic meter ( kg/m 3 ). The volume of concrete, and height above ground level factors, are presented by the actual volume in cubic meter ( m 3 ) of concrete placed, and the actual height in meter (m), relative to the ground level on which the mobile crane or pump is parked, of elements concreted, respectively.
The effects and relative influence of buildability factors investigated on concreting labor productivity were analyzed by using the categorical-regression method. Because the workability is classified into three different qualitative categories, a three-category “dummy” variable was introduced into the multiple regression model to quantify the average difference in labor productivity among the three categories (high, medium, and low). Medium workability was chosen to represent the “base” or “reference” category and thus was omitted from the regression model. The regression coefficients of the high and low workability concrete, therefore, quantify the average difference in concreting labor productivity between the reference, i.e., omitted category, and the corresponding present categories of concrete workability in the model. For more detailed information and discussion of categorical-regression, the reader is referred to Hardy (1993).
It is important to note that because a multiple regression model involves more than one independent variable, which may have different units of measurement, a direct comparison of the size of various coefficients to assess their relative influence on the dependent variable, i.e., labor productivity, could be spurious. Therefore, before a meaningful investigation of the relative influence of the independent variables, i.e., buildability factors, can be conducted, the regression coefficients must be standardized (Kim and Feree 1981). The standardized regression coefficients are then measured on the same scale, with a mean of “0” and a standard deviation of “one”, and thus are directly comparable to one another with the largest coefficient in absolute value indicating the greatest influence on the dependent variable.
To achieve reliable and robust statistical inferences about the regression relationships among buildability factors investigated and concreting labor productivity, the “two-tailed parametric hypotheses testing” method at 5% significance level was used throughout the data analysis phase of this research. The extent to which the data disagree with the “null hypothesis ( H 0 )” (that is, the regression coefficient of the corresponding buildability factor, i.e., the average rate of change or slope of the factor within the regression model is insignificantly different from zero; therefore, its effect on labor productivity is statistically insignificant), was determined by the p -value obtained for each factor investigated. The smaller the p -value of the corresponding factor, the greater the extent of disagreement between the data and the null hypothesis, and the more significant the result is. In general, if the p -value of the regression coefficient is less than the significance level, i.e., p-value<5% , the null hypothesis is rejected in favor of the “alternate hypothesis ( H a )”, that is, the regression coefficient of the corresponding buildability factor, i.e., the average rate of change of the factor in the model is significantly different from zero, and hence its effect on labor productivity is statistically significant (Sincich et al. 2002).
However, the parametric hypotheses testing method requires the data to be approximately normally distributed. Therefore, to fulfill this condition and thus achieve reasonable validity and reliability of the statistical results, it was necessary to collect, for both placement methods investigated, a sufficiently large sample size. On the basis of the “Central Limit Theorem”, a minimum sample size of 30 should safeguard against major deviation from normality (Sincich et al. 2002), nonetheless, this benchmark was substantially exceeded during the data collection phase of this study.