## 2 Materials and Methods
### Statistical Analysis  
For descriptive statistics, I used the boxplot method to evaluate LEED-NCv4 categories and the median-interquartile range (IQR, 25 th-75 th percentile) to evaluate LEED-NCv4 credits instead of the mean \(\pm\) standard deviation because LEED data are associated with an ordinal scale. The boxplot method calculates the median (central mark red line in the figures), the edges of the box are the 25 th and 75 th percentiles of IQR, the whiskers extend to the most extreme data points the algorithm considers to be not outliers, and the outliers are plotted individually (red + in the figures) [20]. The dashed black line refers the possible points for LEED-NCv4 categories. In this study, to evaluate the boxplot results, the (1) median and (2) range between lowest edges of the box/whiskers and highest edges of the box/whiskers were recognized. A wide range was judged as inconsistency in achievement points in the category and a narrow range was judged consistency in achievement points in the category points across different projects. For inferential statistics, the nonparametric [PERSON]'s \(\delta\) effect size test was used instead of the parametric [PERSON]'s d test because the assumption of normality for LEED data was not met. [PERSON]'s \(\delta\) measures the difference magnitude between two distributions [21]. In the present study, effect size was measured between possible and achieved points in a category and credits for each certification level of LEED-NCv4 projects. Three items should be noted: (1) to perform nonparametric tests for independent groups, the minimum sample size was n\({}_{1}\) = n\({}_{2}\) = 4 [22] (p. 19). In the present study, the minimum sample size was n\({}_{1}\) = n\({}_{2}\) = 5. (2) [PERSON] et al. [23] used the Wilcoxon-Mann-Whitney (WMW) nonparametric test when one of the two groups contained the same values (\"somewhat unusual dataset\"). In parallel, [PERSON] [21] noted that the WMW U statistic can be used to estimate nonparametric \begin{table}
\begin{tabular}{c c} \hline \hline
**Certification** & **State 1 (Number of Projects)** \\ \hline \multirow{2}{*}{Certified} & NC (4), MI (3), TX (3), CA (2), FL (2), CT (1), GA (1), HI (1), IN (1), NC (1), PA (1), TN (1), WA (1) \\ \hline \multirow{2}{*}{Silver} & FL (4), CO (2), MA (2), UT (2), CA (1), IA (1), ID (1), IL (1), MI (1), MO (1), MS (1), NJ (1), OH (1), SD (1), TN (1), VA (1) \\ \hline \multirow{2}{*}{Gold} & CA (5), AR (1), FL (1), MA (1), OR (2), PA (1) \\ \hline \multirow{2}{*}{Platinum} & \multirow{2}{*}{CA (2), CO (1), MI (1), VA (1)} \\ \cline{2-2} \cline{4-4}  & & \\ \hline \end{tabular} Notes: 1 AR, Arkansas; CA. California; CO, Colorado; CT, Connecticut; FL, Florida; GA, Georgia; HI, Hawaii; ID, Idaho; IL, Illinois; IN, Indiana; IA, Iowa; MA Massachusetts; MI, Michigan; MS, Mississippi; MO, Missouri; NJ, New Jersey; NC, North Carolina; OH, Ohio; OR, Oregon; PA, Pennsylvania; SD, South Dakota; TN, Tennessee; TX, Texas; UT, Utah; VA, Virginia; WA, Washington.  
\end{table} 
Table 1: Distribution of Leadership in Energy and Environmental Design (LEED)-NCv4 Certified, Silver, Gold, and Platinum projects in the U.S. in 2015-2019.  
effect size. (3) I focused on substantive significance (effect size) but not statistical significance (\(p\) value) in the analysis of LEED-NCv4 projects because statistical significance depends on sample size, whereas effect size does not [24]. [PERSON]'s \(\delta\) ranged between \(-1\) and \(1\); positive (+) values indicate that Group 1 is larger than Group 2, null (0) indicates equality or overlap, and negative (-) values indicated that Group 2 was larger than Group 1 [21]. According to [PERSON] et al. [25], effect size is considered to be negligible if \(|\delta|<0.147\), small if \(0.147<|\delta|<0.33\), medium if \(0.33<|\delta|<0.474\), and large if \(|\delta|\geq 0.474\).