Statistical techniques for analyzing of soil vapor intrusion data: A case study of manufactured gas plant sites

Figures & data

Figure 1. Reporting limits for censored data in indoor air samples. Dotted black line represents U.S. EPA BASE 50th percentile values; solid gray line represents 50th percentile values from NYSDOH study; dashed black line represents median LOQ in U.S. EPA study; and dashed gray line represent laboratory detection limit in NYSDOH study (LOQ, limits of quantitation; EPA 50, EPA 50th percentile value; DOH 50, 50th percentile value from NYSDOH study.) Figure generated using lattice package in R (Sarkar, 2008).

Table 1. Variations of statistical methods used in this work

Method	Description
Percentile computation methods:
KM	Kaplan–Meier method
MLE	Maximum likelihood estimation
SUB	Substitution method (one-half of reporting limit)
REJ	Reject censored data
Sample weighting strategies:
A	Equal weights for all samples
B	Equal weights for all buildings
Bootstrapping strategies:
I	Simple case sampling
II	Conditional bootstrapping
III	Resampling at building level

Table 2. Sample characteristics for MGP-VI database (N = number of samples, RL = reporting limit in μg/m³)

	Indoor Air				Beneath Slab
Compound	N	Percent detected	Minimum RL	Maximum RL	N	Percent detected	Minimum RL	Maximum RL
1,2,3-Trimethylbenzene	599	29.2	0.39	22	165	30.3	0.98	260
1,2,4-Trimethylbenzene	1112	60.6	0.39	20	298	70.8	0.39	64
1,3,5-Trimethylbenzene	1112	23.7	0.39	49.1	298	47.7	0.39	64
Benzene	1118	84.3	0.64	7	304	81.6	0.26	41
Ethylbenzene	1118	66.0	0.35	17	304	72.4	0.35	85
m,p-Xylene	1118	87.7	0.7	7.7	304	86.2	0.35	85
Naphthalene	1148	22.0	0.35	1047.8	292	30.5	1	280
o-Xylene	1118	67.7	0.35	17	304	72.4	0.35	85
Toluene	1118	95.4	0.56	6.7	304	95.1	0.3	74
Indane	922	10.7	0.39	52	258	15.9	0.39	130
Indene	921	1.0	0.12	51	258	3.1	0.07	130

Figure 2. Bootstrap distributions for different hypothesis tests (case B-III). Figure generated using lattice package in R (Sarkar, 2008).

Table 3a. Summary of selected statistical computations for 50th percentile concentration (all concentration values and confidence limits are expressed in μg/m³; percentile values in μg/m³ using substitution method [SUB-A] and by rejecting censored data appear [REJ-A] below the names of the compound)

Compound	Method	Concentration	Bootstrap strategy	Bootstrap concentration	2.5th Percentile bootstrap confidence limit	97.5th Percentile bootstrap confidence limit
Naphthalene (SUB-A = 1.80;REJ-A = 0.61)	KM-A	0.47	I	0.47	0.42	0.52
			II	0.47	0.42	0.52
			III	0.48	0.41	0.56
	KM-B	0.50	III	0.49	0.40	0.58
	MLE-A	0.50	I	0.50	0.46	0.54
			III	0.50	0.43	0.60
	MLE-B	0.47	III	0.47	0.39	0.55
Toluene (SUB-A = 5.80; REJ-A = 6.20)	KM-A	5.80	I	5.83	5.30	6.30
			II	5.83	5.30	6.30
			III	5.85	4.80	6.90
	KM-B	5.70	III	5.71	4.80	6.60
	MLE-A	6.37	I	6.37	5.95	6.82
			III	6.42	5.32	7.69
	MLE-B	6.12	III	6.13	5.37	6.96
Ethylbenzene (SUB-A = 0.95; REJ-A = 1.00)	KM-A	0.78	I	0.78	0.74	0.83
			II	0.78	0.74	0.83
			III	0.78	0.69	0.90
	KM-B	0.78	III	0.80	0.73	0.88
	MLE-A	0.91	I	0.92	0.86	0.98
			III	0.92	0.79	1.07
	MLE-B	0.90	III	0.90	0.81	1.00

Table 3b. Summary of selected statistical computations for 90th percentile concentration (all concentration values and confidence limits are expressed in μg/m³; percentile values in μg/m³ using substitution method [SUB-A] and by rejecting censored data [REJ-A] appear below the names of the compound)

Compound	Method	Concentration	Bootstrap strategy	Bootstrap concentration	2.5th Percentile bootstrap confidence limit	97.5th Percentile bootstrap confidence limit
Naphthalene (SUB-A = 10.50;REJ-A = 6.80)	KM-A	1.80	I	1.85	1.30	2.20
			II	1.85	1.30	2.10
			III	1.79	0.84	2.90
	KM-B	1.60	III	1.49	0.84	2.20
	MLE-A	2.25	I	2.25	1.92	2.61
			III	2.26	1.71	2.95
	MLE-B	2.17	III	2.17	1.68	2.73
Toluene (SUB-A = 28.30; REJ-A = 30.00)	KM-A	29.00	I	28.69	24.00	36.00
			II	28.64	24.00	36.00
			III	29.41	20.00	45.00
	KM-B	25.00	III	25.69	21.10	32.70
	MLE-A	28.25	I	28.29	24.70	32.30
			III	28.45	21.07	37.37
	MLE-B	26.73	III	26.76	21.27	33.48
Ethylbenzene (SUB-A = 4.00; REJ-A = 5.81)	KM-A	4.00	I	4.00	3.50	4.70
			II	4.00	3.60	4.70
			III	4.06	2.70	5.64
	KM-B	3.60	III	3.43	2.40	4.20
	MLE-A	3.89	I	3.90	3.39	4.46
			III	3.91	2.87	5.32
	MLE-B	3.28	III	3.28	2.69	3.98

Table 4. Results of hypothesis test to compare MGP with U.S. EPA BASE data (G _ρ values are for EPA BASE group; p-values based on 5000 repetitions)

		ρ = 0		ρ = 1
Compound	Sample weights and bootstrap strategy	(Gρ)EPA	Bootstrapped p value	(Gρ)EPA	Bootstrapped p value
Naphthalene	B-I	3.9	3.04E-02	4.5	4.00E-04
	B-III	3.9	2.53E-01	4.5	4.42E-02
	A-I	27.9	1.40E-03	27.8	˜0.00
Toluene	B-I	25.3	˜0.00	13.9	˜0.00
	B-III	25.3	˜0.00	13.9	˜0.00
	A-I	108.5	˜0.00	61.8	˜0.00
Ethylbenzene	B-I	28.0	˜0.00	19.9	˜0.00
	B-III	28.0	˜0.00	19.9	˜0.00
	A-I	128.2	˜0.00	89.9	˜0.00