Table 2.

Accuracy of k-means cluster analysis for subgrouping homes by region in the household exposure study (HES; Massachusetts and California) and Green Housing Study (GHS; Boston, Massachusetts, and Cincinnati, Ohio) using concentrations of chemicals detected in at least 10 percent of residential indoor air or dust samples.

Study	Homes ($n$)	Sample matrix	Chemicals in studya ($n$)	Chemicals in cluster analysisb ($n$)	Reporting limits	Accuracyc (%)	Adjusted Rand indexd
HES	122	Air	24	13	Originale	98.4	0.93
HES	122	Air	24	13	Censoredf	92.6	0.72
HES	120	Dust	44	25	Original	96.7	0.87
HES	120	Dust	44	18	Censored	55.8	0
GHS	77g	Air	35	28	Original	80.5	0.36
GHS	77g	Air	35	28	Constanth	80.5	0.36

^aNumber of chemicals measured in the same medium in all homes in each cluster analysis.

^bNumber of chemicals detected in at least 10% of homes given the reporting limits used in each analysis.

^cNumber of homes correctly grouped by region using k-means clustering divided by the total number of homes analyzed.

^dThe adjusted Rand index measures similarity between the two clusters identified by k-means analysis and the two true regional subgroups in the data. It has an expected value of zero for random clusters and a maximum value of 1 in the case of perfect agreement.

^eIn analyses using the original reporting limits, concentrations that were not detected were substituted with the sample-specific reporting limit (SSRL). We calculated the SSRL as the method reporting limit (MRL) divided by the sample-specific volume of air or sample-specific mass of dust.

^fIn analyses with censored reporting limits, we calculated the most frequent MRL reported in each site (in cases of ties we used the lower value). We defined ${\text{MRL}}_{\text{censor}}$ as the higher of the two modal MRLs and calculated censored sample-specific reporting limits (${\text{SSRL}}_{\text{censor}}$) as ${\text{MRL}}_{\text{censor}}$ divided by the sample-specific volume of air or sample-specific mass of dust. For all records where the original SSRL or detected or estimated concentration was lower than ${\text{SSRL}}_{\text{censor}}$, the concentration was substituted with ${\text{SSRL}}_{\text{censor}}$.

^gCluster analysis was performed on 77 homes comprising 105 samples. A total of 49 homes were sampled once, and 28 homes were sampled twice approximately six months apart. For homes sampled twice, we used the average exposure for each chemical.

^hNondetects were substituted with the MRL divided by the median volume of air across Boston, Massachusetts, and Cincinnati, Ohio.