4 Journal of Toxicology Table 4: Correlation analyses of initial autism severity versus urinary metal excretion and initial glutathione. The metal excretion is measured both at Baseline (before DMSA) and after the 9th dose of DMSA. The ﬁrst number in each cell is the correlation coeﬃcient (r) and the second number is the P-value. Correlation coeﬃcients with P < .05 are in bold. The last 2 rows list the total number of positive and negative correlation coeﬃcients, respectively. PbBase SnBase TlBase HgBase SbBase Wbase AsBase CdBase AlBase Pb9 Sn9 Tl9 Hg9 Sb9 W9 As9 Cd9 Al9 Glut1 Number of positive coeﬃcients Number of negative coeﬃcients ATEC total −0.00 (0.96) 0.16 (0.32) 0.13 (0.32) 0.13 (0.33) 0.40 (0.002) 0.16 (0.23) 0.04 (0.74) 0.00 (1.00) −0.06 (0.65) 0.27 (0.04) −0.02 (0.88) 0.26 (0.046) 0.09 (0.52) 0.03 (0.84) 0.11 (0.42) 0.19 (0.16) 0.07 (0.58) 0.06 (0.65) 0.25 (0.04) 17 2 ADOS (social + communication) 0.11 (0.47) −0.11 (0.47) 0.10 (0.49) 0.05 (0.76) 0.35 (0.02) 0.07 (0.67) −0.05 (0.73) 0.11 (0.48) −0.19 (0.20) 0.34 (0.02) 0.00 (0.98) 0.11 (0.51) 0.20 (0.18) 0.20 (0.19) 0.34 (0.02) −0.24 (0.12) 0.34 (0.024) 0.28 (0.059) 0.34 (0.024) 15 4 SAS 0.50 (0.0002) 0.12 (0.41) 0.21 (0.15) 0.15 (0.31) 0.51 (0.0002) 0.26 (0.07) 0.00 (0.98) 0.03 (0.83) −0.05 (0.73) 0.36 (0.01) 0.02 (0.87) 0.27 (0.064) −0.02 (0.91) 0.38 (0.008) −0.00 (0.99) −0.24 (0.11) 0.08 (0.57) 0.25 (0.089) 0.25 (0.09) 15 4 PDD-BI (modiﬁed autism score) 0.22 (0.12) 0.09 (0.52) 0.25 (0.077) 0.18 (0.19) 0.42 (0.0023) 0.17 (0.22) 0.04 (0.76) −0.10 (0.48) 0.02 (0.87) 0.42 (0.0027) −0.12 (0.42) 0.24 (0.098) 0.07 (0.59) 0.26 (0.065) 0.19 (0.18) −0.04 (0.79) 0.15 (0.29) 0.17 (0.24) 0.26 (0.70) 16 3 correlate with higher severity of autism, as expected. Also, the initial glutathione correlates positively with two of the severity scales at P < .05. However, because we are analyzing many correlations, a traditional P-value of <.05 is not a rigorous guide. Since we are analyzing 76 possible correlations, random chance alone would result in approximately 4 results at P < .05. We found 13 instances of P < .05 for toxic metals, and the probability of that occurring randomly is 7 × 10−5, so it is very likely that most, but probably not all, of the correlations represent actual relationships. One way to deal with the problem of multiple correlation analyses is the Bonferroni approach. Using this approach involves dividing the nominal P-value by the number of tests, so that for 95% conﬁdence one needs a P-value less than .05/76, or P < .0007. Using the Bonferroni approach, the correlations between initial Severity of Autism Scale (SAS) and baseline excretion of lead (Pb) and antimony (Sb) are signiﬁcantly diﬀerent from 0 at the 95% conﬁdence level, and these are the only pairs that meet the Bonferroni criterion for the 5% signiﬁcance threshold. Again, it should be noted that this is a conservative approach, designed to ensure that very few nonsigniﬁcant correlations are misrepresented as signiﬁcant. False discovery rate (FDR) is a less conservative method for performing multiple hypothesis tests, based on con- trolling the expected number of false positives among the cases declared signiﬁcant. If we use FDR on the summary severity scores, then in addition to the results obtained from the Bonferroni analysis, the correlation between Initial ATEC Total and baseline excretion of antimony (Sb), and the correlations between Initial PDD-BI Autism Total and baseline excretion of antimony (Sb) and 9th dose excretion of lead (Pb) are signiﬁcantly diﬀerent from 0; we will term these ﬁndings “marginally signiﬁcant.” Next, consider the numbers of positive and negative sample correlation coeﬃcients in the table. If there were no statistically signiﬁcant correlations between autism severity and biological measures then we would expect on average about equal numbers of positive and negative sample correlation coeﬃcients. For the summary severity measures, we observed 63 positive sample correlation coeﬃcients (r’s) and 13 negative r’s. This corresponds to a P-value of 3 × 10−9 for the hypothesis that there is no correlation between the severity measures and biological measures. Thus it is extremely likely that there is a high overall positive correlation between the severity measures as a group and the biological measures taken as a group. Finally, the average of all of the 76 sample correlation coeﬃcients is 0.14. If there were no statistically signiﬁcant correlations between autism severity and the biological measures, the average of 76 sample correlation coeﬃcients