I'm comparing detection frequency of analytes in 150 paired stream samples using two different analytical methods. The results are provided in two columns with concentration reported for each method in ng/L. Nondetections are reported as <RL where RL is the reporting level. I've recoded the results with a 0 for a nondetection and a detection as a 1. I used the matched pair platform (jmp 9.0.3) to compare differences in detections.
We want to know whether one method has significantly more detections than the other method by analyte. I planned to use the non-parametric sign test because we only want to compare detections. The results for one analyte are shown below. The mean difference shows there are about 10 more detections (0.0667 x 150) in 2437 than in 2033 method.
1) The sign test p-value for 2-sided test is not significant (Prob ≥ |M| 0.0755), while the one-sided test is (Prob ≤ M 0.0378). Also the sum of the one-sided p-values does not equal 1, as in the case of the t-test. Can this be correct?
2) Is there a reference or any information on the Test Statistic M?
3) Is the sign test rather than the t-test or Wilcoxon signed rank test the best approach with all data either 0 or 1? Any suggestions on a better way to do this analysis?