Welch's T-Test Comparison
Welch's T-Test Comparison
Description:
Welch's Two Sample t-test is provided in the USEPA Draft Unified Guidance as a test to determine if compliance location measurements are statistically elevated when compared to background. It is a parametric test, and therefore a normal distribution (of residuals) is required, however equal variance is not required for this test. Welch's t-test is a modification of the student's t-test for unequal variances among the populations. In ChemStat, the test can be performed at the 99%, 97.5%, 95%, or 90% confidence levels. The test can be performed comparing all compliance well measurements as a group to the group of background data, or comparison an individual compliance well to the group of background data.
Use:
Use the Welch's t-test to determine if compliance observations as a group are statistically elevated when compared to background as a group, or if an individual well is statistically elevated when compared to background.
Remarks:
At least two background measurements and two compliance measurements are required to prevent divide by zero errors. But this is a bare minimum, and many more samples are recommended for effective use.
Note that statistical significance could mean that either compliance measurements are statistically elevated when compared to background, or background measurements are statistically elevated when compared to compliance measurements.