Statistical Calculation Guidelines

Statistical Calculations

The following statistics are calculated from the specimen groups:

Carryover Mean

Carryover Mean = Low (Test) Mean − Low (Control) Mean

The estimated carryover contamination — the average difference between test specimens (exposed to high-concentration carryover) and baseline controls (unexposed). A positive value indicates that test specimens are reading higher than the baseline, consistent with carryover. A value near zero suggests no meaningful carryover.

Upper Confidence Limit (UCL)

UCL = Carryover Mean + t(df, 0.95) × Standard Uncertainty

The upper bound of the 95% confidence interval for the carryover estimate — the worst-case carryover contamination with 95% confidence. The standard uncertainty accounts for variability in both the Low (Test) and Low (Control) groups. Degrees of freedom are calculated using the Welch-Satterthwaite equation to handle potentially unequal variances between the two groups. This is the primary value compared against the error limit for pass/fail.

Error Limit

Auto: 3 × Low (Control) SD | Concentration: user-defined absolute value | Percent: user-defined % × Low concentration

The maximum acceptable carryover. Three options are available: Auto (3 × the baseline SD — a statistical threshold derived from the observed control variability); Concentration (an absolute value in the same units as the result); or Percent (a percentage of the low specimen concentration value). The auto method is appropriate when no external acceptance criterion exists.

Pass/Fail: The study passes when the Upper Confidence Limit is less than the Error Limit. The UCL represents the worst-case carryover with 95% confidence — if even this upper bound falls below the error limit, the laboratory can be confident that carryover is within acceptable bounds. If the UCL equals or exceeds the error limit, the study fails and the instrument should be investigated.