Statistics for Lab Sciences: Calibration, Uncertainty & QC

What you'll build

What you will be able to do

Each lab ends with a concrete result that you build yourself and the checker confirms, cell by cell.

• Summarise six replicate nitrate results for four samples with the mean, the sample standard deviation and the %RSD, and check whether the QC standard's certified value lies inside the 95% confidence interval.
• Test whether one suspicious result among ten replicates may be rejected: you calculate Grubbs' G and its critical value from the t distribution, make the decision with IF and cross-check with Dixon's Q.
• Fit the straight-line calibration of the nitrate method from seven standards, check R² against the acceptance limit, look at the residuals and draw the curve as a scatter chart with a trendline.
• Turn the mean signal of four samples into concentrations with the calibration line, estimate the standard error of each result with the textbook formula, build a 95% interval and decide whether a sample is above the action level.
• Estimate the limits of detection and quantitation of the nitrate method in two ways (residual SD of a low-level curve and SD of blanks) and label four low results as ND, DNQ or a reportable value.
• Build a small uncertainty budget for the lab's 100 mg/L nitrate stock standard: standard uncertainties from certificates and tolerances, the sum rule for a mass by difference, the product rule for the concentration and the expanded uncertainty with k = 2.
• Put 20 runs of the QC check standard on a Levey-Jennings chart with mean ± 2s and ± 3s lines, turn every result into a z score and let formulas flag the Westgard rules 1-3s, 2-2s and 4-1s.
• Compare a field test kit with the lab method on ten shared samples: differences, the paired t statistic, the p-value with T.TEST and a conclusion, and you see why an unpaired test would miss the bias.