Unit 20
Measurement data and statistics
Every measured result should carry its uncertainty. Starting from the scatter of replicate measurements, this unit covers the Gaussian distribution, confidence intervals and Student’s t; uses t, F and Grubbs tests to decide whether a difference is real; propagates glassware tolerances into a final result; and ends with you building a calibration curve and reporting an unknown’s concentration with its confidence interval and detection limit.
- 1 Errors, the mean and the Gaussian distribution Two titrations differ by 0.08 mL — which is right? Random error spreads results into a bell curve, and averaging n of them tightens the mean by 1/√n — but does nothing for systematic error. 25 min
- 2 Confidence intervals and Student’s t Only four measurements — what does the mean tell you about the true value? Student’s t gives an honest confidence interval, and shows why extra replicates soon bring diminishing returns. 25 min
- 3 Comparing results: t tests, F tests and outliers Rayleigh’s two kinds of “nitrogen” differed by 0.5 %, and that difference led him to argon. Learn to decide whether a difference is real — and whether a suspect value may be rejected. 30 min
- 4 Propagation of uncertainty The burette, the pipette and the standard solution each carry an uncertainty — how do they combine in the final concentration? Absolute uncertainties for sums, relative ones for products, and special rules for logs and powers. 25 min
- 5 Calibration curves and detection limits Instruments give signals; concentrations come from a calibration line. Least-squares fitting, the unknown’s confidence interval, residual plots, detection and quantitation limits — and standard addition to beat matrix effects. 30 min