Environmental Statistics and Instrumentation: Measurement and Inference
This domain tests statistical description and inference alongside analytical measurement principles. Questions combine small data sets with tests, or instrument principles with calibration calculations.
Core rules and concepts
- Descriptive statistics: mean, median, standard deviation with n-1 denominator, coefficient of variation, standard error = s/sqrt(n).
- Inference: Type I error (false rejection) equals the significance level; Type II error is failing to reject a false null; p-value is the probability of results at least as extreme given the null.
- Tests: one-sample and two-sample t-tests, paired t-test, chi-square for categorical data, ANOVA for three or more means, regression with r2 and residual checks.
- Measurement quality: accuracy versus precision; calibration curve and r2; method detection limit; limit of quantification usually about 3 times MDL.
- Instruments: Beer-Lambert for UV-Vis; AAS and ICP-MS for metals; GC-MS for volatiles; HPLC for non-volatile organics; nephelometry for turbidity; electrochemical and optical sensors for pH and DO.
Worked example
A dye has molar absorptivity 1.5 x 10^4 L/mol cm and absorbance 0.45 in a 1 cm cell. c = A/(eb) = 0.45/(1.5 x 10^4 x 1) = 3.0 x 10^-5 mol/L, i.e. 30 umol/L. If the absorbance were 0.90, concentration would double, but above about 1.0 absorbance linearity often fails. The reasoning point is that absorbance is proportional to concentration only within the calibrated linear range.
Traps that cost marks
Dividing by n instead of n-1 for a sample standard deviation; converting absorbance incorrectly (A = 2 - log %T); confusing MDL with LOQ; interpreting a p-value as the probability that the null hypothesis is true.