A lab measures a certified reference material with a known value of pH 7.00 and obtains: 6.72, 6.70, 6.73, 6.71, 6.72. What do these results indicate about the method?
AThe method is accurate but not precise — the results scatter around the true value
BThe method is both accurate and precise — the results are close together and close to 7.00
CThe method is precise but not accurate — the results cluster tightly around a mean that is significantly below the true value
DThe results show only random error, which can be eliminated by taking more measurements
The five readings range from 6.70 to 6.73 — a very tight cluster (high precision, low random error). But the mean (~6.716) is about 0.28 pH units below the certified value of 7.00. This offset is systematic error (bias): something in the method consistently shifts results in the same direction. High precision paired with inaccuracy is the classic signature of a systematic error — perhaps a miscalibrated electrode or a pH buffer that has degraded. Option D is wrong because systematic errors cannot be eliminated by averaging; averaging more replicates shrinks random error but leaves systematic error intact.
Question 2 Multiple Choice
A quality control lab runs 100 replicate analyses instead of 5, hoping to improve the reliability of their results. What will this strategy achieve, and what will it fail to correct?
AIt will reduce both systematic and random error equally, since more data is always better
BIt will reduce the standard deviation of the mean (random error) but will not correct any systematic bias present in the method
CIt will reveal systematic errors by making them statistically significant, thereby automatically correcting them
DIt primarily reduces systematic error; random error is unaffected by sample size
The standard deviation of the mean decreases by 1/√n with increasing replicates — this is the statistical averaging-out of random fluctuations that are equally likely to go high or low. Systematic errors, by contrast, push every single measurement in the same direction. Averaging 100 biased measurements yields a very precise (low spread) but still biased result. Identifying and eliminating systematic errors requires a different strategy: certified reference materials, method blanks, instrument calibration, or independent method comparison. More data cannot fix a broken calibration.
Question 3 True / False
Averaging a large number of replicate measurements will eventually correct for a systematic error in an analytical method.
TTrue
FFalse
Answer: False
This is the most dangerous misconception in analytical chemistry. Systematic errors (determinate errors) are directional — they shift every measurement the same way. Whether you take 5 or 5,000 measurements, if your balance reads 0.003 g too high, every result is 0.003 g too high. Averaging does not cancel directional bias; it only reduces the scatter from random (indeterminate) errors, which are equally likely to be positive or negative. Eliminating systematic error requires finding and correcting the source: recalibration, reagent replacement, blank correction, or method change.
Question 4 True / False
A set of measurements can be highly precise (low standard deviation) while simultaneously being inaccurate (mean far from the true value).
TTrue
FFalse
Answer: True
Precision and accuracy are independent properties. A method with strong systematic error — a contaminated reagent, a miscalibrated instrument, a consistent procedural bias — can produce beautifully reproducible results that are all wrong in the same direction. The dart-board analogy captures this: a precise but inaccurate thrower groups all darts tightly together, but the cluster is far from the bullseye. This independence is why analytical validation must demonstrate both precision (through replicate measurements) and accuracy (through reference material comparison) separately.
Question 5 Short Answer
A new analytical method gives highly reproducible results (RSD < 1%), but when tested against a certified reference material it consistently reads 8% too high across multiple runs and analysts. What type of error dominates, and how would you diagnose and correct it — without simply collecting more data?
Think about your answer, then reveal below.
Model answer: The consistent 8% high bias across multiple runs and analysts is the signature of systematic error (determinate error). It cannot be reduced by replication. Diagnosis involves identifying the root cause: check instrument calibration against traceable standards, test for reagent contamination (run a method blank), perform a spike recovery (add a known amount of analyte and check if it is quantitatively recovered), and compare results with an independent analytical method. Correction targets the identified source — recalibration, reagent replacement, blank subtraction, or method revision.
The key insight is that the corrective action must match the error type. Systematic errors require root-cause investigation: you cannot average your way to the right answer. The suite of diagnostic tools (reference materials, blanks, spikes, independent methods) each targets a specific potential cause. A blank rules out contamination; a spike recovery checks the method's extraction efficiency; an independent method comparison rules out instrument bias. This is why analytical method validation is a structured protocol, not just 'run it more times.'