Dixon’s Q-test for outlier rejection

dixon_q_test() compares the gap between a suspect value and its nearest neighbor, relative to the full data range, against a tabulated critical value (Q_CRITICAL_TABLE) that depends on sample size and confidence level.

from chemistrykit.analytical.systems.qtest import Q_CRITICAL_TABLE, dixon_q_test

Five replicate titration endpoints (mL), one of them clearly off:

replicates = [24.51, 24.55, 24.48, 24.53, 25.10]

for confidence in (0.90, 0.95, 0.99):
    result = dixon_q_test(replicates, confidence=confidence)
    verdict = "REJECT" if result.reject else "retain"
    print(f"confidence={confidence:.0%}: suspect={result.suspect_value}, Q={result.Q_statistic:.4f}, Q_crit={result.Q_critical:.4f} -> {verdict}")

confidence=90%: suspect=25.1, Q=0.8871, Q_crit=0.6420 -> REJECT
confidence=95%: suspect=25.1, Q=0.8871, Q_crit=0.7100 -> REJECT
confidence=99%: suspect=25.1, Q=0.8871, Q_crit=0.8210 -> REJECT

The critical value grows with confidence level (harder to reject at higher confidence) and shrinks with sample size (more data makes a single outlier easier to identify):

print("\nQ_crit(n, 95%) for n=3..10:")
for n in range(3, 11):
    print(f"  n={n}: {Q_CRITICAL_TABLE[n][0.95]}")

Q_crit(n, 95%) for n=3..10:
  n=3: 0.97
  n=4: 0.829
  n=5: 0.71
  n=6: 0.625
  n=7: 0.568
  n=8: 0.526
  n=9: 0.493
  n=10: 0.466

If the suspect value were retained instead (a smaller, more plausible deviation), the Q-test would not reject it even at 90% confidence:

close_replicates = [24.51, 24.55, 24.48, 24.53, 24.62]
result = dixon_q_test(close_replicates, confidence=0.90)
print(f"\nCloser data set: Q={result.Q_statistic:.4f}, Q_crit={result.Q_critical:.4f}, reject={result.reject}")

Closer data set: Q=0.5000, Q_crit=0.6420, reject=False