Chapter 6: Rejection of Data

The fundamental question centers on whether an experimenter should discard a suspicious measurement or retain it for analysis. The chapter distinguishes between two scenarios: when a definite external cause for the anomaly can be identified, such as equipment malfunction or environmental interference, the data point should be rejected without hesitation. However, when no clear external cause exists, the decision becomes subjective and fraught with risk, as discarding data without justification invites accusations of data manipulation while retaining anomalous measurements might suppress important scientific discoveries. Rather than relying on subjective judgment or the impractical approach of repeating measurements hundreds of times, the chapter introduces Chauvenet's criterion, a statistical method grounded in the Gaussian distribution that provides an objective quantitative framework for rejection decisions. This criterion calculates how many standard deviations a suspect value lies from the mean, determines the probability of obtaining such a deviant result, and estimates the expected number of measurements that should be this extreme in a dataset of given size. If this expected number falls below 0.5, the measurement can be rejected according to the criterion. The chapter emphasizes critical limitations of this approach, particularly that the rejection threshold is inherently arbitrary and that uncertainty in standard deviation estimates becomes problematic with small sample sizes. Rather than applying Chauvenet's criterion and then moving forward with the reduced dataset, many researchers recommend a compromise approach: use the criterion to identify suspect data, then perform all analyses both with and without the questionable measurement to assess its actual impact on conclusions. The chapter also addresses practical scenarios such as handling multiple suspect measurements and explicitly warns against applying the criterion iteratively to progressively tighten a dataset. Ultimately, Chauvenet's criterion functions as a defensible last resort when measurement verification or repetition is infeasible, offering statistical rigor while acknowledging the inherent subjectivity embedded in any data rejection decision.