Wait, What? The ugliest point on your graph may be the most scientifically valuable point you measured.

An outlying result can come from a recording mistake, instrument failure, contamination or an uncontrolled variable. But it can also reveal a real transition, hidden mechanism or failure of the model. Deleting it because it “spoils the line” destroys precisely the evidence that might teach you something.

Residuals measure disagreement with the model

For a fitted model, a residual is commonly:

residual = observed value − predicted value

A positive residual means the observation lies above the model prediction; a negative residual lies below it.

Why residual patterns matter

If residuals scatter randomly around zero, the model may be capturing the main trend. If residuals curve systematically from positive to negative and back, the fitted straight line may be missing curvature. If residual spread grows with x, measurement variability may increase with the independent variable.

A residual plot therefore asks a stronger question than “does the graph look straight?”

Anomalous does not mean disposable

An anomalous point is one that differs markedly from the expected pattern or neighbouring repeats. The first response is investigation, not deletion.

• Check the raw notebook entry.
• Check units and transcription.
• Inspect apparatus state.
• Ask whether the procedure changed.
• Repeat the measurement where scientifically and safely appropriate.
• Compare with independent replicates.

Repeat the condition, not the desired answer

If one point looks strange, repeat that experimental condition using the same defined method. Do not keep repeating until a value lands on the line. Repetition is a test of reproducibility, not a search for conformity.

Quantitative window

A model predicts 10.2, 20.1, 30.0, 39.9 and 49.8 units. Observations are 10.4, 19.8, 30.3, 47.5 and 50.1.

Residuals are +0.2, −0.3, +0.3, +7.6 and +0.3. The fourth point is qualitatively different from the others and deserves investigation.

If a repeat at the fourth condition gives 40.2, apparatus or recording failure becomes plausible. If repeats give 47.1, 47.8 and 47.4, the “outlier” may actually reveal a real local effect or wrong model.

When exclusion can be justified

Excluding data is strongest when there is an independent, documented reason: the sensor saturated; the sample spilled; the stopwatch was not started; contamination was observed; a known procedural criterion failed.

“It was far from the line” is not, by itself, an independent reason. That criterion uses the conclusion to decide which evidence is allowed to support the conclusion.

Predefined rules protect integrity

Where possible, decide exclusion rules before seeing the final pattern. For example: discard a trial if the temperature leaves the allowed range, if a negative control fails, or if a sensor exceeds its calibrated range.

Predefined criteria reduce the temptation to remove inconvenient results after the fact.

Outliers can belong to the biology

In biological sampling, genuine individual variation can be large. A tall plant, unusually high enzyme activity or atypical stomatal density may be real rather than erroneous. The sampling design and biological replicate structure determine whether such variation belongs in the population estimate.

Outliers can belong to a phase change

In Physics and Chemistry, an apparent outlier can mark a regime transition: elastic behaviour ending, sensor saturation beginning, boiling starting, equilibrium shifting or a reaction pathway changing. A model valid in one region may not apply across the transition.

Observation versus inference

Observation: “At x = 4, the measured value was 47.5 while neighbouring residuals were within ±0.3 of the model.”

Inference: “This condition is anomalous relative to the fitted model and deserves repeat measurement and apparatus review.”

Overclaim: “The point is wrong.”

Failure modes

• Deleting points because they reduce R².
• Repeating until the desired result appears.
• Calling natural biological variation experimental error.
• Ignoring a cluster of outliers that indicates model failure.
• Using different exclusion rules for different treatments.
• Reporting a cleaned graph without documenting exclusions.
• Confusing a large residual with proof of bad measurement.

Unfamiliar transfer: sensor saturation

A light sensor may respond linearly at low intensity and flatten near its maximum output. High-intensity points then appear as systematic negative residuals from a linear model. Those points are not random rubbish; they reveal the instrument’s range limit.

Secondary → JC → deeper Science

Secondary: identify anomalous results, repeat appropriately and avoid arbitrary deletion.

JC: calculate residuals, inspect patterns, justify exclusions and distinguish outliers from model breakdown.

Deeper Science: extend to robust regression, influence diagnostics, mixture models, change-point detection and preregistered exclusion criteria.

Checkpoint

One point lies far from a best-fit line. There is no recorded apparatus failure. What should you do before excluding it?

Answer key and WHY reasoning

Inspect the raw record and apparatus context, repeat the same condition where appropriate, and check whether the deviation is reproducible. Distance from the fitted line alone does not establish measurement failure.

How to study this

For every strange point ask: data-entry problem, apparatus problem, sample variation, or model problem? Then seek an independent test that distinguishes those explanations.

Evidence boundaries

Residuals measure disagreement with a specified fitted model. They do not identify the cause of that disagreement by themselves. Outlier classification requires context, uncertainty and transparent criteria.

Authoritative next steps

• NIST/SEMATECH e-Handbook of Statistical Methods
• Royal Society of Chemistry practical science resources
• Institute of Physics practical resources

Teaching Guide

Give students a dataset containing one transcription error, one genuine biological extreme and one region where the model bends. Ask them to propose a different diagnostic for each. The objective is to replace “cross out the anomaly” with causal investigation.