Why an Extreme Value Needs Investigation
A very large or small number can draw attention because it differs from most of the values in a data set. That difference is a reason to look more closely, but it does not tell us what happened. The value might be a transcription error, a unit mismatch, or a genuine observation from an unusual case. Treating every extreme value as an error can erase real information; accepting every recorded value without checking can preserve mistakes.
The task is therefore to investigate the value using evidence. Compare it with its source record, confirm that the recorded units match the variable’s definition, and consider relevant measurement and study context. A value should not be changed or removed merely because it looks surprising.
A Flag Is Not a Verdict
A data check can identify a value worth reviewing, but the check and the review answer different questions. The check asks, “Does this value stand out?” The review asks, “Does the value correctly represent what was measured?” A numerical rule or comparison with the rest of the data can help locate candidates for review. It cannot, by itself, establish what was written on a source form, what units were used, or what happened during measurement.
This distinction is important even when a value seems implausible. An apparent impossibility may turn out to be a unit mismatch, or an unusual but accurate measurement. Conversely, a number that falls within a typical range may still be wrong if it was copied incorrectly. Unusualness and accuracy are related questions, not interchangeable conclusions.
A brief justification makes the logic clear. Suppose a flag is based only on whether a recorded value \(x\) is unusually large. Two records can have the same unusual \(x\): in one, the source record confirms the value; in the other, the source shows that a digit was added during entry. The flag is the same in both cases, but the evidence about accuracy differs. Therefore, the flag alone cannot determine whether the value is an error.
A Practical Investigation
Work through the evidence in a consistent order. Start with the recorded field and its definition: what quantity is this variable intended to represent, and in what units? Then compare the entry with the nearest available source record, such as an original form, instrument output, or laboratory record. If the values differ, check whether a transcription or unit conversion explains the discrepancy. Finally, use relevant context—such as repeated measurements, instrument limits, or the circumstances of collection—to assess whether the source value is credible.
Confirm the record, variable, and value under review. Do not assume that a value is wrong simply because it is the largest or smallest.
Compare the data entry with the original or closest available record. Look for misplaced decimal points, transposed digits, or a mismatch between the two values.
Confirm the units expected for the variable and the units in the source. If a conversion is needed, calculate it explicitly and check that the result matches the stored value.
Consider whether the measurement process or other records support the value. Classify it as a confirmed error, a supported valid extreme, or unresolved if the evidence does not settle the question.
The source record is evidence, not an infallible authority. It may itself contain a mistake, and a source may be unavailable. In those situations, context and independent records can help, but uncertainty should not be replaced with a guess. If the available evidence cannot establish what the value should be, leave the case unresolved for now rather than silently substituting a more typical number.
Worked Example: A Confirmed Transcription Error
In a hypothetical data set, adult height is stored in centimeters. One participant’s recorded height is 1,680 cm, far larger than the other values. The original measurement sheet lists the height as 1,680 mm. Determine whether the data entry is an error and what value the source supports in the data set’s units.
Check the units. The data field is in centimeters, but the source sheet gives millimeters. Since 10 mm = 1 cm, convert the source value:
The source value therefore corresponds to 168 cm, not 1,680 cm. The stored value matches the source number but not the required units: the millimeter value was entered into a centimeter field without conversion. This is a confirmed unit-related data error. The evidence supports 168 cm as the value represented by the source record. The conclusion comes from the source and the explicit conversion, not just from the fact that 1,680 cm is extreme.
Worked Example: A Decimal Entry Confirmed by the Source
In a hypothetical laboratory data set, a concentration is recorded in milligrams per liter. One value is 725 mg/L, while the original laboratory report for that sample says 72.5 mg/L. The units match, but the recorded value differs. Is this a valid extreme or an entry error?
Compare the records. The data field contains 725 mg/L; the source report contains 72.5 mg/L. The difference is a factor of 10:
The original report directly supports 72.5 mg/L, whereas the data entry has one misplaced decimal place. Provided the report belongs to this sample and the variable uses the same units, the evidence identifies a transcription error. A value of 725 mg/L might be numerically possible in some setting; that possibility does not override a source record that shows a different result. The decision is justified by matching the record and sample, not by choosing whichever number looks more typical.
Worked Example: A Valid but Unusual Measurement
In a hypothetical health data set, body mass is recorded in kilograms. One participant has a recorded value of 245.0 kg, much larger than most values in the file. The original scale record also shows 245.0 kg. A second measurement taken during the same visit is 244.6 kg, and the scale’s documented capacity is 300 kg. Should the value be treated as an error because it is extreme?
Check the source and units. Both records use kilograms, and the original scale record agrees with the data entry. The second measurement differs by:
The recorded value is also below the stated scale capacity:
These checks support the recorded value: the source agrees, the units match, the nearby repeat measurement is similar, and the instrument capacity does not contradict it. The value is unusual relative to the rest of this hypothetical data set, but the evidence does not indicate a recording error. Retain it as a valid extreme rather than changing or removing it solely to make the data look more typical.
When the Evidence Is Incomplete
Sometimes the source form is missing, the instrument record cannot be matched to a participant, or different records disagree. In those cases, the right conclusion may be that the value is unresolved. “Unresolved” does not mean “probably wrong,” and it does not mean “confirmed valid.” It means the available evidence is not sufficient to classify the value confidently.
For example, suppose a hypothetical study records a participant’s resting pulse as 18 beats per minute, but the original form is unavailable and there is no repeat measurement. The value warrants review, but the data alone cannot show whether a digit was omitted, the measurement was taken incorrectly, or the observation is accurate. The number should not be changed to 81 simply because that seems more familiar. Without supporting evidence, that would replace an observation with a guess.
A careful review separates what is known from what is suspected. Source records can confirm a mismatch; unit calculations can identify a conversion problem; repeated measurements can provide supporting context. But each piece of evidence has limits. A repeat value that differs somewhat does not automatically prove that one measurement is wrong, and an in-range value is not automatically accurate.
Common Mistakes
- Deleting a value because it is the most extreme. Extremeness identifies a candidate for review, not a data error. Check the source and context before deciding how to handle it.
- Changing a value to make it look plausible. A more typical replacement is not justified unless the available evidence supports that specific value.
- Confusing unusual with impossible. A value may be rare without being invalid. Conversely, a value can be wrong even if it falls among the others.
- Ignoring units because the digits look familiar. A number recorded in millimeters cannot be read as centimeters without conversion. Check the variable definition and calculate the conversion.
- Treating one source as unquestionable. Verify that the source belongs to the right record and uses the relevant measurement. If records conflict or are missing, recognize the uncertainty rather than forcing a conclusion.
The practical goal is not to remove every value that looks unusual. It is to preserve observations that are supported, correct values when there is evidence of a recording mistake, and avoid pretending that uncertain cases have been settled.
Check Your Understanding
For each situation, identify what evidence would help and whether the value is confirmed as an error, supported as valid, or still unresolved.
- A height field is defined in centimeters. The data file contains 1,720 for one record, and the source sheet gives 1,720 mm. What conversion should be made, and what does the comparison establish?
- A laboratory value stands far above the others, but the source report matches the data entry and the units agree. Is its unusualness enough to call it a data error? Explain.
- A value differs from its source record by a factor of 10. What should you check before concluding that a decimal-place transcription error occurred?
- An extreme value has no available source record and no repeat measurement. Why is replacing it with a more typical value not justified by the evidence?
- State the difference between an extreme-value flag and a confirmed data error.