You open a dataset of successful companies.
Every company in the file survived long enough to be recorded.
Where are the companies that failed before anyone began collecting the data?
They are not blank rows.
They are absent rows.
That is truncation.
Quick Read
Truncation occurs when observations outside a defined range or observation mechanism are not included in the dataset at all. In left truncation, cases with values below or before a threshold may be absent. In right truncation, cases beyond an upper boundary may be absent. Unlike censoring, where an incomplete case remains visible, truncation can remove the case itself from the observed sample.
One-sentence answer: truncation is lossy because the observation rule can erase entire cases before analysis begins, making the visible dataset a selected subset of the source population.
The Most Dangerous Missing Data Is the Row You Never Knew Existed
A blank cell announces a problem.
A censored observation announces a boundary.
A truncated case may announce nothing because it never appears.
This makes truncation epistemically dangerous. The analyst can receive a perfectly complete table whose population is already distorted.
Left Truncation: You Must Survive Long Enough to Be Seen
Imagine studying longevity by enrolling only people who are alive at age 80.
Anyone who died before 80 cannot enter the sample.
The observed population is conditioned on surviving to the entry point.
Analyse it as though it were a random sample from birth and the resulting survival estimates can be badly biased.
Right Truncation: Only Events That Happened Soon Enough Are Visible
Suppose researchers collect records only for events that occurred before a database cutoff date.
Long-delay cases whose events occur after the cutoff are absent.
The observed sample overrepresents shorter delays because those are the cases able to enter the record in time.
Truncation Is Selection
The defining question is not “which value is missing?”
It is “which cases were allowed to become observable?”
That makes truncation closely related to selection bias. An observation mechanism filters the source population before the analyst sees it.
Survivorship Bias Is Truncation With a Story Attached
Study only investment funds that still exist and failed funds vanish.
Study only bestselling authors and manuscripts that never reached publication vanish.
Study only old buildings that survived and demolished construction disappears from architectural intuition.
The survivors can look as though their characteristics caused success when part of the apparent pattern comes from the selection rule.
Detection Limits Create Truncated Worlds
A telescope detects only sources brighter than a threshold.
A survey records only transactions above a reporting limit.
An archaeological record preserves durable materials better than fragile ones.
The resulting dataset can look like a complete inventory of what exists when it is actually an inventory of what the observation system could admit.
Historical Archives Are Truncated by Survival
Stone survives differently from cloth.
Official documents survive differently from casual conversation.
Powerful institutions often produce and preserve more records than people without institutional infrastructure.
The archive is not merely a sample of the past. It is a population filtered by creation, survival, collection and preservation.
Search Results Truncate Before Ranking
A ranking can order only candidates that entered the candidate set.
If retrieval misses a relevant document, no ranking algorithm can place it first.
This is a powerful distinction: ranking loss happens among visible candidates; truncation loss can remove a candidate before ranking begins.
Education: Attendance Can Truncate the Teacher’s Model
A teacher sees the work students submit.
The student who stops attending, stops submitting or leaves the programme may disappear from the classroom evidence stream.
If later analysis includes only students with complete portfolios, the hardest cases can be systematically underrepresented.
A neat dataset of completers can produce an unrealistically optimistic picture of the intervention.
Publication Bias Can Resemble Truncation
If studies with striking results are more likely to be published, the visible literature is selected from a larger universe of conducted research.
The unpublished studies are not missing cells inside published papers. They may be missing documents from the accessible evidence base.
This is not mathematically identical to every formal truncation model, but the structural warning is similar: the observed collection may be conditioned on passing an entry rule.
Range Restrictions Flatten Relationships
Select only high-performing students and the relationship between prior attainment and later marks can look weaker than it does across the full population because much of the original variation has been removed.
Selection changes the geometry of the data.
A relationship measured inside a truncated range should not automatically be exported to the full source population.
Truncated Distributions Need Truncated Models
If values below zero are impossible or values below a reporting threshold are absent, fitting an ordinary unbounded distribution can assign probability to regions the observation mechanism could never show.
Statistical models can explicitly condition on truncation limits.
The observation rule belongs inside the likelihood because it shaped which data were capable of appearing.
Truncation and Redaction Are Different
Redaction begins with a richer known record and deliberately withholds selected content from a receiver.
Truncation can prevent cases from entering the observed record in the first place.
One is a release decision. The other is an observation or inclusion boundary.
When Truncation Is Legitimate
Every study has a target population.
If a study explicitly concerns adults aged 65 and above, excluding children is not a flaw. The danger arises when conclusions silently expand beyond the population defined by the inclusion mechanism.
A bounded dataset is not dishonest when its boundary is visible and respected.
A Practical Truncation Audit
- Source population: who or what could theoretically exist?
- Entry rule: what must happen for a case to enter the dataset?
- Invisible cases: which cases fail that rule and therefore leave no row?
- Direction: is truncation left-sided, right-sided or more complex?
- Selection: is inclusion related to the outcome or predictors of interest?
- Generalisability: are conclusions being extended beyond the observed range?
- Model: does the analysis account for the truncation mechanism?
Continue Through eduKateSG
Continue with the companion How Lossy Works | Censoring, How Lossy Works | Sampling, and How Lossy Works | Redaction. Censoring leaves a partial case; truncation can remove the case; redaction withholds known information from a receiver.
Final Thought: A Perfect Table Can Still Be Missing the World
Truncation is dangerous because nothing has to look broken.
Every visible row can be complete.
The loss happened before the table began.