Missing Answers vs. Wrong Answers: Why a Blank Is Worth Twice a Confident Guess (2026)

Short answer: a blank and a wrong answer are not two grades of the same problem. Error-correcting codes treat them as formally different things, and price them at exactly two to one. Damage whose location you know is called an erasure; damage whose location you do not know is called an error. A code that can repair one error can repair two erasures from the same budget. The uncomfortable consequence for research is that almost every design choice that pushes a participant to answer rather than letting them decline converts a cheap erasure into an expensive error - and the single most-repeated piece of survey advice in the field tells you to make that trade on purpose.

This is not an article about response rates or about participants who never showed up. Those are questions about who is missing from your sample. This is about a specific participant who is sitting in front of you, on a specific question, who does not know the answer - and about what your instrument does with that fact.

The distinction that does all the work

Coding theory draws a line that survey methodology mostly does not. From the standard treatment of block codes:

C can correct d - 1 erasures. By erasure it means that the position of the erased symbol is known.

That second sentence is the entire idea. An erasure is not a weaker error. It is a different object, defined by one property: you know where it is. You have a marked slot, and you know the mark is there.

An error has no mark. It arrives looking exactly like valid data. Before you can repair it you have to solve two problems - first find it, then fix it. An erasure hands you the first problem already solved.

The exchange rate, written as one inequality

The cost difference is not a matter of degree. It is exact, and it falls out of the standard bound on what a code with minimum distance d can repair:

2t + f < d

where t is the number of errors and f the number of erasures. An error consumes two units of the distance budget. An erasure consumes one. That is the whole result, and everything else in this article is a consequence of it.

The two endpoints of that inequality are the two rules most people already know:

A code with distance d allows the receiver to detect up to d - 1 transmission errors since changing d - 1 positions of a codeword can never accidentally yield another codeword.

Furthermore, if no more than ( d - 1 ) / 2 transmission errors occur, the receiver can uniquely decode the received word to a codeword.

Set f = 0 and the inequality gives t < d/2, which is the correction rule, floor((d-1)/2). Set t = 0 and it gives f < d, which is the erasure rule, d - 1. The same inequality produces both, which is a useful check that you have it right.

A worked table at d = 9

The interesting part of 2t + f < d is the middle, where both kinds of damage are present. At d = 9 the budget is 2t + f <= 8, and every row below spends it exactly:

Read down the table. Each error you eliminate buys you two erasures. The top row is the familiar correction limit of 4, and the bottom row is the familiar erasure limit of 8 - both of which match the two quoted rules independently, which is how you know the table is not decorative.

The practical reading: if you can convert an unknown-bad answer into a known-blank answer, you have not merely made the damage more honest. You have halved its cost.

What counts as an erasure in an interview

An erasure is any answer that arrives pre-labelled as unusable. The label is the whole value.

• An explicit I do not know or not sure that the instrument recorded as such
• A question the participant skipped, where skipping was permitted and logged
• A response the analyst flagged as ambiguous at the moment of coding
• A transcript span marked inaudible rather than guessed at
• An interview scored low on coverage, so you know which questions it cannot speak to

In every case the damage is confined and visible. You can drop those cells, model around them, or go back and re-ask. You always know which cells to treat that way.

What counts as an error

An error is an answer that occupies a valid slot and is wrong, with nothing distinguishing it from a right one.

• A number picked to satisfy a required field
• A preference invented on the spot because the question presupposed one
• A reconstructed memory offered with full confidence
• An excerpt coded to a plausible but incorrect theme
• A straightlined block of ratings that looks like a considered response pattern

None of these announce themselves. They enter your dataset, get averaged, and move the number. To repair one you would first have to know which one it was - and if you knew that, it would have been an erasure.

The measured price of removing the blank

The conversion is not hypothetical, and its size is startling. Waters, Kiviniemi, Hay and Orom, writing in Perspectives on Psychological Science in 2021, assembled what happens to perceived-risk items when the don't know option is withheld. For colon cancer risk, they report that DK prevalence ranged from 6.9%-8.7% without a DK option to 47%-63% with one.

Take the midpoints. Roughly 55% of people will declare ignorance when the instrument lets them, and roughly 8% find some way to signal it when it does not. The gap is about 47 percentage points. For every 100 participants, some 47 who would have handed you a clean erasure instead hand you a number.

Those 47 responses are not missing data. They are data. They are wrong, and they are shaped exactly like the right answers.

Two more figures from the same paper set the scale. Between 49% and 69% of inner-city clinic patients marked no idea on colorectal cancer risk items. And after an explicit prompt encouraging them to use the response scale, 20% of participants in one study continued to respond DK - a hard core who genuinely will not manufacture an answer, and who your forced-choice design would have converted last.

Why the substitutes do not cancel out

The usual defence of forced choice is that invented answers are noise, and noise averages away. It does not, because the substitutions are not symmetric. The same paper reports:

When a don't know option is not provided for items assessing absolute risk perceptions, respondents are more likely to use the lowest option on a scaled response format.

Uncertainty has a preferred exit. People who do not know pick low, not random.

Put the two findings together on a 0-10 scale. Suppose the informed 53% average 5.0. If the 47% who were denied a blank took the lowest option - the extreme end of the direction the paper documents - your observed mean is 0.53 x 5.0 + 0.47 x 0 = 2.65. The headline number falls by 47%, and every participant answered every question. Even at a milder substitution the bias runs one way and does not wash out with more participants, because more participants recruit more of it.

The strongest objection: Krosnick is not wrong

There is a serious counter-argument and it deserves stating at full strength. Jon Krosnick and colleagues have long held that offering a don't know option encourages satisficing - respondents take the cheap exit rather than doing the cognitive work - and have shown that candidate preferences predict actual votes better when researchers discourage DK responses. On that evidence, suppressing the blank improves the data.

Both things are true, and the coding frame explains why. Krosnick's finding is about people who have a retrievable opinion and are declining to spend effort retrieving it. Offering them a blank creates an erasure where a real value existed - a pure loss. Waters and colleagues are describing people who have no value to retrieve. Forcing them creates an error where a blank belonged.

So the rule is not always offer the blank. It is: the blank should cost something to choose, but it must exist. Make the participant step past a probe to reach it - which is exactly what the 20% who held out after prompting did - so that satisficers are filtered out and the genuinely ignorant are still recorded as such. What you must never do is remove the exit entirely, because then the two populations become indistinguishable, and every one of them lands in your data as an error.

Three ways to manufacture erasures on purpose

1. Probe, then permit. One follow-up that asks the participant to try, followed by an accepted decline. This separates the satisficer from the genuinely uninformed rather than flattening both.
2. Ask about the basis, not just the answer. How sure are you, and what are you going by? A confident answer with no basis behind it is an error you have just converted into an erasure, because now it carries a mark.
3. Flag at coding time, not at reporting time. If an analyst hesitated over an excerpt, that hesitation is information. Record it against the excerpt. An ambiguous code that is marked ambiguous costs half of one that is silently resolved.

Where this changes your sample size maths

Most sample size planning treats a missing cell as a lost participant and a wrong cell as no loss at all, because the wrong cell is invisible to the calculation. The inequality says the accounting runs the other way. If your instrument has some fixed tolerance for damage, an error eats twice the budget of a blank - so a study with 12% declared blanks and 3% invented answers is in better shape than one with 0% blanks and 10% invented answers, even though the second looks complete and the first does not. Completeness is a property of the spreadsheet. It is not a property of the evidence.

How Koji handles this

Koji is built so that uncertainty has somewhere to go other than into your averages.

• AI-moderated interviews probe before they accept a blank. The follow-up happens automatically on every participant, which is the probe, then permit rule applied consistently rather than depending on whether a human moderator remembered to push.
• Six structured question types give uncertainty an explicit slot. With open_ended, scale, single_choice, multiple_choice, ranking and yes_no available, you can put a genuine not sure option on a single_choice question instead of relying on participants to find the edge of a scale. See the structured questions guide for how each type is analysed.
• Quality scoring marks the erasure for you. Every interview is scored 1-5 with a breakdown across relevance, depth, coverage and completion. A low coverage score is a location: it tells you which interviews cannot speak to which goals, rather than letting a thin interview average in silently.
• Voice interviews catch the verbal hedge. I guess maybe around seven and seven are the same cell in a survey tool and different data in a conversation. The transcript preserves the hedge and the analysis can act on it.
• Real-time reporting separates the blanks from the values. Distributions show declines as declines rather than folding them into the denominator or dropping them without trace.

The general point is not that Koji fills in more cells. It is that Koji is able to tell you which cells it did not fill, which is worth twice as much.

Common mistakes to avoid

• Treating a complete dataset as a clean one. A 100% completion rate on a question about something most participants have never considered is evidence of a design problem, not a quality achievement.
• Recoding DK to the scale midpoint. This invents a value and destroys the mark at the same time - the worst of both categories. If you must impute, keep the original flag in a parallel column.
• Removing the blank because a pilot showed high DK rates. The high rate was the finding. Koji studies frequently surface a topic where most of the panel has no view, which is a legitimate and actionable result.
• Letting analysts silently resolve ambiguous excerpts. An unmarked judgement call is an error by definition, because nothing downstream can find it.
• Assuming invented answers are random. They are not. They cluster at the low end, and sample size makes the bias worse, not better.

Frequently asked questions

What is the difference between an erasure and an error?

An erasure is damage whose position is known - a blank, a skip, a flagged cell. An error is damage whose position is unknown, so it looks exactly like valid data. The distinction matters because repairing an error requires both locating and fixing it, while an erasure arrives with the locating already done.

Why is a blank worth exactly twice a wrong answer?

Because of the bound 2t + f < d, where t counts errors and f counts erasures in a code of minimum distance d. An error spends two units of the repair budget and an erasure spends one, so any fixed budget repairs twice as many erasures as errors. The two familiar special cases, d - 1 erasures and floor((d-1)/2) errors, are just the two ends of that same inequality.

Should I always include a don't know option?

No. Include it, but make participants step past a probe to reach it. Krosnick and colleagues showed that a freely available blank invites satisficing from people who do have an opinion, while Waters and colleagues showed that removing it entirely converts genuine ignorance into fabricated numbers. A probe followed by an accepted decline filters the first group without punishing the second.

Does forcing an answer really change my results that much?

It can. For colon cancer risk items, reported DK prevalence ran from 6.9%-8.7% without a DK option to 47%-63% with one, a gap of roughly 47 percentage points. Those substituted answers also skew toward the lowest scale option rather than scattering randomly, so the bias runs in one direction and does not average away as you add participants.

Is missing data not just a loss of statistical power?

Only when it is genuinely random. The argument here is narrower and more practical: given that some of your cells are bad, you are far better off knowing which ones. Power loss from a known blank is calculable and bounded, whereas an undetected wrong answer moves your estimate by an amount you cannot compute.

How does Koji reduce fabricated answers?

By probing conversationally before accepting a decline, by preserving verbal hedges that a survey checkbox would flatten, and by scoring every interview on coverage so that thin responses are marked rather than silently averaged in. The goal is to record uncertainty as uncertainty instead of converting it into a number that cannot be distinguished from a real one.

Related Resources

• Nonresponse Bias - the companion problem of participants missing from your sample entirely, as distinct from a known blank inside a completed response.
• Attention Check Questions - how to catch low-effort responses, the detection step that turns an error into an erasure.
• Your Totals Still Add Up - why the checks you already run cannot see certain error classes at all.
• Total Survey Error - the seven-component framework for deciding where a fixed research budget should absorb error.
• Survey Data Quality - practical detection and prevention of bad responses across a study.
• Structured Questions Guide - the six question types, and how each one handles an explicit not-sure response.