Missing, Unknown, and Not Applicable Values

Why the Status of a Value Matters

A data record may have an empty cell, a response such as “don’t know,” or a value marked “not applicable.” These entries can all mean that a usual measurement is unavailable, but they do not say the same thing. One may indicate that nobody recorded an answer; another says the respondent could not provide one; a third says the question does not fit the case at all.

Keeping these states distinct helps make a data set interpretable. It clarifies what was observed, which cases were eligible for a variable, and which records can be used in a particular summary. It also prevents a tempting but incorrect shortcut: treating every unavailable value as zero. Zero is a numerical value with a meaning of its own; it does not mean “we do not have an answer.”

These labels describe the status of information, not necessarily the underlying value. A blank does not tell us why an answer is absent. An “unknown” response tells us that the answer could not be provided, but does not reveal what the answer would have been. A not-applicable response tells us that the question is outside the relevant scope for that case.

Three Different Situations

Consider a hypothetical survey asking people how many shifts they missed at their current workplace during the previous month. The wording assumes the person has a current workplace. The following entries have different interpretations:

The details depend on how a variable is defined. For example, “number of shifts missed at your current workplace” does not apply to someone without a current workplace. A different question—such as “number of paid work shifts missed at any job”—might apply to a wider group. The question’s wording and the case determine applicability.

An unknown response can sometimes be useful in its own right. If the variable being studied is “whether the person knows their monthly medication cost,” then “does not know” is an informative response category. But if the variable is the cost itself, “does not know” is not a cost amount. It should not be mixed with numerical costs as though it were an ordinary amount.

Why Unavailable Values Are Not Zero

Zero is a valid numerical value when it represents none of the measured quantity. A person who had an eligible workplace and missed no shifts can have a recorded count of 0. By contrast, a blank value, an explicit “don’t know,” or a not-applicable response does not report a count of zero. Replacing any of these states with zero changes the meaning of the record.

The effect on a numerical summary can be shown directly. Suppose two applicable, recorded values are 10 and 14 units, while two other values are unavailable. The mean of the two recorded values is 12 units. If the two unavailable values are replaced with zero, the total remains 24 units because adding zero does not change a sum. However, the number of values included in the calculation increases from two to four, so the calculated mean becomes 6 units.

Here, \(\bar{x}_{\text{recorded}}\) is the mean of the available numerical records, not automatically the mean for every eligible case. The calculation with substituted zeros is a different calculation: it treats both unavailable entries as actual zero measurements. Unless zero is known to be the true value for each case, that substitution is not justified.

Worked Examples in Recording and Counting

A Short Justification for Tracking the Denominator

A mean is a sum divided by the number of values being averaged. If the numerical values available for an applicable variable are \(x_1,\ldots,x_m\), their mean is the sum of those \(m\) values divided by \(m\). The number \(m\) must match the values actually included. An unavailable entry is not part of that set unless a defensible rule supplies a value for it.

Suppose the recorded values have sum \(S\), and there are \(m\) recorded values. The mean of those recorded values is \(S/m\). If \(k\) unavailable entries are instead assigned zero, the sum remains \(S\), since \(S+0+\cdots+0=S\), but the denominator becomes \(m+k\). When \(S\) is positive and \(k>0\), \(m+k>m\), so \(S/(m+k)<S/m\). Thus zero substitution can lower the mean even though it did not change the sum. This arithmetic explains the issue; it does not determine whether the recorded cases are representative of cases with unavailable values.

The arithmetic also shows why reporting only a mean can hide important information. A reader needs to know what cases the variable applies to and how many actual numerical values contributed. A mean based on recorded values describes those values. It does not, without further information, tell us the values that were missing or the values for cases where the variable did not apply.

Good Recording Practice

A well-organized data record makes the status of each entry apparent. Preserve the distinction between a numerical value, an explicit response such as “don’t know,” a value that was not recorded, and a not-applicable case. If a system uses codes such as “UNK,” “NA,” or a special number, document what each code means; otherwise, someone reading the data may mistake a code for a real response or measurement.

When reporting a count or summary, state the relevant denominator in words. For example, “Eight of the ten people for whom the question applied provided a numerical count” tells the reader more than “Eight responses were available.” It distinguishes the eligible group from the people who supplied numerical values.

These distinctions are useful even before any advanced analysis. They support accurate descriptions of the data, make record-keeping clearer, and help prevent unsupported assumptions about cases with unavailable values. Whether a later analysis can use additional information or a particular strategy is a separate question; the first requirement is to know which kind of value status each record represents.

Common Mistakes

• Wrong: “The cell is blank, so the value must be zero.” Correction: A blank says that no value was recorded. It gives no numerical answer.
• Wrong: “A respondent who does not know the answer gave the same response as someone who skipped the question.” Correction: “Don’t know” is an explicit response; a blank has no recorded explanation.
• Wrong: “Not applicable means the answer is zero.” Correction: Not applicable means the question does not fit the case as defined. A zero is a numerical answer for an applicable case.
• Wrong: “Filling missing cells with zero leaves a mean unchanged because it does not change the sum.” Correction: The sum of the recorded values remains unchanged, but the number of values used increases. The mean can change because it divides by that larger number.
• Wrong: “A mean of the available values must describe everyone who was eligible.” Correction: The calculation describes the values included. The unavailable records remain unavailable, and the mean alone does not supply their values.