Rare Categories, Missing Responses, and Other

Why Rare and Missing Responses Need Care

A categorical display can be mathematically correct yet still give readers the wrong impression. A tiny bar might represent a genuinely uncommon answer, or it might represent a handful of responses grouped together. A blank answer is different again: it does not tell us which category a person chose. Displaying all three situations with no explanation can hide useful detail or make missing data look like a substantive response.

The aim is not to make every graph equally simple or equally detailed. It is to make clear which answers were recorded, what any combined group contains, and how many eligible observations are represented. A category should not disappear merely because its count is small, and a missing response should not be presented as though it were an answer to the survey question.

Deciding Whether to Combine Rare Categories

There is no universal count or percentage below which a category must be combined. The decision depends on the purpose of the display and whether readers need to see that category on its own. If a small group is important to the question, meaningful to the audience, or substantively different from other groups, retain it as a separate category and label it clearly. If a display would be difficult to read with many very small categories, combining some responses may be reasonable, provided the combination is transparent and does not blur distinctions that matter.

A sound “Other” group follows several practical rules:

• Combine valid response categories, not blanks, nonresponses, or responses that were not applicable.
• Choose the categories to combine for a stated reason, rather than concealing an inconvenient result.
• Use a label such as “Other (scooter or skateboard)” when space permits, or state the component categories in a note or accompanying table.
• Keep the original category counts available. If the components could matter to interpretation, report them even when the display groups them.
• Use the same grouping rule when making comparisons, so a change in the displayed categories does not create a misleading comparison.

“Other” should not be a label for an unexplained collection. When categories are combined, the reader should be able to tell what was combined and how the total was formed. A category with a small count can still be important; grouping it is a display choice, not evidence that the responses are unimportant.

Missing Is Not a Substantive Answer

A person who leaves a question blank has not supplied a category for that question. Similarly, a response recorded as unknown or not applicable does not necessarily identify a substantive answer. These cases should be distinguished from valid answers such as “none” or “prefer not to say.” “None” answers the question when it is an available option. “Prefer not to say” is an explicit response about answering; it is not the same as a blank, though it is not a substantive choice among the question’s answer categories.

For a display of the distribution of answers, calculate percentages among the valid responses to that question. Report how many responses were missing or declined separately, so readers can see how many people did not contribute a substantive answer. If the purpose is to describe response completion, show these counts in a separate note or response-status display. If a graph places a “No response” bar beside answer categories, make its separate status unmistakable; do not let it appear to be another substantive answer.

Why Percentages Among Valid Answers Sum to 100%

The denominator rule can be seen directly from the arithmetic. Suppose a question has \(k\) valid response categories, with counts \(c_1,c_2,\ldots,c_k\), and let \(V\) be the number of valid answers. By definition, \(V=c_1+c_2+\cdots+c_k\). The valid-answer percentage for category \(i\) is \(100c_i/V\). Adding the percentages gives

The result holds because the valid categories account for all \(V\) valid answers. If the denominator is instead the total number of eligible people, the displayed substantive-answer percentages generally sum to less than 100% when some people did not provide a valid answer. That shortfall reflects unanswered or unusable items; it should not be silently redistributed across the substantive categories.

Common Mistakes and Better Practice

• Wrong: “The blank answers are just another category, so I included them in the preference chart.” Correction: A blank does not state a preference. Show it as a response-status count or note, and make clear whether percentages use valid answers or all eligible people.
• Wrong: “Every category under five responses must go into Other.” Correction: There is no universal cutoff. Consider the purpose of the display and whether a rare response is meaningful enough to show separately.
• Wrong: “The Other bar is small, so the reader does not need to know its contents.” Correction: Give the component categories and, when useful, their individual counts. A combined label should explain the combination.
• Wrong: “I can put ‘prefer not to answer’ and a blank together without explanation.” Correction: An explicit decline and an unanswered item are different response statuses. Keep them distinct when that difference is relevant, and do not treat either as a substantive choice unless the question specifically concerns response status.
• Wrong: “The percentages do not add to 100%, so I should adjust the categories.” Correction: First check the denominator. Percentages among valid answers sum to 100% (apart from rounding); percentages of all eligible people may not when some answers are missing.

A careful display helps readers see both the pattern of answers and the limits of the recorded data. Keep important rare categories visible, make every “Other” group traceable to its component responses, and report missingness without implying that it represents an answer. Always state the population counted in the denominator.