With 47 participants there is no such thing as 33 %. Only forty-eight percentages exist, 2.13 points apart, and none of them lands there. A percentage off that grid means the denominator is not the one the table claims.
With N people, the percentages that can exist are 0/N, 1/N, 2/N… up to N/N. That is N + 1 values and nothing else: there is nothing in between.
Which means the smallest step between two percentages is 100/N. With 47 participants, 2.13 points. With 20, a full five points. A 33 % with N = 47 is not generous rounding: it is a number no combination of cases produces.
It is the idea behind the GRIM technique, used since 2016 to audit means of integer data in the psychology literature. Applied here to proportions, which is where it slips through most often because nobody looks.
The denominator is not the total N. The most common and the most legitimate: the percentage was computed over those who answered that question, not the whole sample. That is correct, but it has to be stated, or every row of the table silently rests on a different N.
A column percentage read as a row percentage. In a contingency table without a note, the same figure can be 40 % of the exposed or 40 % of the cases. The reader cannot resolve that ambiguity.
An undeclared missing case. If the percentage fits N − 1 but not N, one person dropped out and nobody mentions it.
And rounding, which is almost never the explanation. Rounding moves a number half a point, not two.
Health samples tend to be small, and the smaller the N, the coarser the grid and the easier an impossible percentage is to spot. With twenty patients, any percentage that is not a multiple of five is an error.
It is also the cheapest check of all: no data request, no understanding of the design, no statistics. Just division.
How to present frequencies and their percentages properly is in Table 1 in APA 7, and the chi-square that usually accompanies them in how to report chi-square.
The check tolerates it: anything within half a grid step is accepted. What rounding cannot absorb is a gap of two or three points, and that is what gets flagged.
Sometimes yes, and it is a standard technique: try small denominators until one produces exactly that percentage. Below a hundred there is usually a single compatible N.
The same idea applies to means of integer data — that is what GRIM does — but with different arithmetic. This page only checks proportions.
Almost never on its own. The usual explanation is an undeclared different denominator, fixed with a clarification. What is a signal is MANY percentages in the same paper failing to reconcile.