Three Dispositions, Three Biases

## The fill is a claim, not a repair A cell with nothing recorded is itself a statement about the world: **no measurement exists for this row**. Writing a constant into that cell replaces the statement with a different one — *the measurement was this value* — and every step after the fill reads the second statement as fact. Nothing in the column says a substitution happened. That is the whole of the problem; everything else is arithmetic that follows from it. With 1,500 of 10,000 cells filled, 15% of the column is now a single repeated value. Call that value the **fill constant**. ## Where the constant sits decides the damage The most common thing said about a constant fill — that it pulls the spread in — is true of only one case. What actually happens depends on where the fill constant sits relative to the values that were genuinely measured. - **Near the centre of the measured values.** The column's average barely moves, because you added mass where the mass already was. But 15% of rows now sit on exactly one point, so the column looks far more tightly concentrated than the real data ever was, and any statement about variability is understated. - **Far from the centre.** Zero, in a column of readings centred near 100, is this case. The average is dragged toward zero roughly in proportion to the share filled, and the column gains a second cluster with nothing in between. Variability is now **overstated**, not understated, and a chart of the column shows two humps where the world has one. - **Outside the plausible range on purpose**, chosen so it supposedly cannot be mistaken for data. This is the worst of the three: it moves the average violently, it dominates any ordering of the column, and the first reader who has not been told the convention treats it as a reading. A value chosen to be obviously fake is only obviously fake to the person who chose it. | fill constant | effect on the average | effect on the spread | what a later reader sees | |---|---|---|---| | the column's own centre value | roughly unchanged | understated | a suspiciously peaked column | | zero, in a column centred well above zero | dragged down | inflated | two clusters, one sitting at zero | | an out-of-range stand-in code | dominated by the code | inflated severely | one extreme value treated as real | | no fill, holes left alone | unchanged | unchanged | absence, visibly absent | ## Zero is the trap, because zero is also a reading In most numeric columns, zero is a value the world can genuinely produce: no purchases that day, no rainfall that hour, a balance that really is empty. Once the fill runs, a substituted zero and a measured zero are the same number in the same column. There is no predicate that separates them — the **absence test**, the predicate that asks cell by cell whether a value is absent, now answers false for both, because the substituted cell holds a real value. Anyone counting zeros, filtering on zero, or reasoning about how often the reading is zero is answering a different question than they think. ## What the fill honestly buys Filling is not always wrong. It buys three things: 1. **Every later step gets a value**, so no operation downstream has to decide what absence means to it, and none of them can decide differently from one another. 2. **The table keeps its rows.** Nothing is deleted, so a sample that was hard to collect stays whole. 3. **Sometimes the constant is known rather than guessed.** A row with no charges genuinely has a charge total of zero; the absence there is a reporting artefact and the fill is a correction, not an invention. The test is whether you can defend the constant without reference to the rest of the column. ## Making the decision survive the handover The cheapest honest version of a fill is a second column beside the first that records, per row, whether that cell was filled. It costs one column and it restores the thing the fill destroyed: a reader can exclude filled rows from a trend, keep them in a total, and see how much of the answer rests on substituted values. Without it, the decision lives only in the code that ran, and the code is not what gets handed on. ## What varies between tools Two things differ enough that you should say which is in play before predicting a result. First, some surfaces take a fill constant **per column** and some accept one value for a whole table at once, in which case a constant that is sensible for one column is silently written into every other. Second, tools differ on whether the fill constant must match the column's **declared representation** — the one physical form every value in that column is stored as. Some refuse a constant of the wrong form, some quietly re-store the column in a wider one to accommodate it, and a column of arbitrary references — one whose cells are references to anything at all — accepts the constant without complaint and leaves you with two kinds of thing in one column.