Science Puzzle
The Absence in the Telescope
Two teams search for a hypothesised planet. Team A uses an instrument powerful enough to detect it easily and searches exactly the region where the theory says it must be. They find nothing.
Team B uses a weak instrument that could not have detected the planet even if it were there, and glances at a tiny fraction of the sky. They also find nothing.
Both reports read "no planet found." Is absence of evidence evidence of absence?
The Answer
It depends entirely on how hard you looked, and where. The slogan "absence of evidence is not evidence of absence" is repeated far too confidently, and taken as a universal rule it is simply false.
Team A's null result is strong evidence. Their instrument would have detected the planet had it been there, and they searched precisely where the theory demanded it be. The theory made a prediction, the prediction was checked with adequate power, and it failed. That is exactly what a refutation looks like, and it is one of the most valuable results in science.
Team B's null result is worth almost nothing. Their instrument could not have seen the planet even if it were sitting in the middle of the field, and they examined a fraction of the sky. Finding nothing was the guaranteed outcome whether the planet existed or not, and an outcome that was guaranteed in advance carries no information.
The general principle: a failed search is evidence of absence in proportion to how likely you were to have found the thing if it existed. Statisticians call this the power of the test. A high-powered search that comes back empty tells you a great deal. A low-powered one tells you almost nothing, and it is not neutral, because it is routinely presented as though it were the first kind.
This is why "no link was found" is such a slippery phrase in reporting. A large, well-designed study finding no link between a chemical and a disease is genuinely reassuring. A tiny, underpowered study finding no link is entirely compatible with a substantial real effect that the study simply could not see. Both get written up with the same three words, and the difference between them is the whole story.
The principle: Null results and statistical power. A failed search is evidence of absence in proportion to how likely it was to succeed. High-powered null results are strong evidence; underpowered ones are nearly worthless.