Science Puzzle
The Anomaly in the Data
Your data falls beautifully along a straight line, except for one point sitting far off it. The trend would be much cleaner without it, and you have a deadline.
What is the scientifically correct thing to do with the anomalous point, and what is the rule that decides whether you may ever remove it?
The Answer
Investigate it. The anomaly is one of two things: an error, or a discovery. You cannot tell which from the fact that it does not fit, because that is exactly what both look like.
The rule that decides is whether you have an independent reason. Independent means a reason that has nothing to do with the point being inconvenient: the thermometer was later found to be faulty, the sample was contaminated, the technician logged an equipment failure at that timestamp, the value is physically impossible. If such a reason exists, documented, then excluding the point is legitimate, and you say so in the write-up.
What you may never do is remove it because it spoils the trend, and it is worth being precise about why that is fatal rather than merely sloppy. It is circular. You are using your hypothesis (the trend is real and linear) to decide which data to keep, and then using the surviving data to confirm the hypothesis. The trend cannot fail such a test, because any point capable of refuting it has been defined as an error and removed. That is not analysis, it is an elaborate way of writing down what you already believed.
The history here is not decorative. Anomalies that survived investigation are where a great deal of physics came from. The perihelion of Mercury refused to fit Newtonian gravity, and it was general relativity. A persistent hiss in a radio antenna that two engineers tried to clean out was the cosmic microwave background. The hole in the ozone layer was initially flagged as an instrument malfunction because the readings were too extreme to believe. In every case the tidy move was to delete the point.
So the anomaly is the most valuable thing in the dataset and the most dangerous. It is where the next theory lives, and it is also where wishful thinking does its quietest work. The discipline is entirely in the order of operations: find the independent reason first, then decide. Never the other way round.
The principle: Handling anomalies. An outlier may be removed only for an independent, documented reason. Discarding it because it contradicts the expected trend is circular reasoning and is how discoveries are lost.