No, sample size is intimately tied to this fallacy. Each observation can be loosely thought to lend power to whatever analysis you choose to run, even those in

No, sample size is intimately tied to this fallacy. Each observation can be loosely thought to lend power to whatever analysis you choose to run, even those including very large numbers of possible explanations. For instance: You know, Rodriguez is 7 for 8 against left-handed pitchers in asymmetric ballparks when the tide is going out during El Niño. is a valid statement if the model you're using includes factors for pitcher-handedness, ballpark design, and weather patterns. This is an extraordinarily broad model though almost every observation is at least a little bit novel at first, so you need a great deal of power to distinguish truly interesting things. If you sample sufficiently (exercise left to the reader) and randomly across all those effects you'd serve a chance of learning something about how they correlate in a statistically profound fashion. The barb of the fallacy is forgetting to watch your possibility space grow as you reach for new explanations. The moment you mention the weather you become beholden to divide your certainty by the total number of weather patterns. Unless you're very careful, that number is usually very, very large.