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The Eddington bias is a selection bias applicable to astronomical surveys that stems from measurement errors and population characteristics. If common items are at times mistaken for rare items, the count of the rare items can be significantly overestimated, whereas an equivalent error in the other direction changes the count of common items by a small fraction, which is less significant. For example, brighter stars are rarer, so if estimates of brightness mistake some percentage of dimmer stars as being brighter, that causes a larger (by percentage) overestimate than if the same percentage of brighter stars are mistaken as being dimmer. Even if the measurement errors are random (e.g., a normal distribution), a sample-set based on the measurements can still be skewed.
This is in contrast to another type of observation bias, the Malmquist bias (See Malmquist bias for the difference).
Eddington bias is an astronomy-centric name for a well-known general issue that is applicable to any type of observation data.