Eddington versus Malmquist

vlk — Thu, 13 Mar 2008 17:53:17 +0000

During the runup to his recent talk on logN-logS, Andreas mentioned how sometimes people are confused about the variety of statistical biases that afflict surveys. They usually know what the biases are, but often tend to mislabel them, especially the Eddington and Malmquist types. Sort of like using “your” and “you’re” interchangeably, which to me is like nails on a blackboard. So here’s a brief summary:

Eddington Bias: What you get because of statistical fluctuations in the measurement (Eddington 1913). A set of sources with a single luminosity will, upon observation, be spread out due to measurement error. When you have two sets of sources with different luminosities, the observed distribution will overlap. If there are more objects of one luminosity than the other, you are in danger of misunderestimating the fraction in that set because more of those “scatter” into the other’s domain than the reverse. Another complication — if the statistical scatter bumps up against some kind of detection threshold, then the inferred luminosity based on only the detected sources will end up being an overestimate.

Malmquist Bias: What you get because you can see brighter sources out to farther distances. This means that if your survey is flux limited (as most are), then the intrinsically brighter sources will appear to be more numerous than they ought to be because you are seeing them in a larger volume. This is the reason, for instance, that there are 10 times more A stars in the SAO catalog than there are M stars. This is a statistical effect only in the sense that a “true” dataset is filtered due to a detectability threshold. Anyone working with volume limited samples do not need to worry about this at all.

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Eddington versus Malmquist