>My daughter actually covered this in science this year. I thought the Malmquist Bias had to do with observing objects at a distance. You only see the brightest objects within a group of objects and we are unable to see the dimmer ones. Supposedly since our technology hasn't improved enough yet to ensure we see all objects regardless of their luminosity it has to be accounted for in any analysis of data or else the results would be innacurate. I'm not sure it can accurately be accounted for though.

This is a good description. I asked Tom Van Flandern if we could tell me about it and this is what he said:

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How possible do you suppose it would be to give a decent summary of what a Malmquist Type II bias for this board in order for readers to sound somewhat educated about the idea if they wish to discuss it with others?

Visualize intrinsic brightness plotted along the x-axis (increasing to the right), and number counts along the y-axis. Then most types of cosmological things, including supernovas, will approximate a normal distribution curve (which looks like a hill). There will be relatively few intrinsically very bright or very faint members of the set, but lots of near-average members (the peak of the hill).

All is well when we can observe a representative sampling of all supernovas. However, in the real universe, we have two factors that can distort the statistics. One is that the volume of space sampled goes up with the cube of distance. The other is that apparent brightness goes down with at least the square of distance. (An argument can be made that apparent brightness actually falls with the cube or fourth power of distance.)

But fainter members of our set are harder to discover. At really large distances, they may even be impossible to discover. So when we start collecting data from high redshifts, we tend to find only the intrinsically brightest members of the set because the fainter ones are difficult or impossible to find. In short, we sample only members sitting at the brightside foot of the hill that represents the distribution of the set of all members.

That means that we tend to see only the intrinsically brightest supernovas at the greatest distances. But those happen to be the ones with the widest (in time) light curves, the ones that take 60 days or more to rise and fall instead of the more typical 30 days. So even without any time dilation, we will see our sample of high-redshift supernovas tend toward longer-duration light curves with increasing distance. And if we make no allowance to correct for this type of sampling bias, we will fool ourselves into thinking that we have detected a time dilation effect even if none exists.
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That really makes Jensen's arguments click for me.