Sampling with equal probability

I left off with an issue that is likely to confuse many people. I appear to say yes and no to the equal probability of sampling issue.

The difference is in what infers what. If cells are sampled with equal probability, then it is true that the sampling method could lead to an unbiased answer. There may other factors that prevent the estimate from being unbiased, but the equal probability of sampling is a good start to obtaining an unbiased result.

On the other hand, if cells are not sampled with equal probability it does not necessarily mean that the results are biased.

There are a number of ways in which sampling with unequal probability leads to a biased result. A well known way is profile counting. That is what most people still do today when they count “cells.” In fact, no cells are counted, just profiles seen under the microscope. The thin sections reveal slices through cells. These slices of the cell are called profiles. A number of ways have been conceived to deall with profiles vs cells.
1. Don’t do anything
2. Skip sections to avoid double counting
3. Abercrombie
4. Floderus
5. Rose-Rohrlich

None of these methods leads to an unbiased result.

The proportionator does lead to an unbiased result and makes use of an interesting form of PPS.

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