- #36
DrChinese
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Lynch101 said:@DrChinese, just to try and clarify further.
My understanding of your statement that we don't know how often cases [1] & [8] occur either implies or allows for the possibility that they occur infrequently, which is why I am thinking we can discount them when calculating the minimum probability, but not exclude them from the possibility space.
Lynch101 said:What I mean by that is, it's always a possibility that cases [1] & [8] occur, so we have to include them in our space of possible outcomes. However, because they are not as likely to occur as the other cases (with a possibility they don't occur in a given statistical sample), we don't count them when calculating the minimum expectation value (of matching outcomes).
Where they occur, they could give us a value ≥0.25.
Here are some relevant rules for calculating any statistical situations:
a) If you include the cases in the denominator, you must also include the associated data in the numerator.
b) You are free to change the weighting of the cases according to your own viewpoint or rationale. For example, while I might suggest all 8 cases are equally likely, you might reasonably argue that cases [1] and [8] are rare - so you weight them as 0%. You might even say case [2] is twice as likely as case [3]. Fine. However, that still leads us to exactly the same minimum of .333 - and not .250. There are no cases with a match % less than .333.
Next, consider this: you can even make up your own results for as many trials as you like, picking whatever cases you like. And unless you pick those cases knowing in advance which 2 measurement settings (of 3) you plan to use, you will never have an average less than .333.