I am preparing to ask a question concerning fair
dice, and found this thread attempting avoid wasting people's times on trivialities and mistakes I might make.
I searched for "fair" dice.
As physics forums is dominant (by funding and perseverance in the internet arena), comments from its famous posters are sure to reach Marilyn's review, eventually -- I wonder if she already has seen this....
I don't grasp how Marilyn necessarily made a psychological mistake as you mention it here.
She did answer a question which might not have been asked, but it also might have been asked
. You yourself indicate I haven't seen the original article question
-- so I judge your response here ONLY on the quote given in the first post of the thread; and I find that very curious.
Please review that for context, as it has been a while.
Would you show how you derive your own "following" question from the original quote of Marilyn?
Are you answering Marilyn's question, the original poster's question, or another of your own?
Marilyn stated a hypothetical Q, which is interpretable: (paraphrase):
prepare to roll a dice 20 times, and THEN (consequently) provide a sequence of all 1's vs a series of mixed numbers; which is more likely to be the true answer about what was rolled?
She could be asking about the psychology and also the statistic about which *sample* from a single run of the test would be more likely to be a lie/outlier? She does say that Both are equally likely as a specific answer according to THEORY, but she NOTES that the signature of mixed digits is seen far more often than the signature of a single repeated digit.
(She is aware of the Hemholtz principle.)
By a fair "Runs" analysis, I am absolutely certain the odds of getting answer (a) would lead a Casino to reject (a) as a loaded dice, but allow (b) as a "fair" dice. (This is one of the questions dealt with regularly when measuring a "Fair" dice.)
The problem is that Marilyn is judging the outcome based on a single example; For this, one would need to analyze based on Chi**2 analysis or an EXACT TEST of the variance
of the 20 INDEPENDENT rolls. As a statistics run analysis --- "111111111111" 20x times would certainly be rejected as a loaded dice; whereas the other value would not.
May I ask, what school did you study probability and statistics at, and what text?
I'm curious if I learned from an equal source...
If you still maintain a case after my gentle
cross examination -- I will bump Marilyn herself, as she does accept my e-mail, and ask her for her own take on this issue.
I do believe it is only right that everyone accused from an entrenched position should be allowed to face their accuser.
That's also why I try to avoid accusing until backed into a corner; I like to practice the virtue of truth in disclosure among disagreeing parties;eg: as a way to come to consensus and NOT compromise.