A calculated probability of 0.0000001 should diminish the emotional strength of any anticipation, positive or negative, by a factor of ten million.
And there goes Walter Mitty and Calvin, then. If it is justifiable to enjoy art or sport, why is it not justifiable to enjoy gambling for its own sake?
if the results are significant at the 0.05 confidence level. Now this is not just a ritualized tradition. This is not a point of arbitrary etiquette like using the correct fork for salad.
The use of the 0.05 confidence level is itself a point of arbitrary etiquette. The idea that results close to identical, yet one barely meeting the arbitrary 0.05 confidence level and the other not, can be separated into two categories of “significant” and “not significant” is a ritualized tradition indeed perhaps not understood by many scientists. There are important reasons for having an arbitrary point to mark significance, and of having that custom be the same throughout science (and not chosen by the experimenter). But the actual point is arbitrary etiquette.
The commonality of utensils or traffic signals in a culture is important, even though the specific forms that they take are arbitrary. The exact confidence level used is arbitrary; it’s important that there is a standard.
Nor is Bayes’s Theorem different from one place to another.
No, but the statistical concept of “confidence” depends on how an experimenter thinks that a study was designed. See for example this discussion of the likelihood principle.
If Alice conducts 12 trials with 3 successes and 9 failures, do we reject the null hypothesis p = .5 versus p < .5 at the 0.05 confidence level? It turns out that the answer depends in the classical frequentist sense on whether Alice decided ahead of time to conduct 12 trials or decided to conduct trials until 3 successes were achieved. What if Alice drops dead after recording the results of the trials but not the setup? Then Bob and Chuck, finding the notebook, may disagree about significance. The “significance” depends on the design of the experiment rather than the results alone, according to classical methods.
How many scientists understand that?
Sorry, ambiguous wording. 0.05 is too weak, and should be replaced with, say, 0.005. It would be a better scientific investment to do fewer studies with twice as many subjects and have nearly all the reported results be replicable. Unfortunately, this change has to be standardized within a field, because otherwise you’re deliberately handicapping yourself in an arms race.
Ah, yes, I see. I understand and lean instinctively towards agreeing. Certainly I agree about the standardization problem. I think it’s rather difficult to determine what is the best number, though. 0.005 is as equally pulled out of a hat as Fisher’s 0.05.
From your “A Technical Explanation of Technical Explanation”:
Similarly, I wonder how many betters on horse races realize that you don’t win by betting on the horse you think will win the race, but by betting on horses whose payoffs exceed what you think are the odds. But then, statistical thinkers that sophisticated would probably not bet on horse races.
Now I know that you aren’t familiar with gambling. The latter is precisely what the professional gamblers do, and some of them do bet on horse races, or sports. Professional gamblers, unlike the amateurs, are sophisticated statistical thinkers. (And horse races are acceptable for sophisticated gamblers because there’s only the small vigorish involved, and there’s plenty of area for specialized knowledge.)
I think you’ve made a common statistical fallacy. Perhaps “someone who bets on horse races is probably not a sophisticated statistical thinker.” But it does not necessarily follow that “someone who is a sophisticated statistical thinker probably does not bet on horse races.” Bayes’s Theorem, my man. :)
I know plenty of math Ph.D.s and grad students who do gamble online and look for arbitrage in a variety on ways. Whether they’re representative I don’t know.