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Edit time ran out: If you can't dispute it, you won't.

Smaug123 10y ago
I'll bite: p-values attempt to measure "Given the null hypothesis, what is the probability that we obtain a more extreme result than we actually did?". What we actually want is "What is the probability of the null hypothesis given the data?". If we are to use p-values successfully to determine truth, then by Bayes we must use prior probabilities somewhere. Discovering p=0.01 is not very helpful when your prior probability was 0.001.
- jsprogrammer 10y ago
  Any valid experiment would assume a prior p-value of 1 (otherwise, what are you hypothesizing?). A null hypothesis does not have a probability. It is either the case, or it isn't. Edit (response to your comment below) [speech restricted at the moment]: "If you can't dispute it, you won't." Edit2 (response to your comment/edit below): It's just a fact. Same as the other simple facts I have stated that remain completely undisputed. Why would you hypothesize an experiment where you already biased yourself (I assume p = 0.01? what?) on the outcome? If your hypothesis is that you will observe no differences, then you have implicitly assigned a prior of 1. Any experimental design will be reducible to this fundamental comparison. The p-value of an ongoing experiment is a measurement of the reproducibility of the [measurement of the predicted observations of the] hypothesis (many hypotheses are not true though; in those cases the p-values are not valid reproducibility measurements). Edit3: >Your misunderstanding in a nutshell is demonstrated by "if you can't dispute it, you won't", which you seem to think means "if you won't dispute it, you can't", in clear violation of Bayes's rule. I think that that is your misunderstanding.
  - Smaug123 10y ago
    I'm not going to continue replying to this apparent troll. Your misunderstanding in a nutshell is demonstrated by "if you can't dispute it, you won't", which you seem to think means "if you won't dispute it, you can't", in clear violation of Bayes's rule.

I'll bite: p-values attempt to measure "Given the null hypothesis, what is the probability that we obtain a more extreme result than we actually did?". What we actually want is "What is the probability of the null hypothesis given the data?". If we are to use p-values successfully to determine truth, then by Bayes we must use prior probabilities somewhere. Discovering p=0.01 is not very helpful when your prior probability was 0.001.

jsprogrammer 10y ago
Any valid experiment would assume a prior p-value of 1 (otherwise, what are you hypothesizing?). A null hypothesis does not have a probability. It is either the case, or it isn't. Edit (response to your comment below) [speech restricted at the moment]: "If you can't dispute it, you won't." Edit2 (response to your comment/edit below): It's just a fact. Same as the other simple facts I have stated that remain completely undisputed. Why would you hypothesize an experiment where you already biased yourself (I assume p = 0.01? what?) on the outcome? If your hypothesis is that you will observe no differences, then you have implicitly assigned a prior of 1. Any experimental design will be reducible to this fundamental comparison. The p-value of an ongoing experiment is a measurement of the reproducibility of the [measurement of the predicted observations of the] hypothesis (many hypotheses are not true though; in those cases the p-values are not valid reproducibility measurements). Edit3: >Your misunderstanding in a nutshell is demonstrated by "if you can't dispute it, you won't", which you seem to think means "if you won't dispute it, you can't", in clear violation of Bayes's rule. I think that that is your misunderstanding.
- Smaug123 10y ago
  I'm not going to continue replying to this apparent troll. Your misunderstanding in a nutshell is demonstrated by "if you can't dispute it, you won't", which you seem to think means "if you won't dispute it, you can't", in clear violation of Bayes's rule.