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I have redefined nothing. Go pull the the Higgs data; it will be as I say. Go read how to form experiments and calculate p-values, nothing will be substantially

I have redefined nothing. Go pull the the Higgs data; it will be as I say. Go read how to form experiments and calculate p-values, nothing will be substantially different than what I have said here.

kgwgk 11y ago
I already explained a few messages ago that the null hypothesis was indeed that there is no Higgs boson and the peak observed in the LHC data is just noise. They made their analysis and rejected the null hypothesis (p-value less than 0.000001). "If you correctly measure a p-value of 0.05, that measurement explicitly means that you expect that 95% of your future observations to be consistent with the hypothesis which you used to determine that p-value of 0.05." Did they correctly measure a p-value of 0.000001? They (and everyone else, apart from maybe you) think that they did. Do you think they expect 95% of their future observations to be consistent with the null hypothesis (that they used to determine that p-value)? I would say they were quite confident that the observed peak was not noise, and therefore they expected the signal to be there again if the experiment was to be repeated, rejecting again the null hypothesis. Which is why they announced they had discovered the Higgs boson. But maybe you can convince the Swedish Academy of Science to take Higgs' prize back...
- jsprogrammer 11y ago
  Here is one paper: http://arxiv.org/pdf/1207.7214v2.pdf http://arxiv.org/pdf/1207.7214v2.pdf Look at Figures 8 and 9. They show the p-value (at whatever level of data was collected when the paper was written) over the parameter space that is being searched. You can see that the values observed have a clear separation -- most are close to 1 (null-hypothesis holds) with just one significant dip towards 0 (null-hypothesis doesn't hold). If you were to animate this graph with the p-values over time (as more observations are made), you would see the trend towards 0 or 1 much clearer. The Boson experimenters would expect a (1 - p) reproduction rate for the next observation made (if the null-hypothesis holds). That is, the next observation has a p probability of fitting within the parameters of the null-hypothesis and (1-p) probability that it is inconsistent with the null-hypothesis. Why would they expect that? Because the math involved in telling you whether or not that is what you should expect is exactly what p-value calculates (again, assuming a well-formed experiement -- which the Higgs experiments probably are). But again, when the null-hypothesis doesn't hold, p-value tells you very little (it's actually undefined in the math).
  - kgwgk 11y ago
    > But again, when the null-hypothesis doesn't hold, p-value tells you very little (it's actually undefined in the math). The p-value is well defined whether the null hypothesis holds or not. You calculate it assuming it does. There you go, you have a properly calculated p-value. That's what physicists do: "Taking into account the entire mass range of the search, 110– 600 GeV, the global significance of the excess is 5.1 σ, which corresponds to p0 = 1.7 × 10−7." You see, they have calculated a p-value. Does the null hypothesis hold? I don't think they had any expectations consistent with the null hypothesis being true before the experiment. After the experiment they clearly think that the null hypothesis is false: "These results provide conclusive evidence for the discovery of a new particle with mass 126.0 ± 0.4 (stat) ± 0.4 (sys) GeV." They don't see any problem in stating a p-value and rejecting the null hypothesis at the same time (in fact, it's because the p-value that they calculated is very small that they conclude that the null hypothesis doesn't hold). Apparently you see a problem, because if the Higgs boson exists and produces the signal in the experiment then the null hypothesis is false and all the p-value calculations they did to get to that conclusion are "wrong". Anyway, I have no need to convince you of anything. I can live with people being wrong on the internet.
    - jsprogrammer 11y ago
      Well, before you go, I implore you to look into the actual computation and theory of 'p-value'. A p-value is simply P(X|H). P(X|H) only means something when H is true. If H is false, P(X|H) tells you nothing. Since H is your null-hypothesis, if it does not actually hold in the real-world, P(X|H) is meaningless. If you read the paper I linked, they never explicitly call out the null hypothesis (nor do, I believe, they show the work for their calculations). There should be another paper somewhere that describes exactly what it is, in the terms I am using. So, phrases like, "[t]hey don't see any problem in stating a p-value and rejecting the null hypothesis" make me think you have no idea what you're talking about. The null hypothesis can never be 'rejected' (ie. p-value can never reach 0). I don't think you will find anyone working on the Higgs boson that will claim otherwise.
      - kgwgk 11y ago

I have redefined nothing. Go pull the the Higgs data; it will be as I say. Go read how to form experiments and calculate p-values, nothing will be substantially different than what I have said here.

kgwgk 11y ago

I already explained a few messages ago that the null hypothesis was indeed that there is no Higgs boson and the peak observed in the LHC data is just noise. They made their analysis and rejected the null hypothesis (p-value less than 0.000001). "If you correctly measure a p-value of 0.05, that measurement explicitly means that you expect that 95% of your future observations to be consistent with the hypothesis which you used to determine that p-value of 0.05." Did they correctly measure a p-value of 0.000001? They (and everyone else, apart from maybe you) think that they did. Do you think they expect 95% of their future observations to be consistent with the null hypothesis (that they used to determine that p-value)? I would say they were quite confident that the observed peak was not noise, and therefore they expected the signal to be there again if the experiment was to be repeated, rejecting again the null hypothesis. Which is why they announced they had discovered the Higgs boson. But maybe you can convince the Swedish Academy of Science to take Higgs' prize back...

jsprogrammer 11y ago
Here is one paper: http://arxiv.org/pdf/1207.7214v2.pdf http://arxiv.org/pdf/1207.7214v2.pdf Look at Figures 8 and 9. They show the p-value (at whatever level of data was collected when the paper was written) over the parameter space that is being searched. You can see that the values observed have a clear separation -- most are close to 1 (null-hypothesis holds) with just one significant dip towards 0 (null-hypothesis doesn't hold). If you were to animate this graph with the p-values over time (as more observations are made), you would see the trend towards 0 or 1 much clearer. The Boson experimenters would expect a (1 - p) reproduction rate for the next observation made (if the null-hypothesis holds). That is, the next observation has a p probability of fitting within the parameters of the null-hypothesis and (1-p) probability that it is inconsistent with the null-hypothesis. Why would they expect that? Because the math involved in telling you whether or not that is what you should expect is exactly what p-value calculates (again, assuming a well-formed experiement -- which the Higgs experiments probably are). But again, when the null-hypothesis doesn't hold, p-value tells you very little (it's actually undefined in the math).
- kgwgk 11y ago
  > But again, when the null-hypothesis doesn't hold, p-value tells you very little (it's actually undefined in the math). The p-value is well defined whether the null hypothesis holds or not. You calculate it assuming it does. There you go, you have a properly calculated p-value. That's what physicists do: "Taking into account the entire mass range of the search, 110– 600 GeV, the global significance of the excess is 5.1 σ, which corresponds to p0 = 1.7 × 10−7." You see, they have calculated a p-value. Does the null hypothesis hold? I don't think they had any expectations consistent with the null hypothesis being true before the experiment. After the experiment they clearly think that the null hypothesis is false: "These results provide conclusive evidence for the discovery of a new particle with mass 126.0 ± 0.4 (stat) ± 0.4 (sys) GeV." They don't see any problem in stating a p-value and rejecting the null hypothesis at the same time (in fact, it's because the p-value that they calculated is very small that they conclude that the null hypothesis doesn't hold). Apparently you see a problem, because if the Higgs boson exists and produces the signal in the experiment then the null hypothesis is false and all the p-value calculations they did to get to that conclusion are "wrong". Anyway, I have no need to convince you of anything. I can live with people being wrong on the internet.
  - jsprogrammer 11y ago
    Well, before you go, I implore you to look into the actual computation and theory of 'p-value'. A p-value is simply P(X|H). P(X|H) only means something when H is true. If H is false, P(X|H) tells you nothing. Since H is your null-hypothesis, if it does not actually hold in the real-world, P(X|H) is meaningless. If you read the paper I linked, they never explicitly call out the null hypothesis (nor do, I believe, they show the work for their calculations). There should be another paper somewhere that describes exactly what it is, in the terms I am using. So, phrases like, "[t]hey don't see any problem in stating a p-value and rejecting the null hypothesis" make me think you have no idea what you're talking about. The null hypothesis can never be 'rejected' (ie. p-value can never reach 0). I don't think you will find anyone working on the Higgs boson that will claim otherwise.
    - kgwgk 11y ago