Proofs of Nulls: P > 0.05



Seems correct. A CI [a,b] means: “IF the parameter would be between a and b, THEN these data would not be significantly different”.

Or more simple: “if the real value would be somewhere around zero, then this sample would be quite normal and to be expected. But we have no idea what the real population value is, because all we have is this sample.”

This in contrast to bayesian logic: “based on previous knowlegde and logic, our best estimation of the population was … Now we have new data, which allows us to update our estimation”. Here the sample doesn’t contain more info neither, but we combine it with other information.


Doesn’t every doctor use background information? The same signals (a cough, a pain somewhere, some blood test results) will lead to different conclusions depending on the patient’s history.


There are two problems:

  • We have no algebra that shows us how to incorporate other information into frequentist results
  • When investigators and readers see p < 0.05 (or p > 0.05) then start to think dichotomously about the evidence and if p < 0.05 they even go so far as to believe the point estimate of effect is the true population value. They are shedding background information at this point.