And the confidence in a hypothesis added by an observation is related to the probability of
the observation given the hypothesis, over the probability of the observation given the alternative — which in this case is that the true value is close to but outside that interval.
The log - likelihood ratio is log (P (O H0) / P (O H1)-RRB- meaning the log of the probability of
the observations given hypothesis H0 is true, divided by the probability of
the observations given hypothesis H1 is true.
Not exact matches
In the early 1980s these
observations gave birth to «the cholinergic
hypothesis» of memory loss.
To test the
hypothesis that publicly available information has an impact over and above direct
observation of school performance, we can compare the ratings
given by respondents whose schools were very close to the cutoffs in the point system used by Florida to assign school grades.
If the predicted cooling by la Nina had not occurred then 2008 would probably have been the same temperature (
given the uncertainties) as every year since 2001 and that in itself would require explanation.I am broadly in favour of the global warmingCO2
hypothesis but I know it is just that, a
hypothesis — and that needs testing against real
observations in the physical world.
At the time, I observed that this meant nothing more than «
given the variability in the data, we need at least 15
observations to reject the null
hypothesis at 95 per cent confidence».
Lindzen has published a couple of hundred papers in climatology, so I think we can assume he knows that the statement «there has been no statistically significant warming since 1995» means nothing more than «
given the variability in the data, we need at least 15
observations to reject the null
hypothesis at 95 per cent confidence», a fact so trite as not to be worth mentioning.
@Dan «I think it woudl be a useful thing for me to identify competing
hypotheses & then I & others can think of
observations that can be made that would
give us more or less reason to believe one or the other of those conjectures is right»
One can not naively apply a criterion like rejection if p < 0.05, and all that means under the best of circumstances is that the current
observations are improbable
given the null
hypothesis at 19 to 1.