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Probability Science - in medicine and in physics

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Probability is increasingly used in modern science, and notably in medicine and in physics, in scientific proof claims. But often probability is used poorly in science and really gives little or no proof of what is claimed.

In medicine, probability is now commonly used in survey data analysis, as where a 10% correlation between peoples illness and peoples behaviour statements is said to prove eg that general behaviour A always has a 10% risk of causing illness B. Often the general behaviour A has no actual effect on the illness B, but has some correlation with the use of some unidentified product C which is the actual cause correlating 100% with illness B.

In physics, probability is now commonly used in experiment data analysis, as where a 10% correlation between photon emissions and some general magnetic event is said to prove eg that general magnetic event A always has a 10% probability of causing photon emission B. Often the general event A has no actual effect on the emission B, but has some correlation with some unidentified specific event C which is the actual cause correlating 100% with emission B.

In science today probability is widely used in different aspects of data analysis. It is used in experiment data analysis and in survey data analysis, and in both areas it is also used in error estimation. But probability is commonly used wrongly.

Probability in Medicine

In medicine, probability is now used both in experiment data analysis and in survey data analysis but here we will consider chiefly the latter (below under Physics we will consider the former). The chief problem with survey data is that it always involves some limited number of selected people being asked some limited number of selected questions. It may be that an illness being studied is caused by ACME soap, but the survey had no question about ACME soap or it did but none of the people surveyed used ACME soap. But still that survey will be probability-tested for that illness, and will probably give some correlations for that illness. It will be announced that some behaviours 'are a risk for the illness', while ACME soap passes unmentioned.
(PS. this is NOT a claim that ACME soap causes any illness, we use the name here only as the name of 'some hypothetical product'.)

We can now consider a hypothetical medical survey to be probability-tested regarding a hypothetical disease A ;

A hypothetical survey probability testing.

Where the unknown facts that the study seeks to discover are,
Disease A is actually caused by using too much of product C or the weaker product D.
Product C is more expensive than product D.
Product C is used more by middle-class vegetarians.
Product D is used more by working-class smokers.
Product C sells in less locations than product D, and some locations sell neither.

And where,
The survey is of pedestrians half from location C and half location D, questions being ;
Do you own a TV ?
Do you regularly smoke cigarettes ?
Do you regularly smoke cigars ?
Do you usually drink more than 4 units of alcohol a day ?
Do you usually eat more than 2 eggs a day ?
Do you usually visit a gym more than once a week ?

This survey actually asks nothing about product C or product D, but will still give correlations for the illness caused only by these products as long as some people surveyed use either product. Hence,
TV-owners, cigar-smokers and gym-users on average may have higher incomes and to differing extents may buy more of the expensive product C than product D.
Egg-eaters on average may have the highest use of products C and D, and may have lower incomes and so buy more of the less expensive product D.
Alcohol-drinkers on average may tend to buy neither product C nor product D.

Survey question answers are used to split the survey population into sub-populations as 'TVowners' and 'non-TVowners'. Then probability testing may be done on illness rates between some answer sub-populations, when it should be done between ALL of the answer sub-populations - eg. between cigarette-smokers v non-smokers AND between cigarette-smokers v non-cigarette-smokers. Of course a survey with many questions can give thousands of sub-populations, and while all should be probability tested, it is proper enough to publish the results only for all cases that exceed some specified significance level. (Alternatively probability testing can be none on illness rates between each answer sub-population and the total survey population, though that will dilute the probability differences and so can hide significant results)

Illness rates will vary between sub-populations, such that it may be reported that 'cigar-smoking carries a 20% risk for this illness' and 'egg-eating carries a 15% risk for this illness'. Of course in this case we know that these behaviours do not at all cause the illness - products C and D cause the illness. So the 'scientific truths' that this study claims are not very truthful. Whence the saying that 'There are lies, damn lies and statistics'.

That holds even when probability studies are done properly, but often they are not. Hence cigarette-smokers v non-smokers may give a non-significant 5% while cigarette-smokers v non-cigarette-smokers may give a significant 11%, but the study may have omitted to get or to publish the latter result. (as was the case for even the acclaimed Doll and Hill 1956 smoking survey study in regard to reported cigarette-lighter use -
Doll R, Hill AB (1956) Lung cancer and other causes of death in relation to smoking. Br Med J 2: 1071).

If there is some strong evidence for any hypothesis, then additional weak evidence will commonly be taken as confirming that. If there is only weak evidence for any hypothesis, then additional weak evidence will commonly be taken as not at all confirming that. But logically only strong evidence should count towards proof, and weak evidence should only count as an indicator of a need to look for strong evidence. Generally there are no 20% causes and so no 20% risks, mostly A actually cause B or actually does not cause B. There may commonly be dose effects, and more rarely there may be multiple causes. But much too commonly medicine is reporting, and governments spread concerns about, relatively low illness 'risks' that are not real scientific truths.

Probability in Physics

Probability testing in Physics and Astronomy is more commonly used in experiment data analysis or observation data analysis. This can have some of the problems seen in the use of probability testing of survey data. Hence where surveys can have omitted questions, experiment or observation can involve omissions in the factors investigated and this may have greater impact in the more contentious areas of Particle Physics and Astronomy.

Probability is also widely used in accuracy estimation, but often ignoring the probability fact that of several experiments or observations it is often NOT the one with the best accuracy that gives the most reliable evidence. Other issues need considering also.

More recent Physics and Astronomy theories also commonly try to incorporate aspects of probability theory, correctly or incorrectly. Deductive assumptions involving infinities or limits often give false answers. So theory handling the infinitely small and infinitely large can ultimately require that the sum of an infinite set of zero probabilities add to a probability of one, which is plainly false. Physics deductions about the infinitely small or the infinitely large can generally be valid only derived correctly relative to some well proven specified finites. More recent physics theories can often involve error related to this issue.

False probability deductions can be due to a failure in specifying the data involved, or to a failure in specifying the assumed prior information involved. So there often can be no valid probability comparison between two physics theories regarding given data, if both involve assumptions about eg 'mass' but both fail to specify the prior information properties of 'mass' that their theories involve.

For some physicists the two-slit light experiment was taken as supporting a probabilistic quantum mechanics, as where there is some probability that an object actually at a specified time occupies one space location and actually at the same specified time in contradiction occupies some other space location. In such a probabilistic physics universe, the universe actually behaves probabilistically whereas in a determinate physics the universe actually involves fully specifiable causes giving fully determinate effects though that may not always arrear to be the case. Probabilistic physics does claim other evidence and claims that misroscopic quantum processes such as superposition and entanglement are involved.

But some physicists do not support probabilistic physics including Einstein who rejected probability physics because "God does not play dice" (though that is maybe no scientific disproof and Einstein still accepted duality contradiction physics). Probabilistic physics is rejected also by others like Schrodinger who reject all contradiction physics, including Einstein dualism, as in his Schrodinger's Cat exposing-probability 'thought experiment' which is perversely often quoted to help 'explain' probabilistic quantum physics. For those who reject contradiction in science, it exposes probability physics as contradiction nonsense. But for those who accept contradiction in science, it helps explain probability physics. Of course it can be said that evidence for a contradiction must be contradictory evidence, and contradictory evidence may reasonably be taken as not being valid factual evidence - eg evidence that Jane is in Paris now AND that Jane is in Tokyo now or evidence that Jane is alive now AND that Jane is dead now ?! Logically it would seem that 'evidence' for a contradiction must be data being misinterpreted.

Probability methods generally are widely used in particle and quantum physics and have some use in almost all areas of physics today, even by physicists who reject actual probability physics. But where it is claimed that it has been proved that some physics is probabilistic, it is maybe best taken as meaning that it has really at most been proved that it is either probabilistic or involves some as yet unidentified non-probabilistic causation.

Some of these physics probability issues were considered at the CERN 2007 conference 'Statistical Issues for LHC Physics', and see Statistical Physics.

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