Treat yourself with the swine flu grappa, namely: the statistical validation - First episode ANSA -
Professor. University of Vienna Hans Krupp said he had found a cure to improve the course of influenza H1N1, better known as swine flu. Have found, or rather to have rediscovered the care of the grandmother, milk and brandy. In one experiment, he administered twice daily in ten patients the cure of his grandmother. The result was that the duration of fever was two and a half days, compared to the average of three patients treated by other means. The scientific community is very divided on the validity of the experiment.
As you may understand, this unusual post is about statistics. More precisely, is how it is possible to draw conclusions from a statistical survey, in this case, the effectiveness of treatment.
Ask yourself if the experiment of Dr. Krupp is valid. The answer is that relying on data alone can not establish the agency ANSA. To do this, we need information about dispersion data. To understand what this loss, we assume two possible scenarios.
In the first scenario we assume that not only the fever caused by swine flu lasts on average three days, ie 72 hours, but almost always have that time. Suppose that patients are rare, untreated or treated by other means, have a fever that lasts less than 70 hours or more than 74. Then ten patients who on average have 60 hours of fever are difficult to explain by coincidence, and we are led to believe they really care functions grandmother. This is a scenario of data with low dispersion.
The second scenario is a scenario of high dispersion. In this scenario, so the fever lasts three days, on average, but there are many sufferers of which lasts one or two days and more or less the same number which lasts four to five days. To fix ideas, in two-thirds of cases, the fever lasts from 48 to 96 hours. In this case, a person of logic is found full of doubts. It may well be that by prof. Krupp works, but instead could be that he randomly chose ten patients of the most robust and has relied on an erroneous conclusion.
In this second scenario, every person of good sense in this case invited Professor. Krupp to repeat the experiment, perhaps in 100 patients. If it should happen that in this new experiment, the average is 66 hours, what can be inferred? Imagine a debate between a fan of the prof. Krupp (K) and a skeptic (S).
K: The experiment was a success! See fact that the average duration of fever in 100 people is less than the duration for untreated patients.
S: It will also be lower, but I would not say that the experiment has been successful. Between 66 hours and 72 hours the difference is small. This is probably due to the fact that patients were chosen in an area where people are generally healthier and more robust.
K: What you say is false. Patients had not selected them to the professor, but an independent statistical agency that has chosen a representative sample by age, health status and residence.
S: But will agree that a gain of less than six hours of fever is very little, it takes something else to say that it found a cure.
K: But it is a step forward. For some, the fever was 24 hours.
S: Yes, but the data I read that others have lasted a week. So what do we do? I would say that with a range so strong, that the fever lasted an average of 66 hours instead of 72 was only one case.
K: No. 66 hours is less than 72 hours, but since the average is about 100 people, the result confirms the validity care.
S: Bullshit! For 30% of patients the fever has lasted even longer than four days, how can you say that these data mean anything? Those numbers are meaningless.
K: It does.
S: No.
K: Yes
S: No. ..
The statistic has an accurate way to tell who is right between K and S. With calculations for the time being thorough, you can determine with some precision what happens if we choose a group of one hundred patients (called sample hundred patients) not processed. These calculations lead to a result like this:
in 99% of cases, the average temperature in a sample of one hundred patients between hours x and y hours.
This is the most difficult concept of this post. The sentence means that if you take a lot, but many!, Groups of 100 patients, and each group, the average, in 99% of this average is between x and y . The beauty is not necessary to take really many hundreds of patients: the statistic calculates x and y from the media and the values \u200b\u200bof the dispersion are known. How do you calculate those values, is a question that we address in this post. Instead, we are interested in the conclusions to be drawn on by Krupp. Consider two possibilities.
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Suppose that the average found by prof. Krupp, 66 hours, is a smaller value of x . If the treatment of brandy and milk does not work, it would mean that the prof. Krupp would have found itself in front of a quell'1% of samples from patients with abnormal media. It 'hard to believe that one chooses a random sample and should take just one flawed, because in fact we do not believe, in this case it is concluded that the treatment has an effect that may be small, but detectable.
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Conversely, suppose the value of 66 hours is between x and y . This would mean that between samples "normal" of 100 untreated patients there are also many for whom the average duration of fever of 66 hours or less! So in this case the statistic gives up. It may be that care Krupp works, but it may be that the deviation from the average duration of 72 hours is simple randomness. In this case, we conclude that the experimental data is not significant, that is not a test. Warning: it is not proven the effectiveness of treatment, but its not even work!
conclusion. Here is some simplification was made. For example, when making medical or pharmacological experiments, it is usually a second sample (called control sample) with a traditional treatment or a placebo treatment. This is because it is a known effect, called placebo effect, for which a treatment with ineffective drugs (such as such as a sugar pill) may have therapeutic effects, due to psychological mechanisms. Then one has to say that any statistical method as it focuses on a certain effect (duration of fever), but is unable to clarify whether this effect was really positive consequences (who tells me that complications are not more frequent when the fever lasts less?)
I adopted the same principle as in some previous post, talking about tressette . And I must admit that I have a little 'made the fool. Meanwhile, when I wrote that the statistics say we are in the normal range, actually I should say that the statistic that says could be to normal, we are like the case 2) of those treated above. In addition, the statistical analysis that I made about the average loads in one hand, because that is what we often complain. But the randomness is a much more complicated. Imagine a software that is random according to the developers, but to distribute loads three-player hands, always . The media is correct, but there seems to be a truly random distribution? I think not.
But an important thing to add. Laymen believe that whoever wrote the software for playing tressette GDM ( www.mygdm.com ) has also made itself some mechanism to create randomness. I have not seen the software, but I am sure it is not. The random number generation is implemented in any programming language, including, I do not know, that the creators of this site will be adopted. This generation is studied in heavy tomes by barbosa pounds of computer scientists, many years. All the technical characteristics of random generation have known (really called pseudorandom ) absolutely reliable. That is why, in my opinion, it is impossible that the GDM software distributes cards in a way different from what we recognize as random.
(End of first bet. If you are interested in their own accounts, there will be a second.)
