Null hypothesis

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Null hypothesis

Post by tasprin on Thu 29 May - 18:44

As this subject is currently taking over other threads perhaps it should have a thread of its own.

Don't believe in the null hypothesis?
Chong Ho (Alex) Yu, Ph.D. (2013)

In a statistical test, the researcher selects between two mutually exclusive hypotheses: the null and the alternate hypothesis. It is a common notion that:

•You don't believe in the null hypothesis
•You do believe in the alternate hypothesis

In this article I explain the logic behind it and why it is not always right.


Again, failing to observe a difference could be attributed to other causes. Thus, in hypothesis testing we must state our conclusion as "failing to reject the null hypothesis," but not "accepting the null hypothesis." We have to leave the explanation open to other possibilities.
At most we can say that we either confirm or disconfirm a hypothesis. There is a subtle difference between "prove" and "confirm." The former is about asserting the "truth" but the latter is noting more than showing the fitness between the data and the model. In philosophy of science this type of fitness is called empirical adequacy. When the data and the model cannot fit each other, again, it is problematic to say that we "prove" the null hypothesis.
In the O. J. Simpson case or the Casey Anthony's case, there is not enough evidence to convict the suspect, but it doesn't mean that we have proven the otherwise. By the same token, failing to reject the null hypothesis does not mean that the null is true and thus we should accept it. At most we can say we fail to reject the null hypothesis because the absence of evidence is not the evidence of absence (proving the null). In the article entitled "Absence of evidence is not evidence of absence," Altman and Bland (1995) gave this warning to medical researchers: "Randomized controlled clinical trials that do not show a significant difference between the treatments being compared are often called "negative." This term wrongly implies that the study has shown that there is no difference" (p.485).


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Re: Null hypothesis

Post by tasprin on Thu 29 May - 18:56

Hypothesis Testing & the Casey Anthony Trial

August 13 2011

Hypothesis testing is one of the most important concepts in scientific studies, but most people don't understand it. Atleast I didn't get it when I took my stats and research class.  In this article, I will try to elucidate this concept by comparing it to the recent Casey Anthony trial

What is hypothesis testing?

Hypothesis Testing: Hypothesis testing is a method used to make a decision in scientific studies. It tries to figure out if a hypothesis is true based on probabilities.
Imagine you want to test if Drug A is better or not in lowering deaths in cancer patients compared to a Drug B. In hypothesis testing, you first come up with 2 hypotheses.
• There is no difference between the drugs. Or nothing important is happening. This is called the null hypothesis.
• There is a difference between the drugs. Or there is something important happening here. This is called the alternative hypothesis.

But why have two hypotheses to prove a single hypothesis?

This didn't make any sense to me when I was introduced to this concept.

If you want to show a difference, why just start with one hypothesis that there is a difference between the drugs and try to prove it? Why the heck should you come up with a hypothesis that there is no difference and then try to disprove it to show there is a difference? It seems counter intuitive to most people, but there is a good reason as you will see.

Popper's Theory: According to Karl Popper, one of the great philosophers, you cannot prove a theory, you can only disprove it. For example, let's say you want to prove a theory that all swans are white. This will be extremely hard to prove since you will have to go to every nook and corner of the world to make sure all swans are white. But it is extremely easy to disprove thee theory: You just have to find one black swan.  And if you tried really hard and couldn't find a black swan, you support the theory that all swans are white (but , mind you, you didn't prove the theory since there might be a black swan hiding somewhere in the world) .

And hence the reason, you come with a hypothesis and then you try to disprove it. If you disprove it, you accept the second hypothesis or the alternate hypothesis. In hypothesis testing we use probability to disprove the hypothesis. Make sense?

Now what has this got to do with Casey Anthony?

Casey Anthony 's trial is a good example of how people don't understand this concept. For people outside US, Casey Anthony is a Florida woman who was recently acquitted of killing her 2-year old daughter. This was one of those murder trials which took the country by storm. Almost everyone thinks that she killed her daughter and she should have been punished.

casey Anthony

The whole hypothesis testing makes a lot of sense when we look at how the American justice system is set up. Just like in hypotheses testing, you come up with 2 hypotheses before the trial.
• The first is the null hypothesis or the default hypothesis that Casey Anthony is not guilty.
• The alternate hypothesis is that Casey is guilty.

US Justice System: Just like in hypothesis testing, the lawyers try to disprove the hypothesis that Casey is not guilty. Instead of using probability, lawyers use evidence in form of DNA, witnesses and so forth.  In the trial, the prosecutors couldn’t disprove the null hypothesis that she is not guilty with the evidence they had. So the jurors had no choice but to accept the null hypothesis that she is not guilty. Just like swan example, this doesn't mean or prove that that she is innocent.

A lot of people in the media were going crazy thinking how on Earth can the jurors think that she is innocent. But the jurors never thought she is innocent.  One of the jurors put it best after the verdict- She said we never said Casey Anthony is innocent. This goes back to the concept of how you cannot prove a theory and we can only disprove a theory with the evidence in hand. The jurors understood this concept very well.


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Re: Null hypothesis

Post by puzzled on Thu 29 May - 19:14

I think it may be pretty dubious to apply the Null hypothesis outside fields where you can gather statistical data. It's really a technique that applies to statistics. More or less, it's the idea that if a correlation exists between two sets of measured data, this may be simply due to chance. There are a variety of statistical tests that can be applied to establish the probability that the correlation is due to chance or not. So, how could we apply this to the McCann case?

Well, let's consider the fact that Kate McCann refused to answer questions. Obviously, we're not in the realms of correlating sets of data here, so what should our null hypothesis be? She was not deliberately trying to cover something up? Maybe. Why would we choose that rather than something else? Statistically, how many innocent people don't answer questions put to them by the police? That would give us something to go on. But of course, she could have simply been nervous.I guess most people would be when being questioned by the police. On the other hand, most people probably realise that it's better to answer their questions honestly and straightforwardly, too. Ultimately, it seems that we have no way of knowing one way or another. But I suppose that if the police regard such behaviour as suspicious, they have very good reasons for doing so.

But there is one area where we are on firm ground, and that's the dogs. We know that statistically, they have a very high level of accuracy. We know that they were taken around apartment 5a, several other apartments, Robert Murat's house, other places where you could hide a body like old tunnels.... they were taken to the McCann's hire car and ten other cars. They only alerted to items linked to the McCanns. So, let's assume that this correlation was due to chance.  If you gave an expert in statistics all the relevant information about the dogs, they could work out exactly what the probability was that it was due to chance. And I'd bet any money you like that this probability would be pretty miniscule.

So this is evidence that can't be explained away. We can all think up alternative scenarios for why Kate McCann didn't answer questions, why they didnt go back for a reconstruction, etc. With the dogs, we can work out exactly how likely it is that they were wrong, and that is evidence that can't be dismissed.

____________________ did you feel the last time you squashed a bug? -psychopathic criminal, quoted in Robert Hare, Without Conscience


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Re: Null hypothesis

Post by tasprin on Thu 29 May - 19:50

Puzzled, regarding the dogs I agree.

If the question was; 'How many innocent parents of an abducted child don't answer questions put to them by the police?' the probability would be miniscule to zero.

Amazing Applications of Probability and Statistics
by Tom Rogers,
Type I and Type II Errors - Making Mistakes in the Justice System
Ever wonder how someone in America can be arrested if they really are presumed innocent, why a defendant is found not guilty instead of innocent, or why Americans put up with a justice system which sometimes allows criminals to go free on technicalities? These questions can be understood by examining the similarity of the American justice system to hypothesis testing in statistics and the two types of errors it can produce. (This discussion assumes that the reader has at least been introduced to the normal distribution and its use in hypothesis testing. Also please note that the American justice system is used for convenience. Others are similar in nature such as the British system which inspired the American system)

True, the trial process does not use numerical values while hypothesis testing in statistics does, but both share at least four common elements (other than a lot of jargon that sounds like double talk):
1.The alternative hypothesis - This is the reason a criminal is arrested. Obviously the police don't think the arrested person is innocent or they wouldn't arrest him. In statistics the alternative hypothesis is the hypothesis the researchers wish to evaluate.
2.The null hypothesis - In the criminal justice system this is the presumption of innocence. In both the judicial system and statistics the null hypothesis indicates that the suspect or treatment didn't do anything. In other words, nothing out of the ordinary happened The null is the logical opposite of the alternative. For example "not white" is the logical opposite of white. Colors such as red, blue and green as well as black all qualify as "not white".
3.A standard of judgment - In the justice system and statistics there is no possibility of absolute proof and so a standard has to be set for rejecting the null hypothesis. In the justice system the standard is "a reasonable doubt". The null hypothesis has to be rejected beyond a reasonable doubt. In statistics the standard is the maximum acceptable probability that the effect is due to random variability in the data rather than the potential cause being investigated. This standard is often set at 5% which is called the alpha level.
4.A data sample - This is the information evaluated in order to reach a conclusion. As mentioned earlier, the data is usually in numerical form for statistical analysis while it may be in a wide diversity of forms--eye-witness, fiber analysis, fingerprints, DNA analysis, etc.--for the justice system. However in both cases there are standards for how the data must be collected and for what is admissible. Both statistical analysis and the justice system operate on samples of data or in other words partial information because, let's face it, getting the whole truth and nothing but the truth is not possible in the real world


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