Null Hypothesis

A Null Hypothesis is a hypothesis posed in a belief test that some statement is default belief.

• AKA: H₀.
• Context:
  • It can be tested against by observation.
  • It can range from being a Rejected Null Hypothesis to being a Not-Yet-Rejected Null Hypothesis.
  • It can be an input to a Null Hypothesis Significance Test.
• Example(s):
  • a Statistical Null Hypothesis, that sample observations result purely from chance.
  • a Legal Null Hypothesis, such as the defendant is innocent.
• Counter-Example(s):
  • an Alternative Hypothesis.
• See: Statistical Hypothesis Test, Random Experiment, Decision Theory.

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References

2011

• (Wikipedia, 2011) ⇒ http://en.wikipedia.org/wiki/Null-hypothesis
  • QUOTE: The practice of science involves formulating and testing hypotheses, assertions that are capable of being proven false using a test of observed data. The null hypothesis typically corresponds to a general or default position. For example, the null hypothesis might be that there is no relationship between two measured phenomena or that a potential treatment has no effect.

    It is important to understand that the null hypothesis can never be proven. A set of data can only reject a null hypothesis or fail to reject it. For example, if comparison of two groups (e.g.: treatment, no treatment) reveals no statistically significant difference between the two, it does not mean that there is no difference in reality. It only means that there is not enough evidence to reject the null hypothesis (in other words, one fails to reject the null hypothesis).

    …

    Much of the terminology used in connection with null hypotheses derives from the immediate relation to statistical hypothesis testing; part of this terminology is outlined here, but see this list of definitions for a more complete set. Simple hypothesis: Any hypothesis which specifies the population distribution completely. Composite hypothesis: Any hypothesis which does not specify the population distribution completely.

    A point hypothesis is more complicated to describe. The term arises in contexts where the set of all possible population distributions is put in parametric form. A point hypothesis is one where exact values are specified for either all the parameters or for a subset of the parameters. Formally, the case where only a subset of parameters is defined is still a composite hypothesis; nonetheless, the term point hypothesis is often applied in such cases, particularly where the hypothesis test can be structured in such a way that the distribution of the test statistic (the distribution under the null hypothesis) does not depend on the parameters whose values have not been specified under the point null hypothesis. Careful treatments of point hypotheses for subsets of parameters do consider them as composite hypotheses and study how the p-value for a fixed critical value of the test statistic varies with the parameters that are not specified by the null hypothesis.

    A one-tailed hypothesis is a hypothesis in which the value of a parameter is specified as being either: above a certain value, or below a certain value. An example of a one-tailed null hypothesis would be that, in a medical context, an existing treatment, A, is no worse than a new treatment, B. The corresponding alternative hypothesis would be that B is better than A. Here if the null hypothesis were accepted (i.e. there is no reason to reject the hypothesis that A is at least as good as B), the conclusion would be that treatment A should continue to be used. If the null hypothesis were rejected, the result would be that treatment B would used in future, given that there is evidence that it is better than A. A hypothesis test would look for evidence that B is better than A, not for evidence that the outcomes of treatments A and B are different. Formulating the hypothesis as a "better than" comparison is said to give the hypothesis directionality.

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