Not unusually, such a hypothesis states that the parameters, or mathematical characteristics, of two or more populations are identical. For example, if we want to compare the test scores of two random samples of men and women, the null hypothesis would be that the mean score in the male population from which the first sample was drawn was the same as the mean score in the female population from which the second sample was drawn:
where:
Alternatively, the null hypothesis can postulate that the two samples are drawn from the same population:
The value of the null hypothesis is that it can be rejected with high probability, while nonnull hypotheses cannot be confirmed with high probability. If experimental observations contradict the prediction of the null hypothesis, it means that either the null hypothesis is false, or we have observed an event with very low probability. This gives us high confidence in the falsehood of the null hypothesis, which can be improved by increasing the number of trials. Confirmation of a nonnull hypothesis confirms only a difference in parameters; it does not provide support for the theory or principles from which the hypothesis was derived, since the difference could be due to one or more of many possible factors.
Rejection of a null hypothesis (that, say, rates of symptom relief in a sample of patients who received a placebo and a sample who received a medicinal drug will be equal) allows us to make a nonnull statement (that the rates differed). Null hypotheses form part of the model of scientific discovery formulated by Karl Popper and followed in several branches of empirical research.
Concerns regarding the high power of statistical tests to detect differences in large samples have led to suggestions for redefining the null hypothesis, for example as a hypothesis that an effect falls within a range considered negligible.
In 2002, a group of psychologists launched a new journal dedicated to experimental studies in psychology which support the null hypothesis. The Journal of Articles in Support of the Null Hypothesis (JASNH) was founded to address a scientific publishing bias against such articles. [1] (http://www.jasnh.com/) According to the editors,
See also: statistical hypothesis testing.
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