Alternate hypothesis
Encyclopedia
In statistical hypothesis testing
,
the alternative hypothesis (or maintained hypothesis or research hypothesis) and the null hypothesis
are the two rival hypotheses which are compared by a statistical hypothesis test
. An example might be where water quality in a stream has been observed over many years and a test is made of the null hypothesis that there is no change in quality between the first and second halves of the data against the alternative hypothesis that the quality is poorer in the second half of the record.
In the case of a scalar parameter, there are four principal types of alternative hypothesis: a point alternative hypothesis, a one-tailed directional alternative hypothesis, a two-tailed directional alternative hypothesis, and an non-directional alternative hypothesis. Point alternative hypotheses occur when the hypothesis test is framed so that the population distribution under the alternative hypothesis is a fully defined distribution, with no unknown parameters; such hypotheses are usually of no practical interest but are fundamental to theoretical considerations of statistical inference
and are the basis of the Neyman–Pearson lemma. A one-tailed directional alternative hypothesis is concerned with the region of rejection for only one tail of the sampling distribution. A two-tailed directional alternative hypothesis is concerned with both regions of rejection of the sampling distribution. A non-directional alternative hypothesis is not concerned with either region of rejection, but, rather, it is only concerned that null hypothesis is not true.
The concept of an alternative hypothesis in testing was devised by Jerzy Neyman
and Egon Pearson
, and it is used in the Neyman–Pearson lemma. It forms a major component in modern statistical hypothesis testing
. However it was not part of Ronald Fisher's
formulation of statistical hypothesis testing, and he violently opposed its use. In Fisher's approach to testing, the central idea is to assess whether the observed dataset could have resulted from chance if the null hypothesis were assumed to hold, notionally without preconceptions about what other model might hold. Modern statistical hypothesis testing accommodates this type of test since the alternative hypothesis can be just the negation of the null hypothesis.
Statistical hypothesis testing
A statistical hypothesis test is a method of making decisions using data, whether from a controlled experiment or an observational study . In statistics, a result is called statistically significant if it is unlikely to have occurred by chance alone, according to a pre-determined threshold...
,
the alternative hypothesis (or maintained hypothesis or research hypothesis) and the null hypothesis
Null hypothesis
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...
are the two rival hypotheses which are compared by a statistical hypothesis test
Statistical hypothesis testing
A statistical hypothesis test is a method of making decisions using data, whether from a controlled experiment or an observational study . In statistics, a result is called statistically significant if it is unlikely to have occurred by chance alone, according to a pre-determined threshold...
. An example might be where water quality in a stream has been observed over many years and a test is made of the null hypothesis that there is no change in quality between the first and second halves of the data against the alternative hypothesis that the quality is poorer in the second half of the record.
In the case of a scalar parameter, there are four principal types of alternative hypothesis: a point alternative hypothesis, a one-tailed directional alternative hypothesis, a two-tailed directional alternative hypothesis, and an non-directional alternative hypothesis. Point alternative hypotheses occur when the hypothesis test is framed so that the population distribution under the alternative hypothesis is a fully defined distribution, with no unknown parameters; such hypotheses are usually of no practical interest but are fundamental to theoretical considerations of statistical inference
Statistical inference
In statistics, statistical inference is the process of drawing conclusions from data that are subject to random variation, for example, observational errors or sampling variation...
and are the basis of the Neyman–Pearson lemma. A one-tailed directional alternative hypothesis is concerned with the region of rejection for only one tail of the sampling distribution. A two-tailed directional alternative hypothesis is concerned with both regions of rejection of the sampling distribution. A non-directional alternative hypothesis is not concerned with either region of rejection, but, rather, it is only concerned that null hypothesis is not true.
The concept of an alternative hypothesis in testing was devised by Jerzy Neyman
Jerzy Neyman
Jerzy Neyman , born Jerzy Spława-Neyman, was a Polish American mathematician and statistician who spent most of his professional career at the University of California, Berkeley.-Life and career:...
and Egon Pearson
Egon Pearson
Egon Sharpe Pearson, CBE FRS was the only son of Karl Pearson, and like his father, a leading British statistician....
, and it is used in the Neyman–Pearson lemma. It forms a major component in modern statistical hypothesis testing
Statistical hypothesis testing
A statistical hypothesis test is a method of making decisions using data, whether from a controlled experiment or an observational study . In statistics, a result is called statistically significant if it is unlikely to have occurred by chance alone, according to a pre-determined threshold...
. However it was not part of Ronald Fisher's
Ronald Fisher
Sir Ronald Aylmer Fisher FRS was an English statistician, evolutionary biologist, eugenicist and geneticist. Among other things, Fisher is well known for his contributions to statistics by creating Fisher's exact test and Fisher's equation...
formulation of statistical hypothesis testing, and he violently opposed its use. In Fisher's approach to testing, the central idea is to assess whether the observed dataset could have resulted from chance if the null hypothesis were assumed to hold, notionally without preconceptions about what other model might hold. Modern statistical hypothesis testing accommodates this type of test since the alternative hypothesis can be just the negation of the null hypothesis.