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The hypothesis of Andreas Cellarius, showing the planetary motions in eccentric and epicyclical orbits. A hypothesis (pl.: hypotheses) is a proposed explanation for a phenomenon. A scientific hypothesis must be based on observations and make a testable and reproducible prediction about reality, in a process beginning with an educated guess or ...
Statistical hypothesis: A statement about the parameters describing a population (not a sample). Test statistic: A value calculated from a sample without any unknown parameters, often to summarize the sample for comparison purposes. Simple hypothesis: Any hypothesis which specifies the population distribution completely.
Simple hypothesis Any hypothesis which specifies the population distribution completely. For such a hypothesis the sampling distribution of any statistic is a function of the sample size alone. Composite hypothesis Any hypothesis which does not specify the population distribution completely. [4]
The consistent application by statisticians of Neyman and Pearson's convention of representing "the hypothesis to be tested" (or "the hypothesis to be nullified") with the expression H 0 has led to circumstances where many understand the term "the null hypothesis" as meaning "the nil hypothesis" – a statement that the results in question have ...
The history of scientific method considers changes in the methodology of scientific inquiry, not the history of science itself. The development of rules for scientific reasoning has not been straightforward; scientific method has been the subject of intense and recurring debate throughout the history of science, and eminent natural philosophers and scientists have argued for the primacy of ...
We define two hypotheses the null hypothesis, and the alternative hypothesis. If we design the test such that α is the significance level - being the probability of rejecting H 0 {\displaystyle H_{0}} when H 0 {\displaystyle H_{0}} is in fact true, then the power of the test is 1 - β where β is the probability of failing to reject H 0 ...
In statistical hypothesis testing, a uniformly most powerful (UMP) test is a hypothesis test which has the greatest power among all possible tests of a given size α.For example, according to the Neyman–Pearson lemma, the likelihood-ratio test is UMP for testing simple (point) hypotheses.
In null-hypothesis significance testing, the p-value [note 1] is the probability of obtaining test results at least as extreme as the result actually observed, under the assumption that the null hypothesis is correct. [2] [3] A very small p-value means that such an extreme observed outcome would be very unlikely under the null hypothesis.