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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 ...
The statement that is being tested against the null hypothesis is the alternative hypothesis. [2] Symbols may include H 1 and H a . A statistical significance test starts with a random sample from a population.
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.
In Dewey's view, the working hypothesis is generated, not directly as a testable statement of, but instead in order to "direct inquiry into channels in which new material, factual and conceptual, is disclosed, material which is more relevant, more weighted and confirmed, more fruitful, than were the initial facts and conceptions which served as ...
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 ...
The statement that is being tested against the null hypothesis is the alternative hypothesis. [2] Alternative hypothesis is often denoted as H a or H 1 . In statistical hypothesis testing , to prove the alternative hypothesis is true, it should be shown that the data is contradictory to the null hypothesis.
The Riemann hypothesis is equivalent to several statements showing that the terms of the Farey sequence are fairly regular. One such equivalence is as follows: if F n is the Farey sequence of order n , beginning with 1/ n and up to 1/1, then the claim that for all ε > 0
"A theory is scientific if and only if it divides the class of basic statements into the following two non-empty sub-classes: (a) the class of all those basic statements with which it is inconsistent, or which it prohibits—this is the class of its potential falsifiers (i.e., those statements which, if true, falsify the whole theory), and (b ...