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When the null hypothesis is predicted by theory, a more precise experiment will be a more severe test of the underlying theory. When the null hypothesis defaults to "no difference" or "no effect", a more precise experiment is a less severe test of the theory that motivated performing the experiment. [4]
Neither of the test methods has been completely abandoned, as they are extensively utilized for different objectives. Textbooks have integrated both test methods into the framework of hypothesis testing. Some mathematicians argue, with a few exceptions, that significance tests can be considered a specific instance of hypothesis tests.
All statistical hypothesis tests and all statistical estimators are derived via statistical models. More generally, statistical models are part of the foundation of statistical inference . A statistical model is usually specified as a mathematical relationship between one or more random variables and other non-random variables.
In short, a hypothesis is testable if there is a possibility of deciding whether it is true or false based on experimentation by anyone. This allows anyone to decide whether a theory can be supported or refuted by data. However, the interpretation of experimental data may be also inconclusive or uncertain.
Testing a hypothesis suggested by the data can very easily result in false positives (type I errors). If one looks long enough and in enough different places, eventually data can be found to support any hypothesis. Yet, these positive data do not by themselves constitute evidence that the hypothesis is correct. The negative test data that were ...
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 ...
A statistical significance test is intended to test a hypothesis. If the hypothesis summarizes a set of data, there is no value in testing the hypothesis on that set of data. Example: If a study of last year's weather reports indicates that rain in a region falls primarily on weekends, it is only valid to test that null hypothesis on weather ...
investigations that do or do not provide a potentially falsifying test of the hypothesis. [7] Evidence contrary to a hypothesis is itself philosophically problematic. Such evidence is called a falsification of the hypothesis. However, under the theory of confirmation holism it is always possible to save a given hypothesis from falsification ...