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Given that the validity of any conclusion drawn from a statistical inference depends on the validity of the assumptions made, it is clearly important that those assumptions should be reviewed at some stage. Some instances—for example where data are lacking—may require that researchers judge whether an assumption is reasonable. Researchers ...
Technical null hypotheses are used to verify statistical assumptions. For example, the residuals between the data and a statistical model cannot be distinguished from random noise. If true, there is no justification for complicating the model. Scientific null assumptions are used to directly advance a theory.
Informally, a statistical model can be thought of as a statistical assumption (or set of statistical assumptions) with a certain property: that the assumption allows us to calculate the probability of any event. As an example, consider a pair of ordinary six-sided dice. We will study two different statistical assumptions about the dice.
An example of Neyman–Pearson hypothesis testing (or null hypothesis statistical significance testing) can be made by a change to the radioactive suitcase example. If the "suitcase" is actually a shielded container for the transportation of radioactive material, then a test might be used to select among three hypotheses: no radioactive source ...
P is the assumption in a (possibly counterfactual) What If question. The adjective hypothetical , meaning "having the nature of a hypothesis", or "being assumed to exist as an immediate consequence of a hypothesis", can refer to any of these meanings of the term "hypothesis".
Then if the assumption is important to the results of the analysis, the results would be only as reliable as the certainty of the assumption. Carrying that example a step further, if one were to research the genetics of a transgenic potato, one might make the general assumption that God does not exist, or at least make the general assumption ...
Most two-sample t-tests are robust to all but large deviations from the assumptions. [ 22 ] For exactness , the t -test and Z -test require normality of the sample means, and the t -test additionally requires that the sample variance follows a scaled χ 2 distribution , and that the sample mean and sample variance be statistically independent .
An "axiom", in classical terminology, referred to a self-evident assumption common to many branches of science. A good example would be the assertion that: When an equal amount is taken from equals, an equal amount results. At the foundation of the various sciences lay certain additional hypotheses that were accepted without proof.