A **hypothesis** (plural **hypotheses**; from the ancient Greek ὑπόθεσις hypothesis, composed of hypo, “under” and thesis, “position”, or supposition) is the premise underlying reasoning or a demonstration; in other words is a suggested explanation for an event, which one can test.

Originally, the meaning of the word indicated a mathematical method capable of simplifying the calculations, or a plausible but not necessarily true idea. With this meaning, Cardinal Bellarmine used the word when he warned Galileo Galilei not to treat the movement of the Earth as real, but to assume the Copernican system only as a hypothesis.

In common usage, a hypothesis is a tentative idea whose value must be ascertained. The hypothesis, therefore, requires an effort by researchers to confirm or deny it. In the hypothetical-deductive method, a hypothesis should be falsifiable, that is, it should be possible to declare it false, usually through observation and consequent formulation of another logical hypothesis.

In a scientific and epistemological sense, a hypothesis is the first formulation of a law, not yet tested or experimental in itself, intended to provide – along with a description of particular events and rules of deduction – an explanation or forecast of certain phenomena; this provisional formulation serves to determine further research from which the hypothesis itself may or may not have confirmation; if the hypothesis refers to an organic complex of laws and if it happens that, after experimental confirmation and technical reworking, the hypothesis assumes a complete and comprehensive form, it will take the name of the theory.

Since it expresses the provisional nature of the data chosen as a starting point or the direction of reasoning assumed, the hypothesis becomes reliable only when, in the subsequent demonstration, it has been proven to be true: otherwise it is rejected. In the field of philosophy of science, some authors have seen in the hypothesis a pure functional element, without any direct relationship to the reality that wants to examine or discover, giving it a mere meaning of an instrument for a demonstration, with no autonomous theoretical scope; others, however, have admitted that a scientific hypothesis – as an ineliminable reference point for any analysis – has already in itself a revelatory capacity towards the structure of a reality that it implies and interprets, but only partial capacity and therefore must be completed by further verification. In any case, a hypothesis, even in its constitutive uncertainty, cannot – in order for its use to be legitimate – escape from a certain set of relationships, from what is already known in a certain scientific field in which it is used, as an essential element for its verifiability and for its effective scientific scope.

In statistics, the concept of hypothesis refers to the assumption concerning the distribution and parameters of a population. Hypothesis testing, or hypothesis verification, or hypothesis control, one of the two forms of statistical inference, is the set of procedures that allow us to determine, in probabilistic terms, whether a given hypothesis should be accepted or rejected. In other words, in hypothesis testing, two values are compared (a sample statistic with a parameter of the universe, or two sample statistics with each other) and, using appropriate tests, it is decided whether the difference between them does not exist, that is due to chance (null hypothesis, indicated with the symbol H_{0}) or exists, that is significant (alternative hypothesis, indicated with the symbol H_{1}). Determined a priori the level of significance of the test, i.e. the probability assigned to the risk of committing an error of the first kind, i.e. rejecting the null hypothesis as false, while in reality it is true, on the basis of sample observations it is decided whether to accept the null hypothesis or the alternative hypothesis, considering due to the case a difference with probability of occurrence due to the case higher than the established level. The theory of hypothesis testing was developed in particular by J. Neyman and E. S. Pearson.