In early usage, scholars often referred to a clever idea or to a convenient mathematical approach that simplified cumbersome calculations as a hypothesis; when used this way, the word did not necessarily have any specific meaning. Cardinal Bellarmine gave a famous example of the older sense of the word in the warning issued to Galileo in the early 17th century: that he must not treat the motion of the Earth as a reality, but merely as a hypothesis.
In common usage in the 21st century, a hypothesis refers to a provisional idea whose merit requires evaluation. For proper evaluation, the framer of a hypothesis needs to define specifics in operational terms. A hypothesis requires more work by the researcher in order to either confirm or disprove it. In due course, a confirmed hypothesis may become part of a theory or occasionally may grow to become a theory itself. Normally, scientific hypotheses have the form of a mathematical model. Sometimes, but not always, one can also formulate them as existential statements, stating that some particular instance of the phenomenon under examination has some characteristic and causal explanations, which have the general form of universal statements, stating that every instance of the phenomenon has a particular characteristic.
Any useful hypothesis will enable predictions by reasoning (including deductive reasoning). It might predict the outcome of an experiment in a laboratory setting or the observation of a phenomenon in nature. The prediction may also invoke statistics and only talk about probabilities. Karl Popper, following others, has argued that a hypothesis must be falsifiable, and that one cannot regard a proposition or theory as scientific if it does not admit the possibility of being shown false. Other philosophers of science have rejected the criterion of falsifiability or supplemented it with other criteria, such as verifiability (e.g., verificationism) or coherence (e.g., confirmation holism). The scientific method involves experimentation on the basis of hypotheses in order to answer questions and explore observations.
In framing a hypothesis, the investigator must not currently know the outcome of a test or that it remains reasonably under continuing investigation. Only in such cases does the experiment, test or study potentially increase the probability of showing the truth of a hypothesis. If the researcher already knows the outcome, it counts as a "consequence" — and the researcher should have already considered this while formulating the hypothesis. If one cannot assess the predictions by observation or by experience, the hypothesis classes as not yet useful, and must wait for others who might come afterward to make possible the needed observations. For example, a new technology or theory might make the necessary experiments feasible.
In the United States of America, teachers of science in primary schools have often simplified the meaning of the term "hypothesis" by describing a hypothesis as "an educated guess". The failure to emphasize the explanatory or predictive quality of scientific hypotheses omits the concept's most important and characteristic feature: the purpose of hypotheses. People generate hypotheses as early attempts to explain patterns observed in nature or to predict the outcomes of experiments. For example, in science, one could correctly call the following statement a hypothesis: identical twins can have different personalities because the environment influences personality. In contrast, although one might have informed one's self about the qualifications of various political candidates, making an educated guess about the outcome of an election would not qualify as a scientific hypothesis: the guess lacks an underpinning generic explanation.
Popper's view is not the only view on evaluating hypotheses. For example, some forms of empiricism hold that under a well-crafted, well-controlled experiment, a lack of falsification does count as verification, since such an experiment ranges over the full scope of possibilities in the problem domain. Should we ever discover some place where gravity did not function, and rain fell upward, this would not falsify our current theory of gravity (which, on this view, has been verified by innumerable well-formed experiments in the past)--it would rather suggest an expansion of our theory to encompass some new force or previously undiscovered interaction of forces. In other words, our theory as it stands is verified, though possibly incomplete.
In recent years philosophers of science have tried to integrate the various approaches to evaluating hypothesis, and the scientific method in general, to form a more complete system that integrates the individual concerns of each approach. Notably, Imre Lakatos and Paul Feyerabend have produced novel attempts at such a synthesis. Both men also happen to be former students of Popper.
According to Schick and Vaughn, researchers weighing up alternative hypotheses may take into consideration: