If we consider the thesis and its converse as definition, then the hypothesis is an hypothesis about the application of the mathematical theory developed from the definition.

If empirical data reach significance under the appropriate statistical formula, the research hypothesis is supported.

If not, the null hypothesis is supported ( or, more correctly, not rejected ), meaning no effect of the independent variable ( s ) was observed on the dependent variable ( s ).

The evidence was compiled by W de Sitter ( 1927 ) who wrote " If we accept this hypothesis, then the ' astronomical time ', given by the earth's rotation, and used in all practical astronomical computations, differs from the ' uniform ' or ' Newtonian ' time, which is defined as the independent variable of the equations of celestial mechanics ".

If confirmed, this would imply special relativity is an approximation to a more general theory, but since the relevant comparison would ( by definition ) be outside the observable universe, it is difficult to imagine ( much less construct ) experiments to test this hypothesis.

If F is continuous then under the null hypothesis converges to the Kolmogorov distribution, which does not depend on F. This result may also be known as the Kolmogorov theorem ; see Kolmogorov's theorem for disambiguation.

If there were such a number then the theory would be inconsistent, contrary to the consistency hypothesis.

If Prout's hypothesis had proven accurate, then the abstract concept of mass, as we now know it, might never have evolved, since mass could always be defined in terms of amounts of the hydrogen atomic mass.

If this hypothesis is correct, it also is likely that male Pteranodon played little to no part in rearing the young ; such a behavior is not found in the males of modern polygynous animals who father many offspring at the same time.

Many of his stories, such as Gulf, If This Goes On —, and Stranger in a Strange Land, depend strongly on the premise, related to the well-known Sapir – Whorf hypothesis, that by using a correctly designed language, one can change or improve oneself mentally, or even realize untapped potential ( as in the case of Joe Green in Gulf ).

If such an Interstellar Internet exists, the hypothesis states, communications between servers are mostly through narrow-band, highly directional radio or laser links.

The theorem " If n is an even natural number then n / 2 is a natural number " is a typical example in which the hypothesis is that " n is an even natural number " and the conclusion is that " n / 2 is also a natural number ".

If the null hypothesis that is rejected, then the alternative hypothesis that and equivalently that causes y cannot be rejected.

If the first person accepts the hypothesis that " All ravens are black " then, according to the argument, about 50 objects whose colors were previously in doubt ( the ravens ) are now thought to be black, while nothing different is thought about the remaining objects ( the non-ravens ).

If the evidence doesn't match up with a hypothesis, one should reject the hypothesis.

If the giant impact hypothesis is correct, they must be due to some other cause.

* If the continuum hypothesis holds then is the unique Parovicenko space, up to isomorphism.

If the Noetherianity hypothesis is dropped, then R can have dimension anywhere between d + 1 and 2d + 1.

If there were such a number then the theory would be inconsistent, contrary to the consistency hypothesis.

If an experiment is carefully conducted, the results usually either support or disprove the hypothesis.

The book commences on a hypothesis of novelistic elements (" If ...") on a when, a someone ... would do what?

If you were a man '' --

If she, Pamela, were being held responsible for his crimes, then hers must be the final act of expiation.

If someone were to drop a match in here, this place would go up like a haystack ''.

If the other pilots were worried, they did not show it.

If it were the enemy, tactically his position was correct.

If it were not for an old professor who made me read the classics I would have been stymied on what to do, and now I understand why they are classics ; ;

If it were not that I knew who it was I could have mistaken it for my Aunt so well did her clothes fit him.

If an automobile were approaching him, he would know what was required of him, even though he might not be able to act quickly enough.

If there were only darkness, all would be clear.

If there were only the mess, all would be clear ; ;

If these people were denied a voice ( do they have a moral right to a voice??

If we were creating a wholly new society, we could insist that our social, political, economic and philosophic institutions foster rather than hamper man ; ;

If living Jews were unavailable for study, the Bible was at hand.

If his scholarship and formal musicianship were not all they might have been, Mercer demonstrated at an early age that he was gifted with a remarkable ear for rhythm and dialect.

If she were not at home, Mama would see to it that a fresh white rose was there.

If the Stearns were not there, grace would be omitted.

If anything, the conservative Democrats were more opposed to Hearst than the Republicans.

If the hardships of the winter at Valley Forge were trying for healthy men, they were, of course, much more so for those not in good health.

If his circumspection in regard to Philip's sensibilities went so far that he even refused to grant a dispensation for the marriage of Amadee's daughter, Agnes, to the son of the dauphin of Vienne -- a truly peacemaking move according to thirteenth-century ideas, for Savoy and Dauphine were as usual fighting on opposite sides -- for fear that he might seem to be favoring the anti-French coalition, he would certainly never take the far more drastic step of ordering the return of Gascony to Edward, even though, as he admitted to the English ambassadors, he had been advised that the original cession was invalid.

If there were no West Berlin problem, imperialist quarters would have invented an excuse for stepping up the armaments race to try to solve the internal and external problems besetting the United States and its NATO partners.

If the new Soviet series has followed the general pattern of previous Russian tests, the shots were roughly half fission and half fusion, meaning a fission yield of 30 to 40 megatons thus far.

If the Hessian troops sent here willy-nilly by the Hessian Government to fight for England in the 1770's were mercenaries, what shall we call the UN troops sent to the Congo willy-nilly by their governments to fight for the United Nations??

If the UN troops are not mercenaries then the Hessians were not mercenaries either.

If he were to go with White, he would be out there two days, not just listening in the dark at some point between here and Papa-san, but moving ever deeper into enemy land -- behind Papa-san -- itself.