Hypothesis

A hypothesis (from Greek ὑπόθεσις; plural hypotheses) is a proposed explanation for an observable phenomenon. The term derives from the Greek, ὑποτιθέναι – hypotithenai meaning "to put under" or "to suppose." For a hypothesis to be put forward as a scientific hypothesis, the scientific method requires that one can test it. Scientists generally base scientific hypotheses on previous observations that cannot satisfactorily be explained with the available scientific theories. Even though the words "hypothesis" and "theory" are often used synonymously in common and informal usage, a scientific hypothesis is not the same as a scientific theory. A working hypothesis is a provisionally accepted hypothesis.
In a related but distinguishable usage, the term hypothesis is used for the antecedent of a proposition; thus in proposition "If P, then Q", P denotes the hypothesis (or antecedent); Q can be called a consequent. 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."

Uses

In Plato's Meno (86e–87b), Socrates dissects virtue with a method used by mathematicians,^[1] that of "investigating from a hypothesis."^[2] In this sense, 'hypothesis' refers to a clever idea or to a convenient mathematical approach that simplifies cumbersome calculations.^[3] Cardinal Bellarmine gave a famous example of this usage 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.^[4]
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.

Scientific hypothesis

People refer to a trial solution to a problem as a hypothesis — often called an "educated guess"^[5] — because it provides a suggested solution based on the evidence. Experimenters may test and reject several hypotheses before solving the problem.
According to Schick and Vaughn,^[6] researchers weighing up alternative hypotheses may take into consideration:

• Testability (compare falsifiability as discussed above)
• Simplicity (as in the application of "Occam's razor", discouraging the postulation of excessive numbers of entities)
• Scope – the apparent application of the hypothesis to multiple cases of phenomena
• Fruitfulness – the prospect that a hypothesis may explain further phenomena in the future
• Conservatism – the degree of "fit" with existing recognized knowledge-systems

Evaluating hypotheses

Karl Popper's formulation of hypothetico-deductive method, which he called the method of "conjectures and refutations", demands falsifiable hypotheses, framed in such a manner that the scientific community can prove them false (usually by observation). According to this view, a hypothesis cannot be "confirmed", because there is always the possibility that a future experiment will show that it is false. Hence, failing to falsify a hypothesis does not prove that hypothesis: it remains provisional. However, a hypothesis that has been rigorously tested and not falsified can form a reasonable basis for action, i.e., we can act as if it were true, until such time as it is falsified. Just because we've never observed rain falling upward, doesn't mean that we never will—however improbable, our theory of gravity may be falsified some day.
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 initial theory as it stands is verified but incomplete. This situation illustrates the importance of having well-crafted, well-controlled experiments that range over the full scope of possibilities for applying the theory.
In recent years philosophers of science have tried to integrate the various approaches to evaluating hypotheses, 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, both former students of Popper, have produced novel attempts at such a synthesis.

Hypotheses, Concepts and Measurement

Concepts, as abstract units of meaning, play a key role in the development and testing of hypotheses. Concepts are the basic components of hypotheses. Most formal hypotheses connect concepts by specifying the expected relationships between concepts. For example, a simple relational hypothesis such as “education increases income” specifies a positive relationship between the concepts “education” and “income.” This abstract or conceptual hypothesis cannot be tested. First, it must be operationalized or situated in the real world by rules of interpretation. Consider again the simple hypothesis “Education increases Income.” To test the hypothesis the abstract meaning of education and income must be derived or operationalized. The concepts should be measured. Education could be measured by “years of school completed” or “highest degree completed” etc. Income could be measured by “hourly rate of pay” or “yearly salary” etc.
When a set of hypotheses are grouped together they become a type of conceptual framework. When a conceptual framework is complex and incorporates causality or explanation it is generally referred to as a theory. According to noted philosopher of science Carl Gustav Hempel “An adequate empirical interpretation turns a theoretical system into a testable theory: The hypothesis whose constituent terms have been interpreted become capable of test by reference to observable phenomena. Frequently the interpreted hypothesis will be derivative hypotheses of the theory; but their confirmation or disconfirmation by empirical data will then immediately strengthen or weaken also the primitive hypotheses from which they were derived.”^[7]
Hempel provides a useful metaphor that describes the relationship between a conceptual framework and the framework as it is observed and perhaps tested (interpreted framework). “The whole system floats, as it were, above the plane of observation and is anchored to it by rules of interpretation. These might be viewed as strings which are not part of the network but link certain points of the latter with specific places in the plane of observation. By virtue of those interpretative connections, the network can function as a scientific theory”^[8] Hypotheses with concepts anchored in the plane of observation are ready to be tested. In “actual scientific practice the process of framing a theoretical structure and of interpreting it are not always sharply separated, since the intended interpretation usually guides the construction of the theoretician.”^[9] It is, however, “possible and indeed desirable, for the purposes of logical clarification, to separate the two steps conceptually.”^[10]

Statistical hypothesis testing

Main article: Statistical hypothesis testing

When a possible correlation or similar relation between phenomena is investigated, such as, for example, whether a proposed remedy is effective in treating a disease, that is, at least to some extent and for some patients, the hypothesis that a relation exists cannot be examined the same way one might examine a proposed new law of nature: in such an investigation a few cases in which the tested remedy shows no effect do not falsify the hypothesis. Instead, statistical tests are used to determine how likely it is that the overall effect would be observed if no real relation as hypothesized exists. If that likelihood is sufficiently small (e.g., less than 1%), the existence of a relation may be assumed. Otherwise, any observed effect may as well be due to pure chance.
In statistical hypothesis testing two hypotheses are compared, which are called the null hypothesis and the alternative hypothesis. The null hypothesis is the hypothesis that states that there is no relation between the phenomena whose relation is under investigation, or at least not of the form given by the alternative hypothesis. The alternative hypothesis, as the name suggests, is the alternative to the null hypothesis: it states that there is some kind of relation. The alternative hypothesis may take several forms, depending on the nature of the hypothesized relation; in particular, it can be two-sided (for example: there is some effect, in a yet unknown direction) or one-sided (the direction of the hypothesized relation, positive or negative, is fixed in advance).
Proper use of statistical testing requires that these hypotheses, and the threshold (such as 1%) at which the null hypothesis is rejected and the alternative hypothesis is accepted, all be determined in advance, before the observations are collected or inspected. If these criteria are determined later, when the data to be tested is already known, the test is invalid.