# Hypothesis

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## Overview

A hypothesis (from Greek Template:Polytonic) consists either of a suggested explanation for a phenomenon or of a reasoned proposal suggesting a possible correlation between multiple phenomena. The term derives from the Greek, hypotithenai meaning "to put under" or "to suppose." The scientific method requires that one can test a scientific hypothesis. Scientists generally base such hypotheses on previous observations or on extensions of scientific theories.

## Usage

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 needs 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. To meet this additional criterion, it must at least in principle be possible to make an observation that would disprove the proposition as false, even if one has not actually (yet) made that observation. A falsifiable hypothesis can greatly simplify the process of testing to determine whether the hypothesis has instances in which it is false. The scientific method involves experimentation on the basis of falsifiable hypotheses in order to answer questions and explore observations.

In framing a hypothesis, the investigator must not currently know the outcome of a potentially falsifying 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". Overemphasizing this aspect fails to convey the explanatory or predictive quality of scientific hypotheses. To define a hypothesis as "an educated guess" resembles describing a tricycle is a "vehicle with three". The definition 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.

## Types of hypothesis

A proposition may take the form of asserting a causal relationship (such as "A causes B"). A proposition often (but not necessarily) involves an assertion of causation. For example, if a particular independent variable changes, then a certain dependent variable also changes. This formulation, also known as an "If and Then" statement, applies whether or not a proposition asserts a direct cause-and-effect relationship.

A hypothesis about possible correlation does not stipulate the cause and effect per se, only stating that "A is related to B". Investigators may have more difficulty in verifying causal relationships than other correlations, because quite commonly intervening variables also become involved, possibly giving rise to the appearance of a possibly direct cause-and-effect relationship, but which (upon further investigation) turn out to have some other, more direct causal factor not mentioned in the proposition. Also, a mere observation of a change in one variable, when correlated with a change in another variable, can actually mistake the effect for the cause, and vice-versa (i.e., potentially get the hypothesized cause and effect backwards).

Empirical hypotheses that experimenters have repeatedly verified may become sufficiently dependable that, at some point in time, they become considered as "proven". Some people may succumb to the temptation to term such hypotheses laws, but they would do so mistakenly, since by definition a hypothesis explains and a law describes (for example, a law can state: "Matter can neither be created or destroyed, only changed in form"). More accurately, one could refer to repeatedly verified hypotheses simply as "adequately verified", or as "dependable".

Statistics features a rather more general concept of a hypothesis: this involves making assertions about the probability distributions or likelihoods of events.

Statisticians use two kinds of hypothesis: first, the null hypothesis or H0; secondly, the alternative hypothesis or H1. To give the simplest non-trivial example, one might formulate two hypotheses about tossing a coin:

• H0: coin-tossing operates "fairly" (equally likely to fall "Heads" or "Tails")
• H1: coin-tossing operates in a biased manner to give a 90% probability of falling "Heads"

No finite sequence of results could utterly falsify either hypothesis. However, various statistical approaches (such as Bayesian statistics and classical statistics (i.e. t-tests)) can quantify the strong intuition that H1 appears much less likely than H0 if, in 1,000 tosses, 495 came out "Heads" — and much more likely if 895 came out "Heads". In more complex sciences, researchers generally evaluate experiments statistically rather than as simple verifications or falsifications.

## Evaluating hypotheses

The hypothetico-deductive method demands falsifiable hypotheses, framed in such a manner that the scientific community can prove them false (usually by observation). (Note that confirming (or failing to falsify) a hypothesis does not necessarily prove that hypothesis: the hypothesis remains provisional.)

For example: someone who enters a new country and observes only white sheep might form the hypothesis that all sheep in that country are white. It can be considered a hypothesis, as it is falsifiable. Anyone could falsify the hypothesis by observing a single black sheep. Provided that the experimental uncertainties remain small (for example, provided that one can fairly reliably distinguish the observed black sheep from (say) a goat), and provided that the experimenter has correctly interpreted the statement of the hypothesis (for example, does the meaning of "sheep" include rams?), finding a black sheep falsifies the "white sheep only" hypothesis. However, one cannot consider failure to find non-white sheep as proof that no non-white sheep exist.

## Scientific hypothesis

People refer to a trial solution to a problem as a hypothesis — often called an "educated guess" — 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, 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 recognised knowledge-systems