A hypothesis (plural: hypotheses) is a proposed explanation, proposition, or assumption put forward for investigation. In science, it connects a question about the world with consequences that can be assessed through observation or experiment. A hypothesis need not already be well supported, but its scientific evaluation requires a sufficiently clear statement of what evidence would support or challenge it. Formulating and testing hypotheses are important activities within the scientific method, although scientific inquiry also includes exploratory observation, measurement, and model building. (plato.stanford.edu)
Meaning and related concepts
A hypothesis differs from an observation: an observation records or characterizes something encountered, whereas a hypothesis proposes how observations might be explained or related. It also differs from a prediction, which specifies an expected outcome under particular conditions. One hypothesis can generate several predictions, and competing hypotheses may generate the same prediction in some circumstances. Consequently, a successful prediction does not necessarily identify a unique explanation. (plato.stanford.edu)
The terms hypothesis and theory overlap in scientific and philosophical usage; there is no universal boundary determined simply by the number of successful tests. A hypothesis may be a particular claim within a broader explanatory framework. In logic, a hypothesis can instead be an assumption used in an argument, without asserting that it describes an observed fact. This distinction separates the validity of reasoning from the empirical truth of its premises. (plato.stanford.edu)
Formulation and testability
Hypotheses arise from existing theories, unexpected observations, analogies, and exploratory investigations. Inductive reasoning can suggest general relationships from particular cases; deductive reasoning derives consequences from an assumed hypothesis. Scientific discovery does not follow one mandatory sequence: observations can prompt revisions, and an unsuccessful test can generate a different question rather than simply ending an investigation. (plato.stanford.edu)
An empirically useful hypothesis identifies relevant conditions and observable consequences. For example, the illustrative claim that increasing illumination raises a plant’s growth rate becomes more precise when the species, illumination range, growth measure, and comparison period are specified. These details make it possible to distinguish the claim from alternatives and to design an appropriate test. Precision does not require certainty; it makes the uncertainty investigable. (plato.stanford.edu)
Falsifiability is the possibility that some conceivable observation would conflict with a claim. Karl Popper emphasized this property in his account of science, distinguishing genuinely risky predictions from claims compatible with every possible outcome. Falsifiability does not mean that a hypothesis is false, and a currently untested hypothesis is not automatically untestable. Its importance and sufficiency as a criterion of science remain subjects within philosophy of science. (plato.stanford.edu)
Testing and interpretation
A hypothesis is generally tested together with background assumptions concerning instruments, initial conditions, measurements, and other relevant processes. If a prediction fails, the result challenges this combined set of assumptions; it does not always show which component failed. Researchers may therefore investigate measurement problems or auxiliary assumptions before abandoning the central hypothesis. Such revisions can themselves produce further testable predictions. (plato.stanford.edu)
Tests can challenge a claim, corroborate it, or leave its status unresolved. Corroboration is not deductive proof: observing predicted results does not exclude every alternative explanation. The evidential importance of a result depends partly on how well it distinguishes competing accounts and on whether the test offered a meaningful opportunity for failure. Multiple observations are therefore not interchangeable merely because they all appear favorable. (plato.stanford.edu)
Statistical hypotheses
In statistics, a hypothesis typically specifies a property of a population, model parameter, or probability distribution. Statistical hypothesis testing often contrasts a null hypothesis, (H_0), with an alternative hypothesis, (H_1). For example, (H_0) might state that two population means are equal, while (H_1) states that they differ. A directional alternative instead specifies which mean is larger. (itl.nist.gov)
A test uses sample data and a decision rule to assess compatibility with the null hypothesis. A Type I error occurs when a true null hypothesis is rejected; a Type II error occurs when a false null hypothesis is not rejected. Statistical power is the probability of rejection under a specified alternative. Failure to reject is not proof that the null hypothesis is true. (itl.nist.gov)
A p-value expresses how unusual the observed test statistic, or a more extreme value, would be under the specified null model. It is not the probability that the hypothesis is true, nor a measure of an effect’s size or practical importance. A confidence interval provides complementary information about parameter values compatible with the estimation procedure. Scientific conclusions cannot be reduced to whether a p-value crosses a threshold. (amstat.org)
Bayesian evaluation
Bayesian inference evaluates hypotheses by updating probabilities in light of evidence. Bayes’ theorem relates prior probability, the likelihood of evidence under a hypothesis, and posterior probability. In parameter estimation, a prior distribution and a likelihood function determine a posterior distribution. The result depends on the specified model and prior assumptions; it does not remove the need to assess those assumptions or consider competing explanations. (arxiv.org)
Exploratory and confirmatory research
Exploratory data analysis can generate hypotheses from patterns not anticipated beforehand. Confirmatory research evaluates specified claims using a planned analysis or independently reserved evidence. Preregistration records hypotheses, methods, and analytical decisions before the relevant results are examined, helping distinguish planned tests from subsequent exploration. It does not prohibit additional analyses: unplanned findings can be reported as exploratory and investigated with further data. The distinction concerns how evidence was obtained, not whether unexpected discoveries are scientifically valuable. (cos.io)