Null hypothesis

nullnull hypotheseshypothesisno noticeable effectsno relationshipnull experimentsnull-hypothesesnull-hypothesisnull-modelrefuting hypotheses considered unlikely
In inferential statistics, the null hypothesis is a general statement or default position that there is nothing new happening, like there is no association among groups, or no relationship between two measured phenomena.wikipedia
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Alternative hypothesis

alternative hypothesesalternativealternatives
In this case, the null hypothesis is rejected and an alternative hypothesis is accepted in its place. In the hypothesis testing approach of Jerzy Neyman and Egon Pearson, a null hypothesis is contrasted with an alternative hypothesis and the two hypotheses are distinguished on the basis of data, with certain error rates.
In statistical hypothesis testing, the alternative hypothesis is a position that states something is happening, a new theory is true instead of an old one (null hypothesis).

Jerzy Neyman

NeymanJerzy Spława-NeymanNeyman, Jerzy
In the hypothesis testing approach of Jerzy Neyman and Egon Pearson, a null hypothesis is contrasted with an alternative hypothesis and the two hypotheses are distinguished on the basis of data, with certain error rates.
Neyman first introduced the modern concept of a confidence interval into statistical hypothesis testing and co-revised Ronald Fisher's null hypothesis testing (in collaboration with Egon Pearson).

Ronald Fisher

R.A. FisherR. A. FisherFisher
In the significance testing approach of Ronald Fisher, a null hypothesis is rejected if the observed data are significantly unlikely to have occurred if the null hypothesis were true.
In this book Fisher also outlined the Lady tasting tea, now a famous design of a statistical randomized experiment which uses Fisher's exact test and is the original exposition of Fisher's notion of a null hypothesis.

Statistical significance

statistically significantsignificantsignificance level
In the significance testing approach of Ronald Fisher, a null hypothesis is rejected if the observed data are significantly unlikely to have occurred if the null hypothesis were true.
In statistical hypothesis testing, a result has statistical significance when it is very unlikely to have occurred given the null hypothesis.

Test statistic

Common test statisticst''-test of test statistics
This class of data-sets is usually specified via a test statistic which is designed to measure the extent of apparent departure from the null hypothesis.
In general, a test statistic is selected or defined in such a way as to quantify, within observed data, behaviours that would distinguish the null from the alternative hypothesis, where such an alternative is prescribed, or that would characterize the null hypothesis if there is no explicitly stated alternative hypothesis.

Statistical hypothesis testing

hypothesis testingstatistical teststatistical tests
In the hypothesis testing approach of Jerzy Neyman and Egon Pearson, a null hypothesis is contrasted with an alternative hypothesis and the two hypotheses are distinguished on the basis of data, with certain error rates.
The comparison is deemed statistically significant if the relationship between the data sets would be an unlikely realization of the null hypothesis according to a threshold probability—the significance level.

Hypothesis

hypotheseshypotheticalhypothesized
Testing (accepting, approving, rejecting, or disproving) the null hypothesis—and thus concluding that there are or are not grounds for believing that there is a relationship between two phenomena (e.g. that a potential treatment has a measurable effect)—is a central task in the modern practice of science; the field of statistics gives precise criteria for rejecting a null hypothesis.
These are called the null hypothesis and the alternative hypothesis.

One- and two-tailed tests

one-tailed testtwo-tailed testone-sided
The choice of null hypothesis (H 0 ) and consideration of directionality (see "one-tailed test") is critical.
This method is used for null hypothesis testing and if the estimated value exists in the critical areas, the alternative hypothesis is accepted over the null hypothesis.

Lady tasting tea

Fisher's original (lady tasting tea) example was a one-tailed test.
The experiment is the original exposition of Fisher's notion of a null hypothesis, which is "never proved or established, but is possibly disproved, in the course of experimentation".

Confidence interval

confidence intervalsconfidence levelconfidence
A statistical significance test shares much mathematics with a confidence interval.
For example, if for some estimated parameter θ one wants to test the null hypothesis that θ = 0 against the alternative that θ ≠ 0, then this test can be performed by determining whether the confidence interval for θ contains 0.

Presumption of innocence

innocent until proven guiltypresumed innocentpresumed innocent until proven guilty
This is analogous to the legal principle of presumption of innocence, in which a suspect or defendant is assumed to be innocent (null is not rejected) until proven guilty (null is rejected) beyond a reasonable doubt (to a statistically significant degree).

Bayes factor

Bayesian model comparisonBayes factorsBayesian model selection
(The most common selection techniques are based on either Akaike information criterion or Bayes factor.)
A frequentist hypothesis test of M 1 (here considered as a null hypothesis) would have produced a very different result.

Randomized controlled trial

randomized controlled trialsrandomized clinical trialrandomized control trial
A complex case example is as follows: The gold standard in clinical research is the randomized placebo-controlled double-blind clinical trial.
The failure to reject the null hypothesis would imply that the treatment shows no statistically significant effect on the treated in a given test.

Likelihood-ratio test

likelihood ratio testlikelihood ratiolikelihood-ratio
If the constraint (i.e., the null hypothesis) is supported by the observed data, the two likelihoods should not differ by more than sampling error.

The Design of Experiments

book
Among other contributions, the book introduced the concept of the null hypothesis in the context of the lady tasting tea experiment.

Counternull

The counternull value is the effect size that is just as well supported by the data as the null hypothesis.

Estimation statistics

estimation
In hypothesis testing, the primary objective of statistical calculations is to obtain a p-value, the probability of seeing an obtained result, or a more extreme result, when assuming the null hypothesis is true.

Egon Pearson

PearsonEgon Sharpe PearsonPearson, Egon
In the hypothesis testing approach of Jerzy Neyman and Egon Pearson, a null hypothesis is contrasted with an alternative hypothesis and the two hypotheses are distinguished on the basis of data, with certain error rates.

Statistical model

modelprobabilistic modelstatistical modeling
Statistical inference can be done without a null hypothesis, by specifying a statistical model corresponding to each candidate hypothesis and using model selection techniques to choose the most appropriate model.

Model selection

statistical model selectionselectingchoose a model
Statistical inference can be done without a null hypothesis, by specifying a statistical model corresponding to each candidate hypothesis and using model selection techniques to choose the most appropriate model.

Akaike information criterion

AICAIC-basedAICc
(The most common selection techniques are based on either Akaike information criterion or Bayes factor.)

Sampling (statistics)

samplingrandom samplesample
Hypothesis testing works by collecting data and measuring how likely the particular set of data is, assuming the null hypothesis is true, when the study is on a randomly selected representative sample.

Statistical population

populationsubpopulationsubpopulations
The null hypothesis assumes no relationship between variables in the population from which the sample is selected.

Scientific control

controlcontrolscontrolled
The test of the hypothesis consists of administering the drug to half of the people in a study group as a controlled experiment.

Statistical inference

inferential statisticsinferenceinferences
In inferential statistics, the null hypothesis is a general statement or default position that there is nothing new happening, like there is no association among groups, or no relationship between two measured phenomena.