Statistical Hypothesis Testing
A statistical hypothesis test is a method of making decisions using data, whether from a controlled experiment or an observational study (not controlled). In statistics, a result is called statistically significant if it is unlikely to have occurred by chance alone, according to a pre-determined threshold probability, the significance level. The phrase "test of significance" was coined by Ronald Fisher: "Critical tests of this kind may be called tests of significance, and when such tests are available we may discover whether a second sample is or is not significantly different from the first."
These tests are used in determining what outcomes of an experiment would lead to a rejection of the null hypothesis for a pre-specified level of significance; helping to decide whether experimental results contain enough information to cast doubt on conventional wisdom. It is sometimes called confirmatory data analysis, in contrast to exploratory data analysis.
Statistical hypothesis tests answer the question Assuming that the null hypothesis is true, what is the probability of observing a value for the test statistic that is at least as extreme as the value that was actually observed?. That probability is known as the P-value.
Statistical hypothesis testing is a key technique of frequentist statistical inference. The Bayesian approach to hypothesis testing is to base rejection of the hypothesis on the posterior probability. Other approaches to reaching a decision based on data are available via decision theory and optimal decisions.
The critical region of a hypothesis test is the set of all outcomes which cause the null hypothesis to be rejected in favor of the alternative hypothesis.
Famous quotes containing the words hypothesis and/or testing:
“The hypothesis I wish to advance is that ... the language of morality is in ... grave disorder.... What we possess, if this is true, are the fragments of a conceptual scheme, parts of which now lack those contexts from which their significance derived. We possess indeed simulacra of morality, we continue to use many of the key expressions. But we havevery largely if not entirelylost our comprehension, both theoretical and practical, of morality.”
—Alasdair Chalmers MacIntyre (b. 1929)
“Today so much rebellion is aimless and demoralizing precisely because children have no values to challenge. Teenage rebellion is a testing process in which young people try out various values in order to make them their own. But during those years of trial, error, embarrassment, a child needs family standards to fall back on, reliable habits of thought and feeling that provide security and protection.”
—Neil Kurshan (20th century)