**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.

Read more about Statistical Hypothesis Testing: The Testing Process, Definition of Terms, Interpretation, Origins, Use and Importance, Education, Cautions, Controversy

### Famous quotes containing the words hypothesis and/or testing:

“It is more than likely that the brain itself is, in origin and development, only a sort of great clot of genital fluid held in suspense or reserved.... This *hypothesis* ... would explain the enormous content of the brain as a maker or presenter of images.”

—Ezra Pound (1885–1972)

“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)