# Package smile.stat.hypothesis

package smile.stat.hypothesis
Statistical hypothesis tests. 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.

Hypothesis testing is sometimes called confirmatory data analysis, in contrast to exploratory data analysis. In frequency probability, these decisions are almost always made using null-hypothesis tests (i.e., tests that 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?) One use of hypothesis testing is deciding whether experimental results contain enough information to cast doubt on conventional wisdom.

A result that was found to be statistically significant is also called a positive result; conversely, a result that is not unlikely under the null hypothesis is called a negative result or a null result.

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.

• Classes
Class
Description
Pearson's chi-square test, also known as the chi-square goodness-of-fit test or chi-square test for independence.
Correlation test.
F test of the hypothesis that two independent samples come from normal distributions with the same variance, against the alternative that they come from normal distributions with different variances.
The Kolmogorov-Smirnov test (K-S test) is a form of minimum distance estimation used as a non-parametric test of equality of one-dimensional probability distributions.
Student's t test.