/*******************************************************************************
 * Copyright (c) 2010 Haifeng Li
 *   
 * Licensed under the Apache License, Version 2.0 (the "License");
 * you may not use this file except in compliance with the License.
 * You may obtain a copy of the License at
 *  
 *     http://www.apache.org/licenses/LICENSE-2.0
 *
 * Unless required by applicable law or agreed to in writing, software
 * distributed under the License is distributed on an "AS IS" BASIS,
 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 * See the License for the specific language governing permissions and
 * limitations under the License.
 *******************************************************************************/

/**
 * 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.
 * <p>
 * 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.
 * <p>
 * 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.
 * <p>
 * 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.
 *
 * @author Haifeng Li
 */
package smile.stat.hypothesis;