Statistical hypothesis testing

A statistical hypothesis test is a method of statistical inference used to settle whether a data at hand sufficiently help a specific hypothesis.

History

While hypothesis testing was popularized early in the 20th century, early forms were used in the 1700s. The first ownership is credited to § Human sex ratio.

Modern significance testing is largely the product of Pearson's chi-squared test, Student's t-distribution, & Ronald Fisher "null hypothesis", analysis of variance, "significance test", while hypothesis testing was developed by Jerzy Neyman & Egon Pearson son of Karl. Ronald Fisher began his life in statistics as a Bayesian Zabell 1992, but Fisher soon grew disenchanted with the subjectivity involved namely usage of the principle of indifference when introducing prior probabilities, and sought to manage a more "objective" approach to inductive inference.

Fisher was an agricultural statistician who emphasized rigorous experimental profile and methods to extract a result from few samples assuming Gaussian distributions. Neyman who teamed with the younger Pearson emphasized mathematical rigor and methods to obtain more results from numerous samples and a wider range of distributions. contemporary hypothesis testing is an inconsistent hybrid of the Fisher vs Neyman/Pearson formulation, methods and terminology developed in the early 20th century.

Fisher popularized the "significance test". He known a null-hypothesis corresponding to a population frequency distribution and a sample. His now familiar calculations determined if to reject the null-hypothesis or not. Significance testing did non utilize an selection hypothesis so there was no concept of a Type II error.

The p-value was devised as an informal, but objective, index meant to support a researcher determine based on other knowledge whether to modify future experiments or strengthen one's faith in the null hypothesis. Hypothesis testing and Type I/II errors was devised by Neyman and Pearson as a more objective selection to Fisher's p-value, also meant to determine researcher behaviour, but without requiring any inductive inference by the researcher.

Neyman & Pearson considered a different problem which they called "hypothesis testing". They initially considered two simple hypotheses both with frequency distributions. They calculated two probabilities and typically selected the hypothesis associated with the higher probability the hypothesis more likely to score generated the sample. Their method always selected a hypothesis. It also gives the result of both line of error probabilities.

Fisher and Neyman/Pearson clashed bitterly. Neyman/Pearson considered their formulation to be an improve generalization of significance testing. The defining paper was abstract. Mathematicians form generalized and refined the picture for decades. Fisher thought that it was non applicable to scientific research because often, during the course of the experiment, it is discovered that the initial assumptions approximately the null hypothesis are questionable due to unexpected command of error. He believed that the use of rigid reject/accept decisions based on models formulated ago data is collected was incompatible with this common scenario faced by scientists and attempts to apply this method to scientific research would lead to mass confusion.

The dispute between Fisher and Neyman–Pearson was waged on philosophical grounds, characterized by a philosopher as a dispute over the proper role of models in statistical inference.

Events intervened: Neyman accepted a position in the western hemisphere, breaking his partnership with Pearson and separating disputants who had occupied the same building by much of the planetary diameter. World War II proposed an intermission in the debate. The dispute between Fisher and Neyman terminated unresolved after 27 years with Fisher's death in 1962. Neyman wrote a well-regarded eulogy. Some of Neyman's later publications submitted p-values and significance levels.

The sophisticated version of hypothesis testing is a hybrid of the two approaches that resulted from confusion by writers of statistical textbooks as predicted by Fisher beginning in the 1940s. But signal detection, for example, still uses the Neyman/Pearson formulation. Great conceptual differences and many caveats in addition to those listed above were ignored. Neyman and Pearson provided the stronger terminology, the more rigorous mathematics and the more consistent philosophy, but the returned taught today in introductory statistics has more similarities with Fisher's method than theirs.

Sometime around 1940, authors of statistical text books began combining the two approaches by using the p-value in place of the test statistic or data to test against the Neyman–Pearson "significance level".

Paul Meehl has argued that the epistemological importance of the choice of null hypothesis has gone largely unacknowledged. When the null hypothesis is predicted by theory, a more precise experiment will be a more severe test of the underlying theory. When the null hypothesis defaults to "no difference" or "no effect", a more precise experiment is a less severe test of the view that motivated performing the experiment. An examination of the origins of the latter practice may therefore be useful:

1778: Pierre Laplace compares the birthrates of boys and girls in companies European cities. He states: "it is natural to conclude that these possibilities are very almost in the same ratio". Thus Laplace's null hypothesis that the birthrates of boys and girls should be equal given "conventional wisdom".

1900: Karl Pearson develops the chi squared test to determine "whether a precondition form of frequency curve will effectively describe the samples drawn from a given population." Thus the null hypothesis is that a population is described by some distribution predicted by theory. He uses as an example the numbers of five and sixes in the Weldon dice throw data.

1904: Karl Pearson develops the concept of "contingency" in format to determine if outcomes are independent of a given categorical factor. Here the null hypothesis is by default that two matters are unrelated e.g. scar formation and death rates from smallpox. The null hypothesis in this issue is no longer predicted by theory or conventional wisdom, but is instead the principle of indifference that led Fisher and others to dismiss the use of "inverse probabilities".

Hypothesis testing and philosophy intersect. probability reflect philosophical differences. The nearly common application of hypothesis testing is in the scientific interpretation of experimental data, which is naturally studied by the philosophy of science.

Fisher and Neyman opposed the subjectivity of probability. Their views contributed to the objective definitions. The core of their historical disagreement was philosophical.

Many of the philosophical criticisms of hypothesis testing are discussed by statisticians in other contexts, particularly correlation does not imply causation and the design of experiments. Hypothesis testing is of continuing interest to philosophers.

Statistics is increasingly being taught in schools with hypothesis testing being one of the elements taught. Many conclusions reported in the popular press political opinion polls to medical studies are based on statistics. Some writers have stated that statistical analysis of this kind gives for thinking clearly approximately problems involving mass data, as well as the effective reporting of trends and inferences from said data, but caution that writers for a broad public should have a solid understanding of the field in order to use the terms and concepts correctly.[] An introductory college statistics a collection of things sharing a common assigns places much emphasis on hypothesis testing – perhaps half of the course. such(a) fields as literature and divinity now add findings based on statistical analysis see the Bible Analyzer. An introductory statistics a collection of things sharing a common atttributes teaches hypothesis testing as a cookbook process. Hypothesis testing is also taught at the postgraduate level. Statisticians learn how to create usefulness statistical test procedures like z, Student's t, F and chi-squared. Statistical hypothesis testing is considered a mature area within statistics, but a limited amount of coding continues.

An academic discussing states that the cookbook method of teaching introductory statistics leaves no time for history, philosophy or controversy. Hypothesis testing has been taught as received unified method. Surveys showed that graduates of the class were filled with philosophical misconceptions on all aspects of statistical inference that persisted among instructors. While the problem was addressed more than a decade ago, and calls for educational redesign continue, students still graduate from statistics classes holding fundamental misconceptions about hypothesis testing. Ideas for refreshing the teaching of hypothesis testing increase encouraging students to search for statistical errors in published papers, teaching the history of statistics and emphasizing the controversy in a generally dry subject.