Statistical hypothesis test
[4] An examination of the origins of the latter practice may therefore be useful: 1778: Pierre Laplace compares the birthrates of boys and girls in multiple European cities.
[5] 1900: Karl Pearson develops the chi squared test to determine "whether a given form of frequency curve will effectively describe the samples drawn from a given population."
[7] The null hypothesis in this case 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".
[9] Fisher emphasized rigorous experimental design 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 many samples and a wider range of distributions.
Modern hypothesis testing is an inconsistent hybrid of the Fisher vs Neyman/Pearson formulation, methods and terminology developed in the early 20th century.
Significance testing did not utilize an alternative hypothesis so there was no concept of a Type II error (false negative).
The p-value was devised as an informal, but objective, index meant to help a researcher determine (based on other knowledge) whether to modify future experiments or strengthen one's faith in the null hypothesis.
Fisher thought that it was not applicable to scientific research because often, during the course of the experiment, it is discovered that the initial assumptions about the null hypothesis are questionable due to unexpected sources of error.
He believed that the use of rigid reject/accept decisions based on models formulated before 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.
[15] Events intervened: Neyman accepted a position in the University of California, Berkeley in 1938, breaking his partnership with Pearson and separating the disputants (who had occupied the same building).
[17] The modern 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[18] (but signal detection, for example, still uses the Neyman/Pearson formulation).
Neyman and Pearson provided the stronger terminology, the more rigorous mathematics and the more consistent philosophy, but the subject taught today in introductory statistics has more similarities with Fisher's method than theirs.
The most common application of hypothesis testing is in the scientific interpretation of experimental data, which is naturally studied by the philosophy of science.
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.
Some writers have stated that statistical analysis of this kind allows for thinking clearly about 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 academic study states that the cookbook method of teaching introductory statistics leaves no time for history, philosophy or controversy.
Surveys showed that graduates of the class were filled with philosophical misconceptions (on all aspects of statistical inference) that persisted among instructors.
[26] While the problem was addressed more than a decade ago,[27] and calls for educational reform continue,[28] students still graduate from statistics classes holding fundamental misconceptions about hypothesis testing.
His test revealed that if the lady was effectively guessing at random (the null hypothesis), there was a 1.4% chance that the observed results (perfectly ordered tea) would occur.
Significance testing has been the favored statistical tool in some experimental social sciences (over 90% of articles in the Journal of Applied Psychology during the early 1990s).
Significance testing is used as a substitute for the traditional comparison of predicted value and experimental result at the core of the scientific method.
The bootstrap is very versatile as it is distribution-free and it does not rely on restrictive parametric assumptions, but rather on empirical approximate methods with asymptotic guarantees.
A statistical test procedure is comparable to a criminal trial; a defendant is considered not guilty as long as his or her guilt is not proven.
The following example was produced by a philosopher describing scientific methods generations before hypothesis testing was formalized and popularized.
One naïve Bayesian approach to hypothesis testing is to base decisions on the posterior probability,[56][57] but this fails when comparing point and continuous hypotheses.
Fisher's significance testing has proven a popular flexible statistical tool in application with little mathematical growth potential.
[82] Textbooks have added some cautions,[83] and increased coverage of the tools necessary to estimate the size of the sample required to produce significant results.
Lehmann said that hypothesis testing theory can be presented in terms of conclusions/decisions, probabilities, or confidence intervals: "The distinction between the ... approaches is largely one of reporting and interpretation.
[77] Advocates of a Bayesian approach sometimes claim that the goal of a researcher is most often to objectively assess the probability that a hypothesis is true based on the data they have collected.
