If and only if the 8 trials produced 8 successes was Fisherwilling to reject the null hypothesis – effectively acknowledgingthe Lady's ability with > 98% confidence (but withoutquantifying her ability). Fisher later discussed the benefits ofmore trials and repeated tests.
Some statisticians have commented that pure "significancetesting" has what is actually a rather strange goal of detectingthe existence of a "real" difference between two populations. Inpractice a difference can almost always be found given a largeenough sample. The typically more relevant goal of science is adetermination of causal . The amount and nature of thedifference, in other words, is what should be studied. Manyresearchers also feel that hypothesis testing is something of amisnomer. In practice a single statistical test in a single studynever "proves" anything.
Null-hypothesis testing just answers the question of "how wellthe findings fit the possibility that chance factors alone might beresponsible."
"A little thought reveals a fact widely understood amongstatisticians: The null hypothesis, taken literally (and that's theonly way you can take it in formal hypothesis testing), is almostalways false in the real world.... If it is false, even to a tinydegree, it must be the case that a large enough sample will producea significant result and lead to its rejection. So if the nullhypothesis is always false, what's the big deal about rejectingit?"(The above criticism only applies to point hypothesis tests. If onewere testing, for example, whether a parameter is greater thanzero, it would not apply.)
Students also find the terminology confusing. While Fisherdisagreed with Neyman and Pearson about the theory of testing,their terminologies have been blended. The blend is not seamless orstandardized. While this article teaches a pure Fisher formulation,even it mentions Neyman and Pearson terminology (Type II error andthe alternative hypothesis). The typical introductory statisticstext is less consistent. The Sage Dictionary of Statistics wouldnot agree with the title of this article, which it would callnull-hypothesis testing."...there is no alternate hypothesis in Fisher's scheme: Indeed, heviolently opposed its inclusion by Neyman and Pearson."In discussing test results, "significance" often has two distinctmeanings in the same sentence; One is a probability, the other is asubject-matter measurement (such as currency). The significance(meaning) of (statistical) significance is significant(important).
Students find it difficult to understand the formulation ofstatistical null-hypothesis testing. In rhetoric, examples oftensupport an argument, but a "is a logicalargument, not an empirical one". A single results in the rejectionof a conjecture. defined science by its vulnerability to dis-proof bydata. Null-hypothesis testing shares the mathematical andscientific perspective rather than the more familiar rhetoricalone. Students expect hypothesis testing to be a statistical toolfor illumination of the research hypothesis by the sample; it isnot. The test asks indirectly whether the sample can illuminate theresearch hypothesis.
Pedagogic criticism of the null-hypothesis testing includes thecounter-intuitive formulation, the terminology and confusion aboutthe interpretation of results.
Numerous attacks on the formulation have failed to supplant itas a criterion for publication in scholarly journals. The mostpersistent attacks originated from the field of Psychology. Afterreview, the did not explicitly deprecate the use ofnull-hypothesis significance testing, but adopted enhancedpublication guidelines which implicitly reduced the relativeimportance of such testing.
Criticism of null-hypothesis significance testing is availablein other articles (for example "") andtheir references. Attacks and defenses of the null-hypothesissignificance test are collected in Harlow et al..
Rejection of the null hypothesis at some effect size has nobearing on the practical significance of the observed effect size.A statistically significant finding may not be relevant in practicedue to other, larger effects of more concern, whilst a true effectof practical significance may not appear statistically significantif the test lacks the power to detect it. Appropriate specificationof both the hypothesis and the test of said hypothesis is thereforeimportant to provide inference of practical utility.
statisticians normallyreject the idea of null hypothesis testing, instead using varioustechniques in . Given a for one or more parameters, sampleevidence can be used to generate an updated . In this framework,but not in the null hypothesis testing framework, it ismeaningful to make statements of the general form "the probabilitythat the true value of the parameter is greater than 0 is p".According to , we have:
The direct interpretation is that if the p-value is less thanthe required significance level, then we say the null hypothesis isrejected at the given level of significance. on thisinterpretation can be found in the .
It is important to note the philosophical difference betweenaccepting the null hypothesis and simply failing to reject it. The"fail to reject" terminology highlights the fact that the nullhypothesis is assumed to be true from the start of the test; ifthere is a lack of evidence against it, it simply continues to beassumed true. The phrase "accept the null hypothesis" may suggestit has been proved simply because it has not been disproved, alogical fallacy known as the . Unlessa test with particularly high is used, the idea of"accepting" the null hypothesis may be dangerous. Nonetheless theterminology is prevalent throughout statistics, where its meaningis well understood.
The test described here is more fully the null-hypothesisstatistical significance test. The null hypothesis represents whatwe would believe by default, before seeing any evidence. is apossible finding of the test, declared when the observed is unlikely to have occurred by chance if the null hypothesis weretrue. The name of the test describes its formulation and itspossible outcome. One characteristic of the test is its crispdecision: to reject or not reject the null hypothesis. A calculatedvalue is compared to a threshold, which is determined from thetolerable risk of error.