It is important to note the philosophical difference between accepting the null hypothesis and simply failing to reject it. The "fail to reject" terminology highlights the fact that the null hypothesis is assumed to be true from the start of the test; if there is a lack of evidence against it, it simply continues to be assumed true. The phrase "accept the null hypothesis" may suggest it has been proved simply because it has not been disproved, a logical fallacy known as the argument from ignorance. Unless a test with particularly high power is used, the idea of "accepting" the null hypothesis may be dangerous. Nonetheless the terminology is prevalent throughout statistics, where its meaning is well understood. Alternatively, if the testing procedure forces us to reject the null hypothesis (H-null), we can accept the alternative hypothesis (H-alt)and we conclude that the research hypothesis is supported by the data. This fact expresses that our procedure is based on probabilistic considerations in the sense we accept that using another set could lead us to a different conclusion. --wikki Yet another common pitfall often happens when a researcher writes the qualified statement "we found no statistically significant difference," which is then misquoted by others as "they found that there was no difference." Actually, statistics cannot be used to prove that there is exactly zero difference between two populations. Failing to find evidence that there is a difference does not constitute evidence that there is no difference. This principle is sometimes described by the maxim "Absence of evidence is not evidence of absence."[12] According to J. Scott Armstrong, attempts to educate researchers on how to avoid pitfalls of using statistical significance have had little success. In the papers "Significance Tests Harm Progress in Forecasting,"[13] and "Statistical Significance Tests are Unnecessary Even When Properly Done,"[14] Armstrong makes the case that even when done properly, statistical significance tests are of no value. A number of attempts failed to find empirical evidence supporting the use of significance tests. Tests of statistical significance are harmful to the development of scientific knowledge because they distract researchers from the use of proper methods.[citation needed] Armstrong suggests authors should avoid tests of statistical significance; instead, they should report on effect sizes, confidence intervals, replications/extensions, and meta-analyses. A common misconception is that a statistically significant result is always of practical significance, or demonstrates a large effect in the population. Unfortunately, this problem is commonly encountered in scientific writing.[15] Given a sufficiently large sample, extremely small and non-notable differences can be found to be statistically significant, and statistical significance says nothing about the practical significance of a difference. Use of the statistical significance test has been called seriously flawed and unscientific by authors Deirdre McCloskey and Stephen Ziliak. They point out that "insignificance" does not mean unimportant, and propose that the scientific community should abandon usage of the test altogether, as it can cause false hypotheses to be accepted and true hypotheses to be rejected.[15][16] Some statisticians have commented that pure "significance testing" has what is actually a rather strange goal of detecting the existence of a "real" difference between two populations. In practice a difference can almost always be found given a large enough sample. The typically more relevant goal of science is a determination of causal effect size. The amount and nature of the difference, in other words, is what should be studied.[17] Many researchers also feel that hypothesis testing is something of a misnomer. In practice a single statistical test in a single study never "proves" anything.[18] meta criticism The criticism here is of the application, or of the interpretation, rather than of the method. Attacks and defenses of the null-hypothesis significance test are collected in Harlow et al..[21] The original purposes of Fisher's formulation, as a tool for the experimenter, was to plan the experiment and to easily assess the information content of the small sample. There is little criticism, Bayesian in nature,[citation needed] of the formulation in its original context. In other contexts, complaints focus on flawed interpretations of the results and over-dependence/emphasis on one test. Numerous attacks on the formulation have failed to supplant it as a criterion for publication in scholarly journals. The most persistent attacks originated from the field of Psychology. After review,[citation needed] the American Psychological Association did not explicitly deprecate the use of null-hypothesis significance testing, but adopted enhanced publication guidelines which implicitly reduced the relative importance of such testing. The International Committee of Medical Journal Editors recognizes an obligation to publish negative (not statistically significant) studies under some circumstances.[citation needed] The applicability of the null-hypothesis testing to the publication of observational (as contrasted to experimental) studies is doubtful.[citation needed] [edit] philosophical Philosophical criticism to hypothesis testing includes consideration of borderline cases. Any process that produces a crisp decision from uncertainty is subject to claims of unfairness near the decision threshold. (Consider close election results.) There is always an arbitrary decision point. The premature death of one experimental rat might make the difference between being published or not being published. And that one extra publication might mean the difference between a tenured position or an adjunct position. The arbitrariness of confidence intervals highlights the subjective nature of the scientific method. Many introductory text books explain that science should be unbiased and objective. The arbitrary statistical significance level .05 required for publication has no mathematical basis, but is based on long tradition. In other words, "... surely, God loves the .06 nearly as much as the .05"[22] For more detail see Philosophy of Science particularly Paul Feyerabend. As Fisher wrote, "it is usual and convenient for experimenters to take 5% as a standard level of significance, in the sense that they are prepared to ignore all results which fail to reach this standard, and, by this means, to eliminate from further discussion the greater part of the fluctuations which chance causes have introduced into their experimental results."[4] This epistemic issue became a focal point of the science wars within the intellectual movement called postmodernism. pedagogic Pedagogic criticism of the null-hypothesis testing includes the counter-intuitive formulation, the terminology and confusion about the interpretation of results. "Despite the stranglehold that hypothesis testing has on experimental psychology, I find it difficult to imagine a less insightful means of transiting from data to conclusions."[23] Students find it difficult to understand the formulation of statistical null-hypothesis testing. In rhetoric, examples often support an argument, but a mathematical proof "is a logical argument, not an empirical one". A single counterexample results in the rejection of a conjecture. Karl Popper defined science by its vulnerability to disproof by data. Null-hypothesis testing shares the mathematical and scientific perspective rather than the more familiar rhetorical one. Students expect hypothesis testing to be a statistical tool for illumination of the research hypothesis by the sample; it is not. The test asks indirectly whether the sample can illuminate the research hypothesis. Students also find the terminology confusing. While Fisher disagreed with Neyman and Pearson about the theory of testing, their terminologies have been blended. The blend is not seamless or standardized. While this article teaches a pure Fisher formulation, even it mentions Neyman and Pearson terminology (Type II error and the alternative hypothesis). The typical introductory statistics text is less consistent. The Sage Dictionary of Statistics would not agree with the title of this article, which it would call null-hypothesis testing.[2] "...there is no alternate hypothesis in Fisher's scheme: Indeed, he violently opposed its inclusion by Neyman and Pearson."[24] In discussing test results, "significance" often has two distinct meanings in the same sentence; One is a probability, the other is a subject-matter measurement (such as currency). The significance (meaning) of (statistical) significance is significant (important). There is widespread and fundamental disagreement on the interpretation of test results. "A little thought reveals a fact widely understood among statisticians: The null hypothesis, taken literally (and that's the only way you can take it in formal hypothesis testing), is almost always false in the real world.... If it is false, even to a tiny degree, it must be the case that a large enough sample will produce a significant result and lead to its rejection. So if the null hypothesis is always false, what's the big deal about rejecting it?"[24] (The above criticism only applies to point hypothesis tests. If one were testing, for example, whether a parameter is greater than zero, it would not apply.) "How has the virtually barren technique of hypothesis testing come to assume such importance in the process by which we arrive at our conclusions from our data?"[23] Null-hypothesis testing just answers the question of "how well the findings fit the possibility that chance factors alone might be responsible."[2] Null-hypothesis significance testing does not determine the truth or falsity of claims. It determines whether confidence in a claim based solely on a sample-based estimate exceeds a threshold. It is a research quality assurance test, widely used as one requirement for publication of experimental research with statistical results. It is uniformly agreed that statistical significance is not the only consideration in assessing the importance of research results. Rejecting the null hypothesis is not a sufficient condition for publication. "Statistical significance does not necessarily imply practical significance!"[25] [edit]