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The significance level is usually denoted by the Greek symbol, α (alpha). Popular levels of significance are 5% (0.05), 1% (0.01) and 0.1% (0.001). If a test of significance gives a p-value lower than the α-level, the null hypothesis is rejected. Such results are informally referred to as 'statistically significant'. For example, if someone argues that "there's only one chance in a thousand this could have happened by coincidence," a 0.001 level of statistical significance is being implied. The lower the significance level, the stronger the evidence required. Choosing level of significance is an arbitrary task, but for many applications, a level of 5% is chosen, for no better reason than that it is conventional.[3][4]
In some situations it is convenient to express the statistical significance as 1 − α. In general, when interpreting a stated significance, one must be careful to note what, precisely, is being tested statistically.
Different α-levels trade off countervailing effects. Smaller levels of α increase confidence in the determination of significance, but run an increased risk of failing to reject a false null hypothesis (a Type II error, or "false negative determination"), and so have less statistical power. The selection of an α-level thus inevitably involves a compromise between significance and power, and consequently between the Type I error and the Type II error. More powerful experiments - usually experiments with more subjects or replications - can obviate this choice to an arbitrary degree.
In some fields, for example nuclear and particle physics, it is common to express statistical significance in units of "σ" (sigma), the standard deviation of a Gaussian distribution. A statistical significance of "nσ" can be converted into a value of α via use of the error function:
The use of σ is motivated by the ubiquitous emergence of the Gaussian distribution in measurement uncertainties. For example, if a theory predicts a parameter to have a value of, say, 100, and one measures the parameter to be 109 ± 3, then one might report the measurement as a "3σ deviation" from the theoretical prediction. In terms of α, this statement is equivalent to saying that "assuming the theory is true, the likelihood of obtaining the experimental result by coincidence is 0.27%" (since 1 − erf(3/√2) = 0.0027).
Fixed significance levels such as those mentioned above may be regarded as useful in exploratory data analyses. However, modern statistical advice is that, where the outcome of a test is essentially the final outcome of an experiment or other study, the p-value should be quoted explicitly. And, importantly, it should be quoted whether or not the p-value is judged to be significant. This is to allow maximum information to be transferred from a summary of the study into meta-analyses.
(reference :
http://en.wikipedia.org/wiki/Statistica ... n_practice)
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