Significance

Let $\delta\equiv z\leq z_{\rm observed}$ . A value $0\leq\alpha\leq 1$ such that $P(\delta)\leq\alpha$ is considered ``significant'' (i.e., is not simply due to chance) is known as an Alpha Value. The Probability that a variate would assume a value greater than or equal to the observed value strictly by chance, $P(\delta)$ , is known as a P-Value.

Depending on the type of data and conventional practices of a given field of study, a variety of different alpha values may be used. One commonly used terminology takes $P(\delta)\geq 5\%$ as ``not significant,'' $1\%<P(\delta)<5\%$ , as ``significant'' (sometimes denoted *), and $P(\delta)<1\%$ as ``highly significant'' (sometimes denoted **). Some authors use the term ``almost significant'' to refer to $5\% < P(\delta) < 10\%$ , although this practice is not recommended.