Significance Levels

The marginal significance level of a test statistic is the probability that a value as large or larger would occur by chance. Another common name for it is the P-value. Thus the marginal significance level is small for extreme values.

If the reported marginal significance level is smaller than your desired level of significance, the result is statistically significant; if it is larger, then it is statistically insignificant. Thus, a reported value of .041 is significant at the .05 level, but not at the .01 level.

Note that the use of a standard .05 threshold for acceptance is not necessarily reasonable in very large data sets (many thousand's of observations). See Diagnostics in Large Samples.