In practice the final decision usually depends on whether the outcome was predicted, or at least expected in advance of the research, or only found post hoc as a result of many analyses and comparisons performed on the data set, or on the total amount of consistent supportive evidence in the entire data set, and especially on "traditions" existing in the particular area of research.

Typically, in many sciences, results that yield p .05 are considered borderline statistically significant, but remember that this level of significance still involves a pretty high probability of error (5%).

Results that are significant at the p .01 (1%) level are commonly considered statistically significant, and p .005 (0.5%) or p .001 (0.1%) levels are often called "highly" significant or even "very highly" significant. But remember that these classifications represent nothing else but arbitrary conventions that are only informally based on general research experience.