The importance of significance and the significance of importance.
This article has attempted to illustrate the following principles of statistical significance. 1. An investigator must state the hypothesis to be tested beforehand, so that a null hypothesis can be constructed and validly tested using standard statistical techniques. 2. A statistically significant difference does not prove that a difference exists. It merely establishes that if no difference exists, there is only a small chance that the results obtained would have occurred. A small chance is traditionally and arbitrarily defined as 5% or less. However, even 5% may be too large when important decisions depend on the results. 3. Failure to establish a statistically significant difference does not prove that no difference exists. Chance alone or the small numbers used may have prevented the investigators from rejecting the null hypothesis. 4. A statistically significant difference may be too small to be clinically useful. Statistical significance can be demonstrated for even the most inconsequential of differences if the number of individuals used in the study is large enough. 5. The clinical usefulness of a statistically significant difference may be limited by the degree of overlap. This is reflected in the standard deviation around the averages. In answer to the questions posed at the beginning of this article: If it is statistically significant, it might be true. If it is statistically significant, it might be important. If it is statistically significant, it might be clinically useful.
D006801:Humans; D012106:Research; D013223:Statistics as Topic