Researchers can confuse statistical significance with substantive significance in one of two ways:
- Results that are found to be statistically significant are interpreted as if they were practically meaningful. This happens when a researcher interprets a statistically significant result as being “significant” or “highly significant” in the everyday sense of the word.
- Results that are statistically nonsignificant are interpreted as evidence of no effect, even in the face of evidence to the contrary (e.g., a noteworthy effect size).
In some settings statistical significance will be completely unrelated to substantive significance. It is entirely possible for a result to be statistically significant and trivial or statistically nonsignificant yet important. (Click here for an example.)
Researchers get confused about these things when they misattribute meaning to p values. Remember, a p value is a confounded index. A statistically significant p could reflect either a large effect, or a large sample size, or both. Judgments about substantive significance should never be based on p values.
It is essential that researchers learn to distinguish between statistical and substantive significance. Failure to do so leads to Type I and Type II errors, wastes resources, and potentially misleads further research on the topic.