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I am writing a paper for submission to a scientific journal. The paper calculates statistical significance for many different things. In the Results section, I find myself writing "X was statistically significant. In case B, there was no statistically significant change in Y." And so on.
I feel I am using the term "statistically significant" too frequently. Is it acceptable to simply write "significant" the third, fourth, etc. time I need to use that phrase?
It's important to remember that significant and statistically significant have overlapping but not identical meanings. Depending on the audience/context, you may need to specify to avoid ambiguity. A lot of papers use the full phrase in the beginning, but use just "significant" as they continue to discuss things.
This Stat.SE post (by a user named Brett) explains the distinction between statistical and "practical" significance well:
Another consideration with large samples is the practical significance of a result. A significant test might suggest (even if we can rule out non-sampling error) a difference that is trivial in a practical sense.
The post goes on to give a good example:
Given a large enough sample, a difference in a few dollars might be enough to produce a result that is statistically significant when comparing income among two groups. Is this important in any meaningful sense?
How about you define the p value being used, and then just report the numerical values in the text, along with the n value? The intended audience for a scientific journal is smart enough to be able to see from the numbers whether the result is statistically significant or not.
Then the phrase "statistically significant" itself could be reserved for the more narratively oriented portions of the article, such as the abstract and the conclusion.
In matters of style like this, I find that personal taste leads to the more fluid writing and reading for each person. My personal taste is too often repeated words or phrases drags down the document, even a technical one. My solution, and the approach I was taught was the more frequently a term is used in close proximity, the less need to repeat it. I would not for instance write a sentence like "A was found to be statistically significant while B was found to have no statistically significance." I would right that more like "A was found to be statistically significant while B was found not to be significant." or maybe: "Statistically, A was found to be significant while B was found not to be significant." I personally would tend to start by using the word maybe once in a sentence and if I found it still seemed too frequent start pairing to once in a paragraph or even a section. If the term has not been used in some time, it may call for a revisit.
I would apply this as long as anytime you use significant, insignificant, not significant, of no significance or other variations to always mean statistical significance, then early in the document use the full phase to make that clear, and slowly reduce the usage. If however the document could ever mix terms, say clinical significance, then I would always be clear even if it seems redundant.
