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As the resident data analyst, I write the Quantitative Analysis sections for policy papers at my work. In doing so I use the word significant if and only if I am discussing statistical significance.

As pointed out in the answer to Connotation of significant or considerable, the term can be used in nontechnical writing without implying statistical significance. In sections of these larger reports other than Quantitative Analysis, the word significant is often used as meaningful, notable, of note etc.

My question is whether or not significant might be used in its lay meaning if I make a point of always using the term "statistically significant" when referring to mathematical significance? (My thought here being that would be similar to using the term "liquid nitrogen" to refer to nitrogen in its liquid state, thereby implying that the word "nitrogen" alone refers to nitrogen in its more common elemental form.)

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That's a reasonable strategy; and it's about the only one you have if you're not editing the final document. If I were in your position, I'd also make sure there was a standard footnote in every QA section I wrote pointing to the meaning of "statistically significant", with links to fuller descriptions and examples. And mentioning why you're using that term so consistently. It will save you a lot of time, and possibly CYA occasionally. Though if you then wanted to use it in a non-technical sense, you'd have to footnote that, too. –  John Lawler Jun 8 '13 at 16:11
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@JohnLawler Great advice (and that is what I do) and you've read the situation perfectly (the quants tend not to get final edit). Thanks. –  batpigandme Jun 8 '13 at 17:00
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Statistical significance is a sophisticated concept, and arriving at statistical significance with raw data involves even more sophistication. Perhaps one person in a thousand knows what "statistically significant" means. I do, but I'll be darned if I could explain it effectively to a person who'd like to know, and that's NOT because I grasp the concept so well that I'd have difficulty dumbing it down!

I say, "When in Rome, do as the Romans." In other words, feel free to use the term without explanation whenever you are in front of your fellow dataphiles, but steer clear of using the term in the presence of laypersons.

In a speech before a mixed audience (dataphiles and laypersons), the occasional use of the term "statistical significance" to reach the former is fine, as long as you break it down and explain it simply to reach the latter. In other words, throw the former a bone; give the latter some milk--it's easier to digest. Even the brilliant apostle Paul said, "I have become all things to all men that by all means I may win some" (I Corinthians 9:22b).

As a rhetorician I have been trained to think pragmatically when attempting to communicate with a mass audience. A good rhetor needs to adapt his or her message to each and every audience, keeping in mind that the audience, the purpose of the speech, and the nature of the occasion determine in large part what one says and how one says it.

And so it is with writing. First answer the following questions: What is my message? Who is my audience? What is my purpose? What is the occasion? Only after answering those questions should you move on to the traditional canons of invention, organization, delivery, and style.

"Statistical significance" is a stylistic choice, as is "significant," but if you have doubts about using either, perhaps you'd be better off using a different term. My goodness, the English language has more words than any other language on earth! Consult a good thesaurus or two; I'll bet you'll find at least a dozen or two equivalent terms (more-or-less) for "significant" and its cognates.

Best wishes.

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I definitely am a big fan of the thesaurus when looking for synonyms for (non-statistical) significance, and you're certainly right that stat-speak is not the most compelling way to make an argument. Thank goodness for graphics and data visualizations! –  batpigandme Jun 8 '13 at 17:05
    
Aren't there even different definitions of "statistical significance", and different levels to address? –  Edwin Ashworth Jun 9 '13 at 7:38
    
@EdwinAshworth yes vis-a-vis p values, confidence intervals, assumptions (lots of different things), all of which are discussed in methods (and are shown in equations etc.) and certainly have to be addressed. –  batpigandme Jun 9 '13 at 17:08
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