I was actually asking the question is what you wrote really the same as the actual result. IE

"A 1 in 20 chance the <whatever> isn't real."

versus

"There is a 1 in 20 chance of observing a result this extreme if the effect isn't real"

Not to be funny, but I really don't see any wording difference between the two except you replaced "the" with "of".

A 1 in 20 chance the **<whatever>** isn't real

a 1 in 20 chance of **<observing a result this extreme if the effect>** isn't real

Let me very clear what the problem is and it is not the terse verbiage. If you say "A 1 in 20 chance the whatever isn't real" you implying the effect has a probability of existence. But for most of these problems it is real or it is not real. Probability 0 or 1.

Well, maybe here is where we differ. Yes, I am very definitely implying the effect has a probability of existence. No test or even a series of tests is definitive. They can only suggest whether the value is closer to either 0 or 1. By

*test*, I mean ANY test, statistical or physical.

As statisticians, we are attempting to verify the existence of some reality through the use of some mathematical model of the real world. It should never be forgotten that mathematics has no foundation in the real world. If you think the client is in danger of forgetting that (or, more likely, is totally unaware) it might be prudent to emphasize it without using language guaranteed to evoke a glassy-eyed condition. Mostly, though, it's YOUR job to verify the statistical model(s) used is(are) appropriate to the situation. You'll quickly discover that your client is assuming that you really did do this and isn't in the least interested in the details.

I suspect that you have spent your entire statistical career in academia and have never really had to interface directly with non-statistician clients. In my engineering training (one of my degrees is in EE), we were required to answer in English and were pounded mercilessly if the prose strayed to far into technical verbiage. The reason: at some point in a EE's career it will become necessary to convey an answer to someone who is NOT a EE. It's an invaluable viewpoint.

My advice: stop trying for language precision and start thinking about ways to convey the concepts in simple terms when dealing with non-statisticians, beginning students or the public in general.

Another complaint is if you perform a slight twist of verbiage and say "there is a 1 in 20 chance that there is no effect." That can be so easily be misinterpreted to mean there is a 1 in 20 chance that the procedure has no effect each and every time you apply it.

Quite correct but that interpretation carries the assumption that the effect is real and if really meant is almost always stated along the lines of "the effectiveness is X". It's hard to see how this interpretation would occur if the impetus of the statistical testing was to verify the assumption of existence.

It is not so much that I am arguing against simple words being bad. I am arguing misleading words are bad--even simple ones.

The places where wording is harmful are actually in places like press releases. All too often, we hear that the likelihood of contracting some condition X from some substance Y doubles with a 95% confidence while leaving out the fact, or perhaps obscuring, that this doubling is from 1:10000000 to 2:10000000. You may be surprised to discover that most of the public reads this as a 95% probability of contracting X if exposed at any time to Y.

It's a public perception like this that resulted in an entire block being evacuated and subsequently invaded by a team in bunny suits recently near me after someone spilled 10 ml of mercury in a school lab.

What most of the public doesn't understand -- and sometimes this extends even to statisticians -- is that if a statistical test is being applied it's usually because it's hard to see the effect because of the noise. I doubt that anyone has ever conducted a statistical analysis to verify that encephalitic interception of high velocity, copper plated, lead projectiles is hazardous to one's health.

Many times, it's not the reporters who are at fault but the originator of the press release. The reporters tend to use press release wording verbatim. Of course, the originator is more likely to be a doctor scientist playing statistician than being a genuine statistician -- not necessarily exclusive, by any means, after all there's R. A. Fisher.