I COMPLETELY agree with Fortiter - the example above is an extremely specific example, where there has been a previous null hypothesis and, therefore, one could argue that the double negative structure is a legitimate, formal method of stating the result of an experiment.
Ordinarily, I would suggest that a double negative would be an incredibly awkward way of expressing uncertainty. With the vast vocabulary available to us in the English language, why would you use a double negative (itself inherently uncertain, as you have mentioned above) to express uncertainty?
Barrie also makes an excellent point regarding context. So much in English is governed by context. This, in my experience, is one of the most difficult aspects of the language for non-native speakers to grasp. Subtle differences in context can have a massive influence on the emphasis and, indeed, sometimes the meaning of an entire grammatical structure.