# Reduced precision has an effect on results, but does not negate them

I am writing a technical research article.

I have an experiment where precision can be easily determined (bid-ask spreads for the economists). Calculating some formula twice based on the precise observation of the upper bound and the lower bound does change the results (obviously) and is not negligible, but it does not negate the theory that is underlying. That is, the effect of the measurement error is clearly visible, but in general the theory can still be accepted.

How do i express this in a concise way?

Thanks.

edit: Per request, more details.

I can observe market values, but with limited precision. I only observe two values, bid and ask, and the true value lies between those. Calculating measurements using bid-values gives me different results than using ask-values. Both results confirm the theory I'm testing. The difference exists, but it does not fundamentally change the conclusion that the theory itself can be confirmed.

Is there a concise expression for 'confirms, but not as strongly' or 'doesn't negate, but differences are considerable'?

I guess it is obvious why I need a concise expression...

• Your title is as good a phrasing as any: exactly what more are you looking for? Feb 3, 2014 at 16:13

I'm assuming from the description that you're referring to uncertainty rather than making errors in execution. If you're making errors in your execution that's on you.

The concept of limited precision seems like it should be implicitly understood in any modern, technical specialty with a handle on statistical reasoning over evidence. If for some reason you're still worried, you can explicitly say one of the following:

[The methods/measurements] confirm [the prediction/model] despite being not ideally precise.

Which is somewhat apologetic and probably not the tone you want to work with, but it's the most most direct translation of your explanation.

Despite small amounts of error, [the methods/measurements] confirm [the prediction/model].

Which both makes the appeal to the reader's knowledge of inaccuracy of measurement and is slightly more concise. It also gives you an opening to follow up with the suggestion of more research into reducing error, which is rarely a bad place to be.

[The methods/measurements] confirm [the prediction/model] within [an acceptable epsilon].

Not only are you not apologizing here, you're proudly noting that you've done serious thinking about how confident you need to be in your results. This implies broader understanding and capability, as well as thorough work.

Repeated [or alternative] calculations diminish, but do not negate, the effect.

• Alternate is not the same as alternative, at least in a scientific paper. Feb 4, 2014 at 9:39
• @TimLymington Good point. I was not clear as to what the various approaches were. I think alternative may be better. Changed accordingly.
– bib
Feb 4, 2014 at 12:44