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I have a certain experiment that I repeat 40 times and get the result:

0.001 +/- 0.004.

Now I've repeated the experiment using a different method (so it is essentially a new experiment) and I get a new value:

-0.002 +/- 0.003

Now, is it true to say there is no statistically significant difference between these two different methods? Even though they lie within each other's standard deviation, I think the fact that I've repeated the experiment 40 times should mean something- it makes me confident that method 2 gives a lower result. I don't know how to translate this confidence into statistical analysis though.

The fact that the means are different is clearly not sufficient to convince anyone... how can I convince someone that method 2 gives a lower result? Let's say I even repeat the experiment another 40 times and get EXACTLY the same means and standard deviations. But I know with more certainty the means are different because I've done more experiments. How do I show this using maths though (without actually having to do the experiments?).

Thanks

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# Confidence intervals for two separate variables?

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