I am performing simulations while measuring a quantity A which depends on the parameter B. I make N independent measurements of A for given values of B. I can then calculate the mean to get an estimation of what the real value of A is. My question is about the error.
I can calculate the 95% confidence interval as 1.96xstddev(A)/sqrt(N) for each value of B. What I often find however is that this is not really representative of the error. For example, if I have the following data:
B A(B) 95%CI 1 2 10 2 4 10 3 6 10 4 8 10
Without knowledge of the error, one would conclude that there is a linear relationship between B and A. And in my experience, as I make more measurements, this relation doesn't change, despite the noise in the measurement. But if I show this result to someone else, they say "given those error bars (+-10 on each point), you can't say anything about the trend".
Since confidence intervals assume a normal distribution, are my measurements somehow more-sharply peaked somehow? Or am I using the 95%CI wrongly? Is there a better way to show the confidence in my data and/or the trend? Any advice is greatly appreciated.