# How should I calculate mean CI - from raw data or mean values?

I have experimenatal data from medical industry. In the experiment 4 observations were weighted, each one 2 times for more precise measurement.

As a final weight, a mean from each pair is reported. So I have 8 values, a pair (2) for each observation and 4 means.

We assume a normal distrubution with unknown mean and standard deviation.

I need to calculate 95% CI for mean weight. I use this formula: $$X¯±t∗S/\sqrt{n},$$ where where $$S$$ is the sample standard deviation and where $$t$$ cuts probability 0.025 from the upper tail of Student's t distribution with $$n−1$$

degrees of freedom.

Should I do this from 8 values (7 df, n=8) or from calculated mean values from each pair(3 df, n=4)?

Maybe a should use another formula? Why?

Well, I think since you do your measurements twice (and take the mean values) then your data becomes the mean-valued-observations. Based on this you should use $$t_{3}$$ (student's distribution with $$3$$ degrees of freedom). This approach is more interpretable since by taking the mean values you, in a way, take more reliable and less noisy data.