Error +/- from the calculated value

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I am performing a biological experiment, giving me a concentration of the measured particles in my sample. I need to ensure that I have at most 10 percents of "error", variation from the measured value. As far as I know, in statistical terms, this means I need a standard deviation from the mean of maximum 10 percent.

By 10% error I mean that I want the value be within a 10 % variation from the expected value in both directions. In other words, it means in either direction, plus and minus.I want to quantify the variability. A confidence interval of 90% would mean that there is a 90% chance that the population mean lies within the interval. I just want to see that the value I measure is close to the expected value with a variability of less or equal 10%.

All the assays and papers I have seen until now, connect the measurement to a confidence interval of 95 percent.

How do I use it to answer to my question? Do I need the confidence interval to measure variability somehow?

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@estherw1,

Not sure why you would use 90% instead of the typical 95% that is routinely used in science but here is how you answer your question. Let's say you take 10 measurements and get a mean of 9 and a standard deviation of 1. The confidence interval around that value assuming a normal distribution is:

9 +/- (Z)(SD)/sqrt(N)

Where SD is the standard deviation (1 in this case), N is the number of samples (10 in this case) and Z is a value depending on the confidence interval you want. 90% is 1.645, 95% is 1.96. You can find these numbers on the Internet by Googling something like "90% z score"

So in this case you get 9+/- 1.645/sqrt(10) = 9 +/- 0.52.

If you were expecting 10, you have shown that the answer is not 10. If you were expecting 9.3, you have not disproved your hypothesis. Note that you have not proved the average is 9.3, after all you measured 9, but you have not disproved the true average is 9.3 (or 8.7 or anything within .52 of 9).

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@engineer,

Hi engineer,

Thanks for answering me!

As far as I know, the confidence interval is a range of value that you can be 90% / 95% certain contains the true mean of the population, but a confidence interval does not quantify variability, it does not contain 90/95% of the values too.

What I want is a formula, a graph showing the correlation between the variability and the occupancy per partition. All the data I found connected the relative uncertainty to the partitioning and I am not sure this reflect what I am looking for.

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@estherw1,

I don't fully understand what you are after. If you want to compare the variances of two populations, you use an F test but it seems you are after something else.

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Error +/- from the calculated value

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