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Author Topic: Concentration determination and 95% CI  (Read 43 times)

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J_Holland

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Concentration determination and 95% CI
« on: Today at 04:37:23 AM »

Hi, I've used regression in excell to determin the 95% concentration interval of the slope and intercept of my lineair calibration. I got a questions about how to determine concentration using the formula you get containing the 95% CI's, a formula like this example: y= 1,5x(± 0,2)x + 1,2(±0,5).

Should I only use the 95% CI of the slope? or also the intercept? I notice I get a very wide range of  possible concentrations when I include both 95%CI's (of the slope and intercept). When I only use the 95% CI of the slope I get much "prettier" result which actually seem usefull.

Can anybody tell me how I should use a formule containing 95% CI limits, to determine the concentration my analysis, and its upper and lower expected concentration (95%)?

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mjc123

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Re: Concentration determination and 95% CI
« Reply #1 on: Today at 07:12:34 AM »

Don't add the CIs (confidence intervals, by the way, not concentration intervals) of the slope and intercept, because the slope and intercept are strongly correlated, so you can't add their variances as if they were independent. That's why you get such wide limits. More detailed analysis of the regression gives (IIRC) the following formula for the confidence interval:
CI = ±t95%*s/sqrt(n)*{1 + (x - x)2/(x2 - x2)}1/2
where t is Student's t-statistic, s is the standard error, and I have written means with underlines because I can't work out how to write overlines. (The means refer to the set of n data points used to calculate the regression line.) Note how this increases as x deviates from x.
Actually this refers to the confidence interval of the regression value of y for a particular value of x. More relevant for you is the prediction interval, which is the likely deviation of a single measurement from the regression line. This is given by
PI = ±t95%*s/sqrt(n)*{n + 1 + (x - x)2/(x2 - x2)}1/2
However, all this refers to the deviation of a y measurement for a given x value. What you want is the deviation of the estimate of x from a measured y value. There is a formula for this, and I worked it out myself once long ago, but I was told by a real analytical chemist not to use it, because it gives a spurious precision to your result - actually, given all the other possible sources of error in a measurement, the uncertainty in your result is much greater than the regression confidence interval. So unfortunately I can't really answer your question!
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J_Holland

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Re: Concentration determination and 95% CI
« Reply #2 on: Today at 08:52:50 PM »

I'm sorry, I meanth "confidence interval" ofcourse :)

And I've asked some old classmates, who told me there was a different formula to determine the possible spread withing 95% chance of a measured sample. So it wasn't related to the formula I mentioned before.

It's a very long formula with parameters in dutch, my native language, so I cant really translate it for you guys. But I found an old excell spreadsheet wich helps me calculate it fast. Thanks for your reply though!
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