I hope someone can help me with this problem.
I have a particular measurement (from a chemical analyser) which is subject
to two independent sources of variance (a sample preparation or weighing
"error" and the noise on the analytical measurement itself). I have
performed an experiment in which each of a number (n1) of weighings have
had a number (n2) of replicate analytical measurements made. I have then
performed a one-way ANOVA to quantify the variance of both the weighing
distribution and of the analytical measurement (the F-value is greater than
the F-crit, indicating both sources of variance are significant).
From knowing the variance of each of the distributions, and the number of
measurements (n1 weighings, n2 replicate analyses) I wish to set a
confidence limit for the mean, based upon the t-distribution, for future
experiments where I have n3 weighings and n4 replicate measurements. For the
present case n3=n4=1, but in general this may not be the case. I am unsure
about how to determine the correct number of degrees of freedom to use when
setting the confidence limit from the t-table.
Do I assume that, as the two sources of variance are independent, I can set
confidence limits for each distribution, and then combine the two in
quadrature. Or is there a method of determining an effective number of
degrees of freedom.?
Any help is greatly appreciated.
Daran Sadler
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Dr. Daran Sadler
PTD
Avecia
Grangemouth Works
Earls Road
Grangemouth
FK3 8XG
Tel: 01324 498382
e-mail: [log in to unmask]
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