hacl,
It follows the bivariate normal distribution,
(1/2*pi*sqrt(1-r^2))exp{(x^2-2rxy+y^2)/(2*(1-r^2))}
Hope I got the brackets right! Basically, a normal distribution with 2 variables x and y, with correlation r between them. The scatter would look something like you’d see in an Isoplot. The marginal distributions would be normal, as your post implies, but there would be correlation if you plot them against each other.
We’re experimenting with using van Belle’s formula. It breaks down the measurement agreement into three components: bias (difference in means), scale (difference in variance), and precision (1 minus the correlation coeff). Note, van Belle’s formula only looks at agreement between two measures of each object, e.g. two operators or two gages or two of whatever. There’s no breakdown into both repeatability and reproducibility.
We’re using the formula to compare values from a model (e.g. a computer analysis) to a physical, measured value. No doubt, one could argue that the computer-generated values violate the assumption of “random” and the statistical inferences are therefore suspect, but we’re trying to solve engineering problems, not win math awards. The formula seems to gives us the breakdown of components in the measurement error that we need, so that alone is useful to us.
I’m open to anyone out there who has a better idea.
Regards,
BC
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