Mathcad Predictor
This is for comparison with the Access Predictor add-in that only gives a one dimensional
view of confidence intervals. Mathcad allows you to simplify probabilities by using integrals. This sheet illustrates general ideas about overlapping areas, probabilities, predictabilities and Type 1 and 2 errors. This is an ideal situation for HTS. In HTS you don't get the statistical
advantage of having many data points for each compound.
Ranges of numbers for the dnorm function to plot.
Normal Curves
Remember the total area of a normal curve is one! Shared areas are
responsible for type II errors after you have set your boundary for
type I errors.
Set rejection region of the positive control curve with a mean
at 100(green curve) at 95% on the lower tail.
Probability of a type II error(B). The chance that a value contained in the
blue curve will show up within the positive controls region of acceptance.
A 2.1% chance of a type II error
Easy!
This is a simple explanation of probabilities. Why integration makes probabilities
easier is because you can find areas using an integral. The following example is
an intuitive example using the same idea. If you have a blue box and and yellow
box and they are far apart, then it is easy to say that the blue pixels belong to
the blue box and the yellow pixels belong to the yellow box.
What happens if the boxes overlap? What is the solution for this situation?
Are the yellow pixels in the blue box or are the blue pixels in the yellow box?
Maybe they are blended. Maybe people have other ideas... Mathematically, there
is a problem. Statistically, do you reject or accept the pixels in the overlapping
regions to belonging to one of the boxes? The same idea is behind type 1 and
type 2 error checking in statistics. If you accept what is in the blue box as being
blue, can you say that it will always be blue. When the boxes overlap you can't.
You do know that 75% of the blue box in blue. OK, the illustration isn't perfect but
the idea is similar to statistical testing.
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