Appendix 1 of
Rengarajan, Mol Vis 2002;
**8**:416-421.

Appendix 1. Estimating sensitivity

This appendix explains the method used to assess the resolutions of the fluorophore systems. The data were collected by measuring the fluorescence enhancement of solutions of known concentrations of dsDNA. Linear models of the expected value of Y given X (E(Y|X)) were developed of the form:

The resolution for each method is the smallest difference that can be
detected by that method. We chose a statistical criteria for detecting
the differences. To do this, we used a balanced design that greatly
simplifies the computations. In computations, we also assumed the usual
regression assumption of homoscedasticity held, though this was verified
after the data were collected. Our approach used the t-test for
detecting significant differences. It can be shown that for a two sample
t-test [9] with a balanced design and equal variance (s_{e}^{2}),
the test statistic is:

Substituting equation 1 in equation 2 and simplifying, we see that:

At the point where statistical significance is reached, the test
statistic equals the critical value (t_{c}) and we can solve for
resolution (ΔX):

Within an experiment, t_{c} and n are constant. These are also
constant across experiments of identical design. Estimates of the other
quantities are easily taken from the output of regression software. The
slope of the regression line estimates β_{1} and the mean square
error estimates s_{e}^{2} (or root mean square error estimates
s_{e}). This allows us to easily compare the resolutions from
identically designed experiments using the relative resolutions
(θ):

Thus, large values of β_{1} give a better resolution, as we
would expect. Similarly, the statistical noise seen in a larger variance
limits the resolution.

Rengarajan, Mol Vis 2002;

©2002 Molecular Vision <http://www.molvis.org/molvis/>

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