Sunday, April 25, 2010

Signal to Noise Ratio Concept in biostats...

I would like to share this wonderful concept that forms the basis of many theories in biostats.

This originates from the signals received by radio transmitters.If the sound is not clear, we say it is noise. The sound has to cross a certain threshold level to be labelled as a 'signal'. This is analogous to the 'within group variances' (compared to 'noise') and 'between group variances' (compared to 'signal').

Ratio of variances between the groups to variance within the groups is known as F-ratio that we use in comparing more than two groups by ANOVA method.

Now, there emerges four possibilities from this analogy. These are:
1. Signal present and detected
2. Signal present but not detected
3. Signal absent and no signal detected
4. Signal absent but signal detected
The first and third points are detecting the facts. In the second and fourth point, we find that these are errors. Not detecting a signal when it is present is what we call as a type II error (the opposite of which, i.e. detecting a signal when present is power). Similarly, detecting a signal when there is none is the type I error.

I have found my life easier (not in every way but w.r.t. type I and type II errors) after this concept and hope the same for the reader of this post.
Bye for now.....


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