8.3 years ago by

Bergen, Norway

I just gave this some theoretical thoguht, I didn't look at how software does it or if there are papers out there. My 50cent is there cannot be a single best solution. Let's assume for a moment that the score values want to tell you something important. They are still arbitrary scores and have no probabilistic interpretation. We can than simply treat them as observations of a random variable, say X_i, where *i* is the consensus base position, and we have x_1 ... x_n observations, then I would say, theoretically, the best consensus score would be E(X_i) the expected value of X_i, estimated from the x_1 ... x_n.

But: You do not know anything about the distribution of X, it might be on an interval scale, but that's all, so it is hard to estimate the Expected value, e.g. the arithmetic mean will be a very bad estimator, if the distribution isn't central or asymmetric.

So here are several valid options you might want to test:

- Ignore combined scores: If the estimate is bad anyway, and there is no good interpretation of them, why bother? (my approach)
- Set to a constant: Same argument as above but some software might want scores
- Use a quantil-based estimate which doesn't make assumption about the distribution:
- median
- minimum, maximum score (of only the bases which are equal to the consensus?)
- mode (value with highest frequency)
- try to find out, which distribution the scores follow and model them

Comments appreciated.

Edit: I was a bit wrong with "no probabilistic intepretation". If they are phred scores http://www.phrap.com/phred/
they can have one: "The quality scores are logarithmically linked to error probabilities, as shown in the following table..."

if that is the case and the qualities are independ, the values would be additive as well the error probabilities can be simply multiplied.

In the second example, I am assuming that A is the correct base.

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