## List Consensus Confidence

The Confidence Value consensus algorithm (see section Consensus Calculation Using Confidence Values) produces a consensus sequence for which the expected error rate for each base is known. The option described here (which is available from the gap4 View menu) uses this information to calculate the expected number of errors in a particular consensus sequence and to tabulate them.

The decibel type scale introduced in the Phred program uses the formula -10xlog10(error_rate) to produce confidence values for the base calls. A confidence value of 10 corresponds to an error rate of 1/10; 20 to 1/100; 30 to 1/1000; etc.

So for example, if 50 bases in the consensus had confidence 10, we would expect those 50 bases (with an error rate of 1/10) to contain 5 errors; and if 200 bases had confidence 20, we would expect them to contain 2 errors. If these 50 bases with confidence 10, and 200 bases with confidence 20 were the least accurate parts of the consensus, they are the bases which we should check and edit first. In so doing we would be dealing with the places most likely to be wrong, and would raise the confidence of the whole consensus. The output produced by List Confidence shows the effect of working through all the lowest quality bases first, until the desired level of accuracy is reached. To do this it shows the cumulative number of errors that would be fixed by checking every consensus base with a confidence value less than a particular threshold.

The List Confidence option is available from within the Commands menu of the Contig Editor and the main gap4 View menu. From the main menu the dialogue simply allows selection of one or more contigs. Pressing OK then produces a table similar to the following:

```Sequence length = 164068 bases.
Expected errors =  168.80 bases (1/971 error rate).

Value   Frequencies     Expected  Cumulative    Cumulative      Cumulative
errors    frequencies   errors          error rate
--------------------------------------------------------------------------
0          0             0.00         0          0.00         1/971
1          1             0.79         1          0.79         1/976
2          0             0.00         1          0.79         1/976
3          3             1.50         4          2.30         1/985
4         30            11.94        34         14.24         1/1061
5          2             0.63        36         14.87         1/1065
6        263            66.06       299         80.94         1/1867
7        151            30.13       450        111.06         1/2841
8        164            25.99       614        137.06         1/5168
9         96            12.09       710        149.14         1/8344
10         80             8.00       790        157.14         1/14069
```

The output above states that there are 164068 bases in the consensus sequence with an expected 169 errors (giving an average error rate of one in 971). Next it lists each confidence value along with its frequency of occurrence and the expected number of errors (as explained above, frequency x error_rate). For any particular confidence value the cumulative columns state: how many bases in the sequence have the same or lower confidence, how many errors are expected in those bases, and the new error rate if all these bases were checked and all the errors fixed.

Above it states that there are 790 bases with confidence values of 10 or less, and estimates there to be 157 errors in those 790 bases. As we expect there to be about 169 errors in the whole consenus this implies that manually checking those 790 bases would leave only 12 undetected errors. Given that the sequence length is 164068 bases this means an average error rate of 1 in 14069. It is important to note that by using this editing strategy, this error rate would be achieved by checking only 0.48% of the total number of consensus bases. This strategy is realised by use of the consensus quality search in the gap4 Contig Editor (see section Search by Consensus Quality).