Probability and Phred Scores
The Phred score shown in FASTQ is a numeric scale for base-call quality. It converts the probability that one base was read incorrectly into a compact value. Every 10-point increase in Q reduces the error probability by a factor of ten.
Reading 1,000 bases
Section titled “Reading 1,000 bases”Suppose you read 1,000 bases at the same quality. At Q30, the error probability for each base is 1 in 1,000, so in the long run you would read about one base incorrectly on average.
| Phred Q | Error probability for one base | Accuracy |
|---|---|---|
| Q20 | 1/100 | 99% |
| Q30 | 1/1,000 | 99.9% |
| Q40 | 1/10,000 | 99.99% |
This table does not mean that a particular FASTQ file must contain exactly that many errors. It describes the expected average after many repeated calls under the same conditions.
Why use a logarithm?
Section titled “Why use a logarithm?”Error probabilities such as 0.01, 0.001, and 0.0001 accumulate zeros. A logarithm converts these long decimals into convenient intervals such as Q20, Q30, and Q40.
Here, is the error probability. Substituting gives . Because of the minus sign, Q grows as the error probability becomes smaller.
FASTQ stores the values as characters
Section titled “FASTQ stores the values as characters”FASTQ converts each Q value into one ASCII character. The first base in the sequence corresponds to the first character in the quality string, the second base corresponds to the second quality character, and so on. The sequence and quality strings must therefore always have the same length.
You do not need to memorize the characters. FastQC and analysis tools convert them back into numbers. For manual review, remembering that Q30 corresponds to an error probability of about 0.1% is enough.
Summary
Section titled “Summary”A Phred score is a logarithmic representation of error probability. A 10-point increase in Q reduces the error probability by a factor of ten, and a higher Q indicates a more reliable base call.