Selection bias is the distortion of statistics by the way in which a sample is selected. Self-selection bias is the distortion caused when the sample chooses itself — certain characteristics are over-represented because they correlate with willingness to be included.
Survivorship bias, which often distorts historical studies of returns, is a form of selection bias. Backfill bias, which has a significant effect on many hedge fund indices, is a form of self-selection bias.
A more deliberate form of self-selection bias often occurs in measuring the performance of investment managers. Typically, a number of funds are set up that are initially “incubated”: kept closed to the public until they have a track record. Those that are successful are marketed to the public (through an IPO if exchange traded), while those that are not successful remain in incubation until they are.
In addition, persistently unsuccessful funds (whether in an incubator or not) are often closed, creating survivorship bias. This is all the more effective because of the tendency of investors to pick funds from the top of the league tables regardless of the performance of the manager's other funds.