Observational Selection

The error of only counting or including data that supports one position or conclusion while ignoring the data that doesn't support it or even flat-out refutes it. This frequently results when one starts a conclusion and looks for evidence to support it, rather than starting with the evidence and forming a conclusion based on it. (And if you ever want to see how that kind of thinking can mess with your head, go check out A Fun Experiment To Disprove Claims of Sinister Symbology.)

Those who have formed beliefs based on Hasty Generalizations may employ this fallacy to maintain their beliefs and avoid examining them critically - EG, after James decides that all women are disloyal, abusive, and cruel based on his and his friends' bad experiences, he refuses to acknowledge the women who don't act that way as evidence against his belief, but he takes any and all who do as evidence for it.

Or, Jill goes to see Miss Annie, who claims to be a psychic who can help her communicate with her dead mother. Miss Annie supposedly relays information from Jill's mother - "I sense a feminine presence, and a color... blue... red... purple..." Jill, remembering her mother's fondness for the color purple, immediately affirms that her mother indeed wore purple. The wrong guesses (red and blue) that Miss Annie made are quickly forgotten because Jill desperately wants the whole thing to be real.

Or, Mark creates a device that when turned on, will supposedly make plants grow faster and healthier. He tests his device out in a greenhouse, and when several plants do indeed come out particularly large and lush he writes up and publishes a report (complete with pictures!) on the Internet... while leaving out that the fact that only 10% of the plants came out this way, a result which could have nothing to do with the device at all, but are probably due to one or more of other reasons such as the health of the seeds, the quality of the soil, or the amount of water given.

Or, Pamela is investigating a murder case, and she's extremely sure that Adam is guilty because witnesses report seeing him near the murder scene around the time the murder took place, plus he has a criminal record already. But when DNA evidence implicates someone else and Adam's family can vouch that he was at home with them at the time, Pamela disregards this new evidence and arrests Adam anyway.