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optional starting / optional stopping
Optional starting and stopping refers to a common practice among psi researchers. In many tests of psychic powers the subject is allowed to start or stop whenever he or she feels like it. For example, the subject may go through some warm-ups trying to psychically receive numbers or Zener card icons being psychically transmitted by another person. The responses of the warm-ups are recorded, however, and if they look good (i.e., seem to be better than would be expected by chance) then the responses are counted in the experimental data. If not, then the data is discarded. Likewise, if the psychic has had a good run at guessing numbers of card suits and starts to have a bad run, he can call it quits.
This phenomenon seems to be related to another common factor in psi testing: optional keeping and optional disregarding of data. You get to keep all data favorable to your hypothesis and you get to disregard all unfavorable data. Psi researchers consider this practice to be justified since psychic powers may come and go.
Any reasonable test of psychic powers should have a protocol which specifies exactly when the experiment will begin and when it will end. Imagine letting a card player have a few practice rounds and if he's winning he gets to declare that those weren't practice rounds, but if he's losing he gets to declare that those really were practice rounds.
Optional starting and stopping should not be confused with displacement effects, a practice of counting an event as a "psychic hit" not only if one guesses the target card, but also if one guesses either the one before or after the target card, thereby significantly increasing one's odds of a "correct" guess.
See also parapsychology.