The Correction for Chance Success in Carrying out Experiments According to the Method of Constant Stimuli
DOI:
https://doi.org/10.24160/1993-6982-2019-6-71-76Keywords:
detection probability, false alarm probability, threshold contrast, likelihood ratio, random guessingAbstract
A new expression for the “correction for chance success” is derived, which is necessary for processing the results of experimental investigations into the probability characteristics of a vision system obtained according to the constant stimuli method under forced choice conditions. There may be five possible responses of the observer in conducting experiments according to the constant stimuli method:
An object has been detected in the field of view — the answer is “there is an object”.
No object has been detected in the field of view — the answer is “there is no object”.
A background without an object has been detected in the field of view — the answer is “there is a background”.
A background without an object has not been detected in the field of view — the answer is “there is no background”.
It is not clear what there is in the field of view — the answer is “it is not clear what it is”.
If there is a forced choice, the observer can give only two possible answers out of five possible versions:
An object has been detected in the field of view — the answer is “there is an object”.
A background without an object has been detected in the field of view — the answer is “there is a background”.
Since it is prohibited to give the answer “it is not clear what it is”, the observer is forced to resort to random guessing. To eliminate the influence of random guessing, H. Blackwell derived an expression for the “correction for chance success” in the following form:
Роб = (Р эоб – Р элт)/(1 – Р элт). An analysis carried out based on the vision system statistical model has shown that the expression for calculating this correction should be as follows: Роб = Р эоб – Р элт.
The reason why the obtained expression differs from the “correction for chance success” proposed by H. Blackwell is because he mistakenly conjectured that the observer always resorts to random guessing in seeing a background. The analysis carried out in the paper has shown that an observer correctly detects the presence of a background without an object with a probability close to Роб, and it is only in the remaining (1 – Роб) cases that the observer resorts to random guessing.
The difference between the threshold contrasts calculated using the new and classical expressions reaches 14%.
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Для цитирования: Боос Г.В., Григорьев А.А., Рыбина В.А. Поправка на «случайный успех» при проведении экспериментов по методу постоянных стимулов // Вестник МЭИ. 2019. № 6. С. 71—76. DOI: 10.24160/1993-6982-2019-6-71-76.
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For citation: Boos G.V., Grigoryev A.A., Rybina V.A. AThe Correction for Chance Success in Carrying out Experiments According to the Method of Constant Stimuli. Bulletin of MPEI. 2019;6:71—76. (in Russian). DOI: 10.24160/1993-6982-2019-6-71-76.
