Eliminating subjective biases in judging the loudness of a 1-kHz tone

It is possible to eliminate most of the known subjective biases that affect judgments of sensory magnitude using numbers. Experiments are described which do this, and which also investigate some of the biases. The least biased estimate for doubling the loudness of a 1-kHz tone is found to be about 11.5 dB. This value is still slightly affected by the logarithmic bias, although the bias could be eliminated. It is also affected by the stimulus equalizing bias, produced by the inequality between the finite range of loudnesses to which the ears are sensitive and the infinite range of numbers to which the loudnesses are matched. This last bias cannot be eliminated completely in direct magnitude estimation.